The package, developed by JoonHo Lee and Alison Hooper and released under an MIT license, grew out of a practical evaluation problem in early childhood education. Analysts studying pre-kindergarten programs often want to know what proportion of enrolled children have families receiving nutrition assistance. Sometimes they hold individual student records; sometimes they have only published counts, often with different denominators across sites and sometimes with values deliberately suppressed by the publisher. Before sitemix, preparing proportions and their standard errors from these heterogeneous inputs required ad hoc calculations scattered across scripts, with assumptions rarely stated explicitly. The package replaces that improvisation with a common set of functions that return a standardized table of estimates, standard errors, and provenance information for every site and year.

The central technical insight of sitemix is that a standard error is meaningless until you specify what the proportion is intended to describe. Administrative records may cover an entire cohort, a selected subset, or a probability sample, and each interpretation demands a different variance calculation. The package’s default binomial model treats the observed count as arising from independent Bernoulli trials with a common underlying probability, so the variance of the observed proportion is the familiar theta times one minus theta divided by n. Under this model, uncertainty concerns repeated outcomes at a fixed sample size. Alternatively, analysts may want the proportion in a fixed finite population of N individuals, in which case uncertainty comes from which n individuals were sampled, and a finite-population correction adjusts the sampling variance. Crucially, observing the entire population gives zero design-based sampling variance, even when the population consists of a single person. The package forces users to choose between these targets rather than silently applying one formula to all data.

Once the target is defined, sitemix offers a menu of established calculations with their assumptions stated openly. For proportions of exactly zero or one, where the plug-in variance collapses to zero, the package supplies a Wilson-derived standard error surrogate by default, with options for the Agresti-Coull adjustment or a retained zero variance. For reporting on transformed scales, the default is the arcsine square-root transformation, whose first-order working standard error is simply one divided by two n, an approximation that depends only on the denominator. An optional Anscombe adjustment refines this transformation for small samples. The package also implements a bias-corrected binomial variance that replaces the denominator n with n minus one for interior cells. None of these boundary surrogates or working approximations guarantee confidence-interval coverage, and the documentation says so explicitly, a refreshing departure from software that presents approximations as exact.

Perhaps the most technically sophisticated part of the package concerns covariance between overlapping indicators. Suppose an analyst wants to know not just the share of children eligible for free and reduced-price meals and the share enrolled in SNAP, but how these indicators vary together. Separate totals for two assistance programs do not reveal how many children participate in both; only joint records or co-occurrence counts can estimate that covariance. When complete joint information is available, sitemix computes the plug-in covariance from the observed joint proportion minus the product of the marginal proportions, divided by n. For a single categorical variable partitioned into mutually exclusive categories, complete counts determine a multinomial covariance matrix whose rows sum to zero, preserving the constraint that category proportions total one. The package validates these matrices against the properties required by their construction rule, recording scale, indicator order, and sampling design metadata alongside every covariance carrier.

The package’s treatment of published aggregate counts reveals what such summaries actually retain. When numerator-denominator pairs match the record-based inputs, the aggregate route reproduces the record-based estimates and standard errors exactly, a property the authors demonstrate across 250 simulated site-year cells. But separate marginal counts for several indicators generally do not determine covariance between them. When only margins are available, sitemix returns a diagonal covariance matrix explicitly labeled as working independence, recording whether the margins describe the same, different, or unknown sampled units. Equal denominators alone do not establish that the units are the same. For complete, unsuppressed margins from the same units, the package computes Fréchet identification intervals, the mathematically sharp bounds on the joint proportion given the observed margins: the joint share must lie between the maximum of zero and the sum of the two proportions minus one, and the minimum of the two marginal proportions. These are identification intervals, not confidence intervals, and the simulated example shows how wide the joint-proportion range can remain without co-occurrence counts, falling on an endpoint at 13 of 50 sites.

Suppression handling is another distinctive feature. Publishers routinely withhold small or sensitive counts, and software that treats withheld values as observed zeros would silently corrupt the analysis. sitemix keeps suppressed values distinct from observed zeros throughout, requires users to explicitly acknowledge sensitivity values, stores them in separate columns, and excludes them from ordinary covariance and Fréchet calculations. A dedicated suppression report audits the data before estimation begins. The diagnostic function sm_diagnose checks objects, rows, and covariance matrices, returning results on a severity scale from error through warning, note, and ok, so analysts can review missing values, small denominators, and covariance compatibility before feeding the output into another model.

The validation effort behind the package is unusually thorough for statistical software. The authors checked all 263 scalar and finite-population configurations against reference values computed from closed-form identities, score-quadratic roots, and finite-population sample enumeration, with the largest absolute discrepancy at 8.88 times ten to the minus sixteenth, essentially machine precision. All 118 categorical and Fréchet assertions passed, covering simplex constraints, positive semidefiniteness, sparse categories, boundary surrogates, and census behavior. The full test suite passed 6,918 expectations across 53 files with no failures, and test-based line coverage reached 91.37 percent. The authors also examined the accuracy of the arcsine working variances by computing exact variances across a grid of sample sizes and probabilities, finding that the unadjusted working variance could be anywhere from 0.405 to 10.23 times the exact variance across interior grid points, a sobering reminder that transformed-scale approximations demand scrutiny at small samples.

To illustrate the workflow, the authors provide prek_sim, a simulated panel of 7,845 student-year rows from 50 sites over 2021 to 2025, containing four overlapping binary indicators: eligibility for free and reduced-price meals, enrollment in SNAP, participation in WIC, and receipt of TANF. Site-year cells contain between 6 and 134 children. The examples walk through estimating site-level proportions, computing covariance from jointly observed indicators, reproducing record-based estimates from matching counts, and examining what marginal counts alone cannot recover. A final empirical Bayes illustration shows how the estimate-standard error pairs can feed a normal-normal shrinkage analysis on the arcsine scale, where sites with small denominators move noticeably in rank after borrowing strength across sites, though the authors caution that rank uncertainty is not quantified and the normal approximation requires assessment for sparse cells.

The impact of sitemix lies in making uncertainty preparation repeatable and transparent. Each estimate retains its denominator, reporting scale, suppression status, and method information, so analysts can review how a table was produced when updating it or sharing it with colleagues. The count interfaces extend the workflow to settings where individual records are unavailable, while the Fréchet machinery helps analysts decide which additional counts they actually need. The package does not pool proportions across sites, fit hierarchical models, or handle complex survey designs; its only cross-site model is an optional experimental variance smoother. Instead, it focuses on preparing estimates and uncertainty summaries for subsequent analysis, leaving the modeling choices where they belong: with the analyst, justified separately. For a field drowning in published proportions of unknown provenance, that discipline may prove quietly transformative.

Subject of Research: Statistics; Software; Data Science

Article Title: sitemix: An R package for site- and group-level proportions and uncertainty from individual records and aggregate counts

Article References: Lee, J., & Hooper, A. (2026). sitemix: An R package for site- and group-level proportions and uncertainty from individual records and aggregate counts. SoftwareX, 36, Article 103131. https://doi.org/10.1016/j.softx.2026.103131

Image Credits: AI Generated

DOI: 10.1016/j.softx.2026.103131

Keywords: R package, statistics, uncertainty quantification, proportions, empirical Bayes, open-source software, education research, covariance, sitemix, package, site-, group-level

The core insight behind the new framework is that impulse noise is not merely a visual nuisance but a statistical anomaly. Uncorrupted patches of a natural image tend to show smooth intensity histograms and strong spatial correlation between neighboring pixels. When an impulse spike lands in a patch, it distorts these regularities in measurable ways. Rather than applying a single fixed detection rule, the algorithm treats each sliding spatial neighborhood as a localized probability density function and interrogates it through three complementary statistical pathways, each tuned to a different type of corruption.

The first pathway, Path A, fits the intensity values of a local window to a continuous Beta distribution. The Beta distribution is strictly bounded between zero and one, which makes it a natural model for normalized pixel intensities. Shape parameters alpha and beta are estimated through the method of moments, and cumulative distribution function thresholds then flag any pixel falling outside the expected probability tails as noise. This bounded modeling proves especially valuable against random-valued impulse noise, a particularly sneaky corruption in which the noise value can be any arbitrary integer across the intensity spectrum rather than an obvious boundary spike. Because such in-range outliers can masquerade as ordinary pixel values, they fool linear filters and standard thresholding, but they distort the fitted distribution’s tails in ways the algorithm can detect with high statistical confidence.

The second pathway, Path B, leans on higher-order statistics, specifically skewness and kurtosis. Skewness, the third statistical moment, captures the asymmetry that an impulse spike injects into a local histogram, while kurtosis, the fourth moment, measures the tailedness of the distribution. A clean uniform window shows low skewness with a fixed kurtosis; an impulse outlier shatters that balance, producing a pronounced skewness and a sharp kurtosis spike. Pixels located in windows where either moment exceeds an empirically obtained threshold are declared outliers. This pathway offers a reasonable balance between sensitivity and cost, though the study notes it requires a minimum five-by-five window to keep the higher moments stable, since a three-by-three sample set is too restricted and produces elevated false positives near sharp natural edges.

The third pathway, Path C, deploys the Median Absolute Deviation, a classical robust estimator with a fifty percent breakdown point. This means the scale estimator remains mathematically bounded even when up to half the neighborhood is severely corrupted, a property that ordinary averages and standard deviations cannot claim. For high-density salt-and-pepper noise, where corrupted pixels sit exactly at the extreme borders of the quantization range, the MAD produces a strict threshold that ignores outlier spikes entirely. On the benchmark image Lena, Path C achieved a false acceptance rate of just 0.08 percent under salt-and-pepper contamination, meaning almost no clean pixels were wrongly sent to the reconstruction engine. The trade-off appears on high-frequency textures like the fine stripes in Barbara, where the pathway struggles to separate high-contrast physical edges from true noise and the false acceptance rate rises to 0.65 percent.

Detection alone, however, would be of limited value without speed, and this is where the study’s second pillar comes in. Conventional spatial filtering slides a window across the image grid using nested loops, an approach that scales poorly in interpreted languages. The framework instead uses the im2col transformation to rearrange every local neighborhood into a distinct column of a stacked feature matrix. After mirror-reflection padding to prevent boundary data loss, an image of P pixels and a k-by-k window becomes a matrix of k-squared rows by P columns, with every column holding all localized neighborhood intensities for a particular coordinate. Statistical functions such as median, MAD, skewness, and kurtosis then operate in parallel across the rows through linear algebra kernels, allowing the framework to analyze every single neighborhood at once without any loops.

The measured speedup is striking. A 256-by-256 image that took 1.84 seconds to process with standard nested loops was handled in 12.3 milliseconds with the vectorized architecture, a 149.5-fold acceleration. At 512-by-512 resolution the gap widened to 156.4 times, and at 1,024-by-1,024 it reached 156.9 times, with the vectorized pipeline completing in 198.2 milliseconds what previously demanded 31.10 seconds. Memory overhead stays modest: for a standard 512-by-512 image with a three-by-three window, the intermediate matrix contains roughly 18.8 megabytes in single-precision float, well within the budgets of modern embedded edge processors. The total time complexity of the framework is O(k-squared times P), eliminating the loop overhead inherent to non-vectorized filtering.

Restoration fidelity was benchmarked on three reference images chosen for their structural diversity: Lena with smooth textures and gradients, Peppers with color edges under varied lighting, and Barbara with complicated high spatial frequencies. Noise was injected at densities from ten to ninety percent in ten-percent steps, covering both salt-and-pepper noise and random-valued impulse noise. Under 50 percent salt-and-pepper contamination, Path C restored Lena to a peak signal-to-noise ratio of 35.7 decibels with a structural similarity index of 0.968, while the standard median filter baseline managed only 22.1 decibels and 0.741. Against random-valued noise, Path A proved superior, reaching a false rejection rate of 2.45 percent on Lena compared with 3.12 percent for Path C. The framework also outperformed recent state-of-the-art architectures, including a Rayleigh-Monte Carlo stochastic method and a topological filter structure, with the Monte Carlo approach suffering a false rejection rate of 5.12 percent on uniform random-valued noise because in-range spikes were integrated into its random sampling pools.

The system architecture separates detection from reconstruction in a two-stage design. Multi-spectral or color images are first transformed into a color space such as YIQ or HSV, decoupling brightness from chrominance, and statistical analysis proceeds only over the luminance or value channel. The vectorized sliding-window computation then produces an exact binary noise map, and clean coordinates are left entirely untouched through hard logical matrix masking, overcoming the chief weakness of the old median filter, which applied identical operations to every pixel and blurred edges as a consequence. Reconstruction applies only to flagged coordinates, using nearby verified uncorrupted pixels as structural anchors for targeted interpolation. If a search window contains no clean pixels due to extreme noise density, the window size is dynamically expanded by increments of two until at least one anchor is found.

What makes the framework notable for practitioners is its interpretability. Unlike convolutional neural networks whose decision-making processes are mathematically opaque, every detection here follows from explicit distribution fitting, moment analysis, or robust estimation, and the author argues this transparency is essential for edge computing deployments where computational budgets are tight and trust matters. The study points toward several future directions, including a smart switching engine that routes smooth regions through the fast MAD pipeline while sending complex textural patches to the Beta engine, translation of the vectorized operations from MATLAB to hardware description languages for FPGA and ASIC acceleration, and extension to video and multispectral imagery. For now, the work demonstrates that a return to classical statistics, executed with modern matrix machinery, can match the accuracy of heavyweight models while running fast enough for the edge.

Subject of Research: Computer Science

Article Title: Impulse noise removal via local statistical analysis and vectorized matrix processing

Article References: Abbas, J. K. K. (2026). Impulse noise removal via local statistical analysis and vectorized matrix processing. Frontiers in Applied Mathematics and Statistics, 12, Article 1948970. https://doi.org/10.3389/fams.2026.1948970

Image Credits: AI Generated

DOI: 10.3389/fams.2026.1948970

Keywords: image processing, impulse noise, statistics, matrix vectorization, edge computing, signal processing, computer vision, algorithms, Impulse, noise, removal, local

The research, led by Eslam Hussam of Capital University and Prince Sattam Bin Abdulaziz University, together with Ehab M. Almetwally of Delta University and Imam Mohammad Ibn Saud Islamic University and T. S. Taher of Zagazig University, focuses on the type II heavy-tailed Weibull (TII-HTW) distribution. This three-parameter model keeps the familiar Weibull kernel used across engineering and survival analysis but adds a tail-weight parameter that lets extreme observations occur with non-negligible probability. When the tail parameter equals one, the model collapses back to the standard two-parameter Weibull; when it falls below one, the right tail becomes heavier, exactly the behavior seen in skewed failure and mortality data.

What makes the study technically distinctive is the censoring scheme under which the authors estimate the model. Lifetime experiments are expensive, so researchers rarely observe every unit until failure. Classical type I censoring stops the test at a fixed time regardless of how many failures have occurred, while type II censoring stops after a fixed number of failures no matter how long it takes. Both have well-known drawbacks: type I can end with few or even zero observed failures, and type II can drag on indefinitely. Hybrid schemes blend the two, and the unified progressive-hybrid censoring scheme (UPHCS) used here goes further. It specifies two failure counts and two time thresholds, guaranteeing that the experiment terminates with a meaningful number of observed failures while never running forever.

The authors add another layer of realism: binomial removal. In progressive censoring, surviving units are withdrawn from the test at each failure time, and the number removed is usually fixed in advance. Under the binomial scheme, the removals are instead generated randomly from a binomial distribution with a pre-specified removal probability, which the authors treat as a known design quantity. Because the removal mechanism is assumed independent of the lifetimes, it does not enter the conditional likelihood, simplifying the inferential machinery while still reflecting how real tests are often run.

Three estimation methods were compared head to head. Maximum likelihood estimation (MLE), the workhorse of parametric statistics, was implemented with Newton-Raphson numerical optimization, with asymptotic confidence intervals built from the observed Fisher information matrix and the delta method. The maximum product of spacings (MPS) method, introduced by Cheng and Amin, maximizes the geometric mean of the gaps between fitted cumulative probabilities rather than the likelihood itself; the authors report that this is the first application of MPS under UPHCS with binomial removal, and it proved notably more stable than MLE in several settings, particularly under moderate censoring. Finally, Bayesian estimation assigned independent gamma priors to the three parameters, whose hyperparameters were elicited from an independent pilot simulation using moment matching, and drew posterior samples via a random-walk Metropolis-Hastings algorithm run on the logarithmic scale to preserve positivity.

The Monte Carlo experiment was substantial: 10,000 replications per design configuration, sample sizes of 40 and 100, scheduled failure counts ranging from 28 to 90, and removal probabilities of 0.3 and 0.8. Convergence of the Markov chain Monte Carlo runs was verified with trace and autocorrelation plots, the Gelman-Rubin potential scale reduction factor near one, effective sample sizes above 1,000, and acceptance rates between 20 and 45 percent. Across all configurations, mean squared errors and relative absolute bias shrank as sample size and the number of observed failures increased, exactly as asymptotic theory predicts.

The headline result is that Bayesian estimators generally produced lower mean squared errors and shorter credible intervals than both classical competitors, an advantage the authors attribute to the informative, data-driven gamma priors. Bayesian highest posterior density intervals also achieved coverage probabilities closer to the nominal 95 percent level than the asymptotic confidence intervals based on MLE, which were sometimes shorter but less accurate. Higher removal probabilities reduced the effective sample size and widened all intervals, yet the Bayesian procedure remained the most robust under those harsher conditions. The authors recommend Bayesian estimation with informative priors for this framework, with MPS as a competitive fallback when prior information is unavailable.

To test the model against real data, the team analyzed four datasets spanning engineering, business, medicine, and public health: 213 successive failure times from the air-conditioning systems of a Boeing 720 fleet, 36 pizza franchise start-up costs, 19 observations from type 2 diabetic nephropathy patients, and 224 COVID-19 mortality rates from Canada. Three of the four showed pronounced right skewness and kurtosis, the statistical fingerprints of heavy tails. The UPHCS design with binomial removal was imposed artificially on these complete samples purely to demonstrate the methodology under censored conditions.

The TII-HTW distribution outperformed a battery of rivals, including the inverse power Lomax, three-parameter Burr XII, power Lomax, Singh-Maddala, inverted exponentiated Lomax, classical Weibull, and Kies distributions, judged by Akaike, Bayesian, Hannan-Quinn, and consistent Akaike information criteria along with Anderson-Darling, Cramér-von Mises, and Kolmogorov-Smirnov statistics. For the Boeing data, estimated reliability at the stopping time held near 0.68 and the hazard near 0.031 regardless of removal intensity. For the pizza franchise data, the fitted survival function of roughly 0.73 to 0.75 implies that about 74 percent of start-up costs exceed 75,000 dollars, consistent with the data’s right skew. The COVID-19 mortality analysis yielded a stable reliability near 0.69 across all censoring scenarios. Even the light-tailed diabetic dataset, with only 19 observations, produced reasonably stable estimates, though with appropriately wider confidence intervals.

The broader message is that heavy-tailed thinking belongs in the reliability toolkit wherever extreme outcomes carry real consequences, from epidemic mortality waves to catastrophic equipment failures. Standard light-tailed Weibull models can underestimate the probability of such events, leading to inadequate tail inference precisely when risk assessment matters most. By pairing a flexible heavy-tailed distribution with a censoring design that guarantees both a minimum number of failures and a bounded experiment duration, and by demonstrating that Bayesian inference with carefully elicited priors delivers the tightest and most accurate uncertainty quantification, the study offers practitioners a concrete recipe for extracting reliable conclusions from incomplete, heavy-tailed lifetime data. The authors point toward future work extending the framework to competing risks, prediction, and other censoring regimes.

Subject of Research: Bayesian and classical estimation of the type II heavy-tailed Weibull distribution under unified progressive-hybrid censoring with binomial removal

Article Title: Bayesian Inference with binomial removal for type II heavy-tailed Weibull distribution under unified progressive-hybrid censoring: simulation and application

Article References: Hussam, E., Almetwally, E. M., & Taher, T. S. (2026). Bayesian Inference with binomial removal for type II heavy-tailed Weibull distribution under unified progressive-hybrid censoring: simulation and application. Frontiers in Applied Mathematics and Statistics, 12, Article 1932119. https://doi.org/10.3389/fams.2026.1932119

Image Credits: AI Generated

DOI: 10.3389/fams.2026.1932119

Keywords: statistics, Bayesian inference, reliability analysis, censoring, heavy-tailed distributions, Weibull distribution, MCMC, survival analysis, Bayesian, Inference, binomial, removal

The traditional picture treats dielectric breakdown as a purely random process. Under sustained electric stress, defects such as oxygen vacancies accumulate in the insulating layer until a conducting filament bridges two electrodes, an event whose time of occurrence is statistically distributed and traditionally characterized by the Weibull model. Because a larger area contains more potential breakdown sites, the weakest of them fails first, and the time-to-breakdown shrinks with area according to extreme-value statistics. Wu and Ando contend that this weakest-link competition has been misinterpreted as a simple winner-takes-all process, obscuring the fact that breakdown statistics involve a distribution nested within many underlying distributions — many near-breakdown events in competition that ultimately control the observed extreme-value outcome.

What makes breakdown unique among failure mechanisms is that the dielectric layer itself transforms under stress, moving from pristine to degraded and ultimately to a fragmented state. Recent conductive atomic force microscopy reconstructions of a 25 square micrometer ReRAM device vividly revealed multiple completed filaments — 89 percent complete and 11 percent incomplete — of various sizes, directly confirming this fragmental picture. After breakdown, electrical measurements show current fluctuations spanning orders of magnitude, with current sometimes recovering to near-original levels before the final hard breakdown. Until now, there has been no clear account for these recovery events. The new model proposes a physically plausible explanation: defects are not permanently created but can be annihilated.

The key insight is that oxygen vacancies, the defects widely identified with breakdown filament formation, cannot exist in isolation. Their counterpart, the oxygen interstitial, is generated in pairs with them through a Frenkel-pair process whose thermodynamics closely resemble electron-hole pair generation in semiconductors. The separation between two chemical potentials plays the role of the energy gap, and the interstitial oxygen acts as an annihilation center, readily recombining with a vacancy. Density functional theory calculations have shown a recombination time of roughly 500 femtoseconds for positively charged oxygen vacancies in intrinsic undoped HfO2, driven by Coulombic attraction. Extrinsic species such as hydrogen can also passivate vacancies, providing a second annihilation channel.

Building on this thermodynamic foundation, Wu and Ando extended the classic cell-based percolation model to include both defect generation and annihilation. In their framework, defects and annihilation centers are randomly distributed across the device area, and both processes scale with area. The time evolution of each density follows a power law, with annihilation-center density decaying over time as centers are consumed by the ongoing recombination process. Crucially, this time-decaying behavior is naturally compatible with maximum-value statistics, in contrast to the minimum-value statistics that govern defect generation. The joint interplay of these two extreme-value statistics, combined over all possible annihilation times, yields a net defect-generation probability density function whose peaks coincide with the onset of breakdown observed experimentally.

The experimental trigger for this theoretical advance came from hydrogen plasma-treated HfO2 ReRAM devices. Wu, Ando, and colleagues demonstrated that the traditional inverse area-scaling law can be reversed and diminished through process innovation. In bilayer stacks exposed to hydrogen plasma, forming voltages obtained from ramped voltage stress showed reverse and diminishing area dependence across a range of process conditions. In some samples, larger devices actually survived longer than smaller ones — a result that contradicts a century of conventional wisdom. The new model captures these diverse area-scaling schemes, from reverse through diminishing to forward and traditional inverse scaling, using a single set of parameters for each split, demonstrating both validity and predictability.

The probability density function analysis reveals the underlying dynamics in detail. For reverse area scaling, the defect-generation PDF decreases monotonically with time, while the annihilation PDF rises to a peak at roughly 0.1 microseconds and then declines. At short times, generated defects are quickly annihilated and cannot contribute to breakdown. Beyond the peak, annihilation becomes less effective, defects survive, and net defect generation dominates filament formation. The annihilation PDF at device level drops by approximately seven orders of magnitude from the unit-cell PDF, reflecting the large imbalance between annihilation-center and defect densities — a dominant factor responsible for reversing the traditional scaling law. Notably, the estimated time span of the annihilation PDF aligns well with DFT-based estimates of 1.6 nanoseconds to 1.6 microseconds for hydrogen substitution into oxygen vacancies, based on a swap activation energy of roughly 0.5 electron volts.

Perhaps the most striking conclusion is that the traditional inverse area-scaling law is merely a special case of the more general defect-generation-annihilation framework, obtained by assuming infinitely long annihilation times. Even in conventional breakdown, where annihilation is not obviously at work, the model suggests it plays an equally critical role. The authors found a strong correlation between the variability of the time-to-breakdown-versus-area relationship and the net defect-generation rate, a quantity strongly modulated by the presence of annihilation. This correlation spans the full range of experimental area-scaling behaviors, implying that annihilation is not a peripheral effect but an essential and dynamic process ultimately leading to breakdown.

The implications reach beyond fundamental physics. The traditional inverse area-scaling law has become one of the most critical bottlenecks for technology scaling in ReRAM chips and metal-insulator-metal capacitors in CMOS technology. A diminishing area dependence would mean that devices of different areas can share the same breakdown reliability, offering a pathway to overcome scaling limits for the semiconductor industry. The authors also note that contemporary modeling efforts, including sophisticated multiscale atomistic simulations, sidestep the area-dependent competition between defect generation and annihilation. One multiscale simulation predicted a progressive breakdown residual time of roughly 10^8 seconds, which would imply an unphysically large breakdown spot density; including annihilation could delay the first filament formation and yield more reasonable residual times.

Wu and Ando conclude that area-dependent defect-generation-annihilation competition is an essential, inevitable physical process that distinguishes breakdown from other degradation phenomena such as bias-temperature instability and hot-carrier degradation, which leave the dielectric in a degraded but unfragmented state. Their work highlights a large gap between experimental reality and theoretical modeling frameworks, particularly for large-scale and high-throughput approaches, and argues that a comprehensive physical understanding of dielectric breakdown cannot be achieved without acknowledging that the root cause of area dependency is the most critical and inevitable element of the phenomenon itself.

Subject of Research: Physics

Article Title: Statistics and physics of area-dependent dielectric breakdown: an overlooked yet inevitable natural phenomenon

Article References: Wu, E. Y., & Ando, T. (2026). Statistics and physics of area-dependent dielectric breakdown: an overlooked yet inevitable natural phenomenon. Frontiers in Nanotechnology, 8, Article 1885901. https://doi.org/10.3389/fnano.2026.1885901

Image Credits: AI Generated

DOI: 10.3389/fnano.2026.1885901

Keywords: dielectric breakdown, area scaling, HfO2, ReRAM, defect annihilation, extreme-value statistics, oxygen vacancies, hydrogen doping, nanotechnology, semiconductor reliability, Statistics, physics

The technique belongs to a field called quantitative ultrasound, or QUS. Conventional B-mode ultrasound, the grayscale image familiar from maternity wards and emergency rooms, displays anatomy but says little about what the tissue is actually made of at the microscale. QUS goes a step further by treating the raw backscattered radiofrequency signal as data. When an ultrasound pulse travels into tissue, it scatters off microscopic structures such as cells, vessels, and extracellular fibers. The amplitude of the returning echo, known as the envelope, carries a statistical fingerprint of those scatterers: their density, their spatial organization, and their clustering. By fitting probability distributions to the envelope, researchers can extract numbers that correlate directly with tissue microstructure, numbers that a standard grayscale image simply cannot provide.

The team evaluated three complementary statistical models. The Homodyned-K distribution, the most general of the three, separates the echo into a coherent component, arising from periodically arranged scatterers, and a diffuse component, arising from randomly distributed ones. Its parameter alpha describes scatterer clustering, while a derived parameter k captures the ratio of coherent to diffuse signal power. The Nakagami distribution, a simpler model, uses a shape parameter m that reflects the effective number density of scatterers and a scale parameter Omega related to backscattered energy. The Burr distribution, the newest addition to the envelope-statistics toolkit, assumes that scatterers exhibit multi-scale, power-law behavior, making it sensitive to fractal and elongated structures such as the branching vascular networks and fibrillar collagen that characterize tumors. Its shape parameter b reflects the density of fractal scattering structures, while its scale parameter lambda relates to echo amplitude.

To test whether these statistics could distinguish tumor from healthy tissue, the researchers worked with forty human tissue samples, twenty glioblastoma specimens resected from patients aged 15 to 68 and twenty normal brain samples obtained from the NIMHANS brain bank. Because surgeons cannot safely remove healthy brain tissue during tumor surgery, the control specimens came from post-mortem donations collected within 24 hours. Each sample, fixed in formalin and cut into blocks a few millimeters thick, was embedded in a solidified agarose phantom to hold it steady during imaging. A fraction of every sample was processed for histopathology, and two experienced neuropathologists with 10 and 25 years of experience independently confirmed the diagnoses, providing a ground truth against which the ultrasound statistics could be validated.

Ultrasound data were acquired with a Verasonics Vantage 128 research system driving a linear array transducer at a center frequency of 7.6 megahertz, focused 14 millimeters into each sample. Five independent imaging planes were collected per specimen, with the transducer translated by roughly one millimeter between acquisitions, a distance greater than the lateral beamwidth, ensuring that consecutive measurements sampled genuinely different regions of tissue. Before any statistics were computed, the team measured the frequency-dependent acoustic attenuation of the samples using a broadband pulse-echo insertion-loss technique with a separate 20-megahertz single-element transducer. Because formalin fixation and tissue composition alter how sound is absorbed as it propagates, the raw radiofrequency data were compensated for attenuation in the frequency domain before envelope analysis, preventing absorption artifacts from masquerading as microstructural differences.

The results were striking. Every parameter from all three distributions differed significantly between glioblastoma and normal brain. The HK clustering parameter alpha was higher in tumor tissue, while the coherent-to-diffuse ratio k was lower, indicating increased scatterer clustering together with a greater contribution of diffuse scattering, findings that align with the necrotic zones and microvascular proliferation visible under the microscope. The Nakagami parameters m and Omega were both elevated in tumor samples, reflecting a higher effective density of scatterers and greater backscattered energy, consistent with the dense, pleomorphic tumor cells and high nuclear-to-cytoplasmic ratios of glioblastoma. The Burr parameters b and lambda were also higher in tumor tissue, suggesting that the tumor’s fractal vessel networks and its remodeling of the extracellular matrix, with increased deposition of fibrillar collagens, fibronectin, and laminin, create elongated, anisotropic scattering sites that produce heavy-tailed echo amplitudes. Effect sizes were medium to large for most parameters, with Cohen’s d values exceeding 1.0 for several, indicating robust group separation.

The researchers then fed these features into machine learning classifiers, including logistic regression, linear support vector machines, random forests, and multilayer perceptron neural networks. Performance was assessed at two levels: per-sample, where the five imaging planes were averaged into a single observation per specimen, and per-plane, where each image counted as an independent observation. To avoid optimistic bias, the team used leave-one-out cross-validation for per-sample analysis and group K-fold cross-validation for per-plane analysis, ensuring that planes from the same specimen never appeared in both training and test sets. Hyperparameters were tuned with the Optuna framework, and a stricter nested cross-validation was also performed. Among individual distributions, HK-derived features achieved the highest single-model performance at 90.0 percent per-sample accuracy. Combining all six features pushed the linear SVM to 97.5 percent per-sample accuracy with an area under the receiver operating characteristic curve of 0.985, and a reduced four-feature subset, dropping the scale parameters, achieved comparable results, indicating that shape-related parameters carry most of the discriminative information.

Per-plane classification, a tougher test because individual imaging planes capture localized heterogeneity within a sample, still reached 80.5 percent accuracy with an AUC of 0.854 using the six-feature set. Under nested cross-validation, the strictest evaluation, per-sample accuracy decreased to 90.0 percent, a reduction consistent with the optimistic bias expected when model selection and evaluation share the same data splits, but the overall performance trends across feature subsets remained unchanged. Feature importance analysis using random forests identified the HK clustering parameter alpha and the Nakagami scale parameter Omega as the most discriminative features, underscoring the central role of scatterer organization and backscattered energy in telling tumor from healthy tissue. Notably, increasing model complexity did not consistently improve performance, suggesting that the envelope statistics features are largely separable with simple, interpretable decision boundaries, an encouraging property for any future clinical deployment.

The authors are careful to frame this as proof of concept rather than a ready-made clinical tool. Formalin fixation alters acoustic properties relative to fresh tissue, with previous studies reporting attenuation changes ranging from minus 29 to plus 55 percent after fixation, although because both tumor and control samples were fixed under identical conditions, the relative trends are likely to remain valid. The tumor and control cohorts also came from different sources, with potential confounds in post-mortem interval, handling, age distribution, and sex balance, and the dataset of forty samples was imbalanced toward males. Attenuation compensation relied on group-specific average coefficients rather than sample-specific measurements, which could not be obtained for all tissues due to limited dimensions and insufficient signal-to-noise ratio. The authors also note that whole-region parameter averages do not capture spatial heterogeneity within individual samples, a limitation for margin assessment where local variation is exactly what matters.

Even so, the study opens a genuinely exciting translational path. Because ultrasound is cheap, portable, and already standard in neurosurgical operating rooms, a multiparametric envelope-statistics framework could one day complement conventional B-mode imaging by overlaying quantitative microstructural maps onto the surgeon’s view, helping delineate tumor margins in real time without the expense of intraoperative MRI or the limited sensitivity of fluorescence-guided resection. The researchers envision next steps using freshly excised tissues and, ultimately, in-situ examination of brain tumors in patients with a specialized intraoperative probe. If those studies succeed, the statistical whisper of scattered ultrasound echoes, invisible in a grayscale image, could become a powerful new voice in the fight against one of medicine’s most formidable cancers.

Subject of Research: Science

Article Title: Ultrasound echo envelope statistics to differentiate glioblastoma multiforme from normal brain tissue ex vivo: a proof-of-concept study

Article References: Patil, J. M., Agarwal, M., Rao, S., Vazhayil, V., Pandya, H. J., Mahadevan, A., Shekhar, H., & Mercado-Shekhar, K. P. (2026). Ultrasound echo envelope statistics to differentiate glioblastoma multiforme from normal brain tissue ex vivo: a proof-of-concept study. Frontiers in Acoustics, 4, Article 1882624. https://doi.org/10.3389/facou.2026.1882624

Image Credits: AI Generated

DOI: 10.3389/facou.2026.1882624

Keywords: glioblastoma, quantitative ultrasound, envelope statistics, machine learning, tumor margins, medical imaging, brain tumor, Ultrasound, echo, envelope, statistics, differentiate

The most common response to incomplete records is deceptively simple: throw them away. Analysts who delete every row containing a missing entry, an approach known as complete-case analysis, end up with a dataset that is smaller, potentially biased and statistically less powerful. If the people who failed to answer a questionnaire differ systematically from those who did, the surviving sample no longer represents the population it was drawn from. Even when the missingness is benign, discarding data inflates uncertainty and weakens statistical estimates, a cost that grows rapidly as the proportion of missing entries climbs.

Imputation offers an alternative. Instead of deleting incomplete cases, imputation methods replace each missing value with a plausible estimate inferred from the rest of the data. Done well, this preserves sample size, retains information that deletion would destroy and yields more reliable downstream estimates. The catch is that imputation is itself a prediction problem: to fill in a missing number, an algorithm must model how that number relates to everything else in the record. The quality of the fill-in therefore depends entirely on the quality of the predictive model doing the filling, which is precisely where the new study concentrates its effort.

Asif and Samart’s proposal, Layered Stacking, is built on the idea of stacking, an ensemble strategy in which multiple different models are trained to solve the same problem and their predictions are then combined by a higher-level model that learns when to trust each one. Rather than relying on a single imputation algorithm, Layered Stacking organizes several base learners into layers, letting each layer refine the estimates produced by the one beneath it. The architecture is designed specifically for continuous missing values, the numeric fields where small imputation errors can compound into distorted means, variances and regression coefficients.

To find out whether the added complexity pays off, the researchers ran comprehensive simulation studies built on four distinct data-generating processes. Each simulated dataset was generated under the missing-at-random mechanism, the widely assumed scenario in which the probability that an entry is missing depends on other observed variables but not on the missing value itself. The experiments spanned sample sizes of 500, 1,000, 5,000 and 10,000 observations, and missingness rates of 10, 20, 30 and 40 percent, a grid that captures everything from small studies with modest gaps to large datasets with substantial holes.

The benchmark competition was demanding. Layered Stacking was pitted against five imputation techniques that are widely used in practice: k-nearest neighbors, which averages the values of the most similar complete records; support vector regression, which fits flexible boundaries in a transformed feature space; decision trees, which partition the data through a cascade of yes-or-no questions; random forests, which average many decorrelated trees; and extreme gradient boosting, the sequential ensemble method that has dominated tabular machine-learning competitions for years. Each method was asked to impute the same missing entries under the same conditions, allowing a direct, like-for-like comparison.

Performance was scored with two complementary metrics. The mean squared imputation error, or MSIE, penalizes large mistakes heavily and therefore rewards methods that rarely produce wildly wrong estimates. The mean absolute percentage imputation error, or MAPIE, expresses the average error as a percentage of the true value, making results comparable across variables measured on different scales. The authors also reported the standard deviation of the errors across replications, along with 95 percent confidence intervals, so that differences between methods could be judged against the noise inherent in repeated simulation runs rather than a single lucky or unlucky draw.

The headline result is that Layered Stacking generally achieved lower MSIE than all five benchmark models, with its advantage becoming particularly pronounced on larger datasets. That pattern makes intuitive sense: ensemble methods that learn how to combine base learners need enough data to estimate the combination reliably, so the payoff of stacking grows as sample size increases. For analysts working with the large, messy datasets that characterize contemporary research, the finding suggests that the extra computational cost of a layered ensemble may be repaid in measurably more accurate imputations, which in turn feed into more trustworthy statistical models built on top of the completed data.

Simulations alone can flatter a method in ways real data never do, so the authors also tested Layered Stacking on two real-world datasets. These datasets bring irregularities that no data-generating process fully captures: skewed distributions, awkward correlations between variables and missingness patterns shaped by human behavior rather than mathematical rules. The real-data evaluation served as a sanity check on the simulation findings, and the study reports that the method’s performance carried over, reinforcing the case that the gains are not an artifact of carefully controlled synthetic conditions.

The broader significance of the work lies in what it says about the state of imputation practice. Methods like k-nearest neighbors and random forest imputation have become default choices in statistical software, and extreme gradient boosting has been increasingly adopted for its raw predictive power. Showing that a layered stacking ensemble can beat these established baselines, especially at scale, nudges the field toward treating imputation not as a preprocessing afterthought but as a modeling problem worthy of the same ensemble sophistication applied to prediction tasks. For anyone who has watched a regression analysis wobble because a fifth of the data contained holes, the message is appealing: the blanks in a dataset need not be a permanent tax on statistical accuracy, and the tools for filling them are getting better.

Subject of Research: Machine learning methods for imputing missing continuous data

Article Title: A layered stacking ensemble approach for missing data imputation

Article References: Asif, M., & Samart, K. (2026). A layered stacking ensemble approach for missing data imputation. PLOS One, 21(10), e0359843. https://doi.org/10.1371/journal.pone.0359843

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0359843

Keywords: missing data, imputation, stacking ensemble, machine learning, PLOS One, simulation study, missing at random, random forest, gradient boosting, statistics, data science, mean squared error

The research, published in Machine Learning with Applications by Christoph Lehmann and Yahor Paromau, proposes a deceptively simple reframing: view ML training as a controlled scientific experiment with repeated measurements. By varying one confounding factor at a time — the train–test split, the initial weights, the data augmentation scheme, the dropout configuration, or the hyperparameter optimization procedure — while holding everything else fixed via random seed control, each training run becomes a sample from the distribution of a target metric of interest. Repeating the run with different seeds yields repeated measurements, and with them the tools of classical inferential statistics become applicable: quantiles, confidence intervals, and explicit uncertainty quantification.

The scale of the empirical work is unusual for this kind of methodological study. The authors ran roughly 500 to 1,000 seed-controlled training repetitions for each source of variation across three real-world use cases: image classification of Simpsons characters with convolutional neural networks, the standard CIFAR10 benchmark with a VGG11 architecture, and a regression task predicting the critical temperature of superconductors using deep neural networks and gradient boosting trees. The effort consumed approximately 19,000 GPU hours on NVIDIA A100 and H100 accelerators, producing empirical performance distributions dense enough to serve as near-ground-truth references against which small-sample statistical methods could be validated.

The core statistical move is a shift from means to quantiles. A quantile answers a risk-oriented question that a mean cannot: the 25% quantile of accuracy tells you the accuracy falls below that threshold in only a quarter of runs, while the 90% quantile of RMSE tells you the error exceeds that value in just one run out of ten. The authors draw an explicit parallel to Value-at-Risk in financial regulation, where a quantile of the loss distribution defines the threshold exceeded only with a small pre-specified probability. For high-stakes applications — medicine, banking, criminal justice — this threshold language maps naturally onto acceptance criteria: a model can be required, in advance, to keep its error below a bound with a stated probability, something a mean-based evaluation cannot certify.

Quantiles, however, are harder to estimate than means. They are sensitive to the shape of the distribution, and the more extreme the quantile level, the more data is needed. The study characterizes this trade-off precisely. Exact nonparametric confidence intervals, built from order statistics and the binomial distribution, exist only when the sample size clears a minimum that grows steeply toward the distribution’s tails: estimating a 10% quantile with 90% confidence requires at least 22 runs, while a 1% quantile demands 230. Asymptotic intervals based on the normal approximation of sample quantiles have their own requirements, and the authors show a clever sign transformation — analyzing the negated metric — that converts a costly lower-tail quantile into a cheaper upper-tail one, cutting the required sample size for a 10% quantile from 42 to 25 runs.

For situations where even those minimums cannot be met, the authors evaluate a semiparametric bootstrap that extrapolates into the distribution’s tails using the spacing of the outermost order statistics. This method remains applicable where the closed-form intervals are undefined, at the price of extrapolation that may not match the true tail behavior. Across 42 experimental settings and a simulation study spanning skewed Beta distributions, normal mixtures, and Gumbel-distributed errors, the asymptotic nonparametric interval emerged as the practical default, offering a favorable balance of coverage, interval length, and simplicity. Bootstrap intervals remained a usable fallback for very small samples, though with coverage dropping to around 0.85 and noticeably wider intervals.

The practical payoff is demonstrated with two worked examples. In the Simpsons classification task, two training configurations — one varying hyperparameter optimization, one varying data augmentation — had nearly identical mean accuracies of 0.874 and 0.872, indistinguishable by any mean-based comparison. But their 10% quantile confidence intervals, estimated from just 25 runs each, did not overlap at all: [0.870, 0.873] for hyperparameter optimization versus [0.860, 0.868] for data augmentation. The hyperparameter-optimized configuration was substantially more resistant to producing poor runs, a fact invisible in the means. Against a deployment requirement that accuracy not drop below 0.87 in more than 10% of cases, only one configuration qualified — a statistically grounded model selection decision that point estimates could never support.

The regression example on superconductors showed the complementary value of the framework. A deep neural network and a gradient boosting tree differed clearly in mean RMSE, 10.47 versus 9.59, and their confidence intervals for the mean, the 10% quantile, and the 90% quantile were all cleanly separated with similar widths. That uniform pattern, the authors note, is the empirical signature of a simple location shift between the two distributions — and its absence of tail-specific effects is itself informative, justifying a mean-based comparison in this case. Across 2,000 repeated paired draws, the quantile intervals separated the two models in 92 to 99 percent of draws at n=25, while the mean separated them essentially always.

The study also distills concrete guidance for practitioners working under realistic compute budgets. With fewer than 10 repetitions, only a t-interval for the mean is advisable. Between 10 and 15 runs, exact nonparametric intervals for the quartiles become feasible, with a maximum recommended confidence level of 0.9. At 25 runs, asymptotic intervals with the sign transformation extend coverage to the 10% and 90% quantile levels, and at 50 or more runs, extreme quantiles such as the 5% and 95% levels come within reach. Interval lengths themselves carry diagnostic value: a median interval markedly longer than the mean’s t-interval signals low density near the center and hints at bimodality, while asymmetric tail intervals reveal skewness. The authors also caution that metrics like accuracy are formally discrete, computed on a grid set by test-set size, and recommend inspecting the fraction of distinct values in a sample before trusting quantile estimates.

What emerges is a bridge between two communities that rarely speak. Statisticians have long treated experimental outcomes as random variables deserving of distributional analysis; machine learning practice, optimized for leaderboard positions and single benchmark numbers, has largely resisted that view. This work shows that the statistical machinery is not merely compatible with modern deep learning — it is affordable. Even 10 to 25 seed-controlled runs, a modest addition to any training budget, unlock tail behavior, stability assessment, and requirement-driven evaluation that no point estimate can provide. As models move into domains where a single bad run can mean a misdiagnosis or a denied loan, the authors’ message lands with force: the average is not the answer, and the distribution is the evidence.

Subject of Research: Distributional uncertainty quantification in machine learning performance evaluation using quantile estimation and confidence intervals

Article Title: Beyond point estimates: Distributional uncertainty in machine learning performance evaluation

Article References: Lehmann, C., & Paromau, Y. (2026). Beyond point estimates: Distributional uncertainty in machine learning performance evaluation. Machine Learning with Applications, 26, Article 101033. https://doi.org/10.1016/j.mlwa.2026.101033

Image Credits: AI Generated

DOI: 10.1016/j.mlwa.2026.101033

Keywords: machine learning, model evaluation, uncertainty quantification, confidence intervals, quantiles, statistics, reproducibility, deep learning, risk assessment, benchmarking, hyperparameter optimization, experimental design

ProD, short for “prodding” the Probability Densities, was developed by Jin Cheng Liaw, Francisco Geu Flores, and Wojciech Kowalczyk and published in the journal Machine Learning with Applications. It is a univariate filter method for feature selection, meaning it ranks features based purely on the statistical properties of the training data rather than by training and testing a specific machine learning model. That model-agnostic design carries real advantages: the ranked features can be confidently paired with any downstream algorithm, and because no iterative modeling is required, filter methods are dramatically cheaper to run than wrapper or embedded alternatives.

The core idea is borrowed from an unexpected place: ecology. Ecologists have long used the niche overlap coefficient to measure how much two coexisting species share the same resources. ProD adapts this concept to classification by estimating, for each feature, a probability density function separately for every class, and then computing the geometric intersection area between those density curves. If the distributions of two classes barely overlap on a given feature, that feature is a strong discriminator; if the curves lie almost entirely on top of one another, the feature carries little class-relevant information. The resulting score is a literal proportion between 0 and 1, which is precisely what makes the method so visually intuitive.

That visualizability is ProD’s defining departure from classical divergence metrics such as Kullback-Leibler divergence, the Bhattacharyya distance, and the Hellinger distance. These traditional measures remain popular largely because of mathematical convenience, offering closed-form solutions under Gaussian assumptions and, in the case of KL divergence, smooth differentiability suited to gradient-based optimization. But they are abstract, hard to plot, and prone to numerical instabilities when estimated non-parametrically. KL divergence, for instance, can blow up through division by zero in the tails of kernel density estimates. ProD sidesteps these problems by combining kernel density estimation with continuous numerical integration, producing a bounded, directly interpretable geometric quantity that faithfully reflects complex, multi-modal distributions without forcing parametric assumptions.

The method also distinguishes itself from mutual information and Relief-based filters, two other pillars of the feature selection literature. Mutual information, grounded in Shannon entropy, measures dependency between feature and target in bits or nats; Relief-family algorithms assign weights by repeatedly comparing each instance’s feature values with those of nearest neighbors of the same and different classes, effectively computing a spatial margin. Both are well established, but their outputs are proxy statistics that domain experts often find difficult to interpret. Because ProD evaluates the physical overlap area of continuous densities, practitioners can validate a feature ranking at a glance by simply plotting the class distributions, rather than trusting an opaque number.

Technically, the pipeline is straightforward. Each feature is min-max normalized to the interval from 0 to 1, split into class-specific subsets, and smoothed with Gaussian kernel density estimates along a fine evaluation grid. Bandwidth selection, which controls how much the densities are smoothed, is automated using Scott’s or Silverman’s classic rule-of-thumb formulas, with Scott’s rule emerging as the better default in testing. The intersection area between every pair of class densities is then computed by numerical integration and averaged across all class pairs. The authors also built in safeguards for awkward data: when the interquartile range collapses to zero on highly discrete or skewed arrays, the algorithm falls back on the sample standard deviation, and grid tails can be extended to handle boundary-heavy data.

Benchmarks were extensive. On synthetic datasets engineered with known relevant, redundant, and irrelevant features, including circuit-inspired ANDOR and ADDER problems and simulated microarray data with 4,060 features, ProD using Scott’s rule achieved the highest average index of success at 76.90, edging out established competitors such as ReliefF, I-Relief, LH-Relief, mutual information, the ANOVA F-ratio, and mRMR, while remaining highly robust across repeated dataset iterations. On real datasets spanning cancer microarrays, epilepsy electroencephalograms, gait recognition, human activity recognition, and network intrusion detection, ProD performed comparably to the strongest methods while running orders of magnitude faster than Relief-based approaches, which scale quadratically with sample size. ProD’s theoretical complexity grows only linearly in both samples and features, and its per-feature evaluation parallelizes cleanly across processor cores.

The method is not without limitations. As a univariate filter, it evaluates each feature in isolation and does not deliberately remove redundancy or capture multi-feature interactions, a deliberate trade-off that buys complete immunity to the curse of dimensionality and total ranking stability even when massive numbers of noisy features are added. Its reliance on kernel density estimation also makes it sensitive to sample size, with the authors warning users when a class contains fewer than five observations. On purely discrete data, probability mass functions or information-theoretic metrics remain theoretically more appropriate, and experiments confirmed that ProD’s selection ability is less reliable in discrete feature spaces unless bandwidths are carefully tuned.

One of the most instructive findings concerns multiclass problems. ProD’s default setting averages overlap areas over all pairs of classes, which implicitly assumes that an informative feature must separate every class pair simultaneously. On the synthetic ADDER dataset and the human activity recognition dataset, this default penalized features that brilliantly distinguished broad activity categories but failed on specific confusing sub-pairs, such as sitting versus standing. Switching the combinatorial hyperparameter from pairwise comparisons to evaluating all classes at once produced dramatic improvements, including perfect success rates on the discrete ADDER datasets and top-tier accuracies on the activity recognition task. A built-in heatmap of pairwise overlap areas lets users diagnose exactly which class pair is causing a feature to fail.

Beyond raw performance, the authors position ProD as a tool for human-in-the-loop machine learning, an increasingly urgent need in high-stakes domains like healthcare and drug discovery where black-box models have struggled to deliver on their promise. Because the method renders the underlying class distributions of every top-ranked feature, users can spot outliers that may be mislabeled samples, or peculiar clusters hinting at systematic errors in data collection, and iteratively refine both the dataset and the model. In interactive machine learning, where fast iteration often matters more than optimal first-pass results, a filter that is simultaneously fast, model-agnostic, and fully visualizable may prove to be exactly the kind of transparent interface that lets domain experts, not just algorithms, steer the science.

Subject of Research: A visualizable filter feature selection method based on class probability density overlap

Article Title: ProD: A visualizable filter-feature selection method based on “prodding” the class {Pro}bability {D}ensities for overlappping

Article References: Liaw, J. C., Geu Flores, F., & Kowalczyk, W. (2026). ProD: A visualizable filter-feature selection method based on “prodding” the class {Pro}bability {D}ensities for overlappping. Machine Learning with Applications, 26, Article 101035. https://doi.org/10.1016/j.mlwa.2026.101035

Image Credits: AI Generated

DOI: 10.1016/j.mlwa.2026.101035

Keywords: feature selection, machine learning, kernel density estimation, class overlap, niche overlap coefficient, filter methods, explainable AI, human-in-the-loop, high-dimensional data, bioinformatics, statistics, open-source software

The Southeastern Universities Research Association is a consortium of research universities that works to advance collaborative research and education across the region and to strengthen the scientific enterprise of the United States more broadly. The organization supports research operations and workforce development in partnership with member universities, government agencies and national laboratories. Its Graduate Awards program is designed to identify and support emerging STEM talent at a pivotal moment, when students are transitioning from master’s-level training into the sustained, independent inquiry that defines doctoral research. Each recipient receives 5,000 dollars to support professional development and to help reduce the financial barriers that often accompany the start of doctoral study, a stage at which promising researchers can otherwise be forced to divide their attention between scholarship and outside employment.

Anab’s research trajectory illustrates the increasingly practical orientation of modern computer science graduate training. During his master’s studies at Georgia State, he applied data science and artificial intelligence techniques to real-world datasets, developing webcam-based systems capable of stress signal detection, emotion recognition and real-time sign language translation. These projects sit at the intersection of computer vision, machine learning and human-computer interaction, requiring models that can interpret subtle visual cues from video streams in real time rather than analyzing static images after the fact. Webcam-based sensing is an area of growing interest in digital health because it turns an ordinary camera already present in most laptops and phones into a passive monitoring instrument, avoiding the cost and friction of dedicated wearable sensors while raising important questions about accuracy, robustness and privacy that researchers in this field must confront directly.

As a doctoral researcher, Anab plans to build on that foundation by developing AI-enabled digital health technologies. The ambition is to move from laboratory demonstrations toward practical tools that can improve how human well-being is monitored and understood, combining advances in artificial intelligence, sensing and digital health into systems that are reliable enough for everyday use. In his own words, receiving the SURA Graduate Award is a meaningful recognition of his research journey and a motivation to continue developing technologies that can have a real impact on human health, with support that will help him advance doctoral research aimed at creating practical tools for monitoring well-being. The transition from detecting stress signals in controlled settings to deploying dependable health technologies is a demanding one, and sustained fellowship support of the kind the SURA award provides is often what allows doctoral students to pursue it rigorously.

Cui’s work addresses a different but equally consequential frontier: the statistical theory that underpins machine learning and data science. During his master’s research in Georgia State’s Department of Mathematics and Statistics, he developed new multivariate modeling approaches for high-dimensional datasets, work that has produced a first-author paper currently under review. High-dimensional data, in which the number of variables approaches or exceeds the number of observations, is now the norm in fields ranging from genomics to finance to large-scale behavioral studies, and it poses a fundamental challenge to classical statistical methods that were designed for settings with many more data points than parameters. Cui has described what excites him most as building statistical methods that stay reliable when data are high-dimensional and messy, which is precisely the regime in which machine learning tools are hardest to trust. His selection as one of two students chosen for the department’s machine learning concentration reflects the growing recognition within mathematics departments that rigorous statistical theory is essential to the credibility of modern artificial intelligence.

The distinction between Cui’s theoretical orientation and Anab’s applied systems work captures two complementary halves of the contemporary data science enterprise. Applied AI systems such as webcam-based health monitors depend on statistical guarantees to behave predictably when confronted with noisy, shifting, real-world inputs, while theoretical advances in multivariate modeling gain relevance when they inform the design of learning algorithms that must operate on imperfect data at scale. That both researchers emerged from the same college at the same university, and were recognized in the same year by the same consortium, suggests how deeply data-driven methods now permeate disciplines that were once sharply separated, from computer science departments focused on engineering working systems to statistics departments focused on inference and uncertainty.

Both students are based in Georgia State’s College of Arts & Sciences, and their recognition carries institutional weight beyond the individual honor. Donald Hamelberg, the university’s Vice President for Research and Economic Development and himself a Georgia State doctoral alumnus, attended the ceremony honoring this year’s awardees at the SURA Annual Members Meeting and accepted Cui’s award on his behalf. Having two Georgia State students among the four awardees, he noted, speaks to the strength of the university’s graduate research community, and he expressed pride in seeing the two students’ efforts recognized as a reflection of the talented researchers advancing discovery at the institution. For a university that has invested heavily in building research capacity across the computational and quantitative sciences, the concentration of awards in artificial intelligence and statistics is a visible signal of where that investment is bearing fruit.

The selection process itself was led by M. Omar Faison, chair of the SURA Committee for Collaborative Capacity Building, who oversaw the evaluation of candidates from member universities. He described the students as selected for their academic excellence and dedication to advancing research as outstanding members of the next generation of STEM talent, and emphasized that the SURA Graduate Award offers awardees an added measure of support during a key moment in their research journeys. The framing matters: early-career awards of this kind do more than provide money. They signal to doctoral advisors, hiring committees and funding agencies that a researcher has been independently vetted by a multi-institutional body, and they give recipients the freedom to take intellectual risks in the first years of a doctorate, when the direction of a research career is often set.

The setting of the recognition added its own symbolic resonance. Anab and Cui were honored at the 2026 SURA Annual Members Meeting held at the Thomas Jefferson National Accelerator Facility, a U.S. Department of Energy national laboratory in Newport News, Virginia, known widely as Jefferson Lab. The facility, which probes the fundamental structure of matter using high-energy electron beams, represents the kind of large-scale, collaborative scientific infrastructure that consortia like SURA exist to connect with university research programs. Honoring emerging researchers in artificial intelligence and statistics at a national laboratory dedicated to experimental physics underscores how the boundaries of STEM research continue to blur, with computational and statistical expertise now indispensable to nearly every scientific domain, from particle physics to digital health.

For the two awardees, the award arrives as they begin doctoral work that will unfold over the coming years, in fields that are evolving almost faster than curricula can be updated. Anab’s plan to develop AI-enabled digital health technologies places him in one of the most competitive and fastest-growing areas of computer science, where the difference between a compelling prototype and a deployable clinical tool often comes down to years of careful validation. Cui’s focus on statistical theory for high-dimensional machine learning addresses a foundational vulnerability of the AI systems now reshaping science and society, since methods that cannot be trusted on messy data cannot be trusted at all. The SURA recognition, and the financial support that accompanies it, gives both researchers a measure of runway at exactly the stage when sustained focus matters most, and it offers an early, externally validated vote of confidence in the directions they have chosen to pursue.

Subject of Research: SURA 2026 Graduate Awards recognizing two Georgia State doctoral students in artificial intelligence and statistical modeling

Article Title: Two Georgia State students recognized among emerging STEM leaders

Article References: Two Georgia State students recognized among emerging STEM leaders. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: SURA, Georgia State University, graduate awards, STEM, artificial intelligence, digital health, computer vision, statistics, machine learning, high-dimensional data, doctoral research, Jefferson Lab

The stakes of this finding are enormous. Frameworks such as the Hierarchical Taxonomy of Psychopathology, or HiTOP, were built on the premise that the Diagnostic and Statistical Manual of Mental Disorders fails to carve nature at its joints, producing a rampant comorbidity problem that can be solved by reorganizing symptoms into broad dimensions. Factor analyses of population data consistently reveal two such dimensions, internalizing, which encompasses conditions marked by intense negative emotion such as depression and anxiety, and externalizing, which captures disorders of behavioral and emotional dyscontrol such as conduct disorder and substance use disorder. Because these dimensions correlate at roughly 0.5 to 0.6, researchers proposed an even broader construct, the p-factor, a single dimension claimed to explain a person’s liability to mental disorder, comorbidity among disorders, persistence over time, and symptom severity.

Watts and colleagues argue that this entire inferential chain rests on a statistical artifact. Their central insight borrows from ecology and computer science, fields that have long recognized that measures of association are dramatically influenced by the base rates and skewness of the variables involved. In psychiatric epidemiology, the overwhelming majority of people endorse few or no symptoms. Around 70 percent of the population receives no mental disorder diagnosis in a given year, and between 17 and 40 percent never receive one across their entire lives. When such a flood of asymptomatic cases enters a covariance-based analysis, the shared absence of symptoms inflates the apparent overlap between dimensions, making them look tightly linked when, among genuinely symptomatic people, they may be barely related at all.

To test this idea rigorously, the team turned to the Adolescent Brain Cognitive Development Study, one of the largest longitudinal studies of youth ever conducted, tracking 11,868 nine- and ten-year-olds across 21 US sites. Using caregiver reports on the Child Behavior Checklist, a 113-item assessment of psychiatric symptoms, they measured internalizing, externalizing, attention problems, and thought problems across four annual waves. Crucially, the data were far from normal: at wave one, 81 percent of children showed nonclinical levels of both internalizing and externalizing, and only 5.3 percent exhibited at-risk or clinical levels of both simultaneously. The distributions were highly skewed and kurtotic, violating the assumptions that underpin the standard linear models used throughout psychopathology research.

Instead of assuming linearity, the researchers deployed Bayesian change point models, statistical tools that allow the relationship between two variables to shift at different points along their joint distribution. These models, also known as broken-stick or threshold models, are routinely used in ecology to detect behavioral transitions in animals and environmental thresholds, but had rarely been applied to psychopathology. The results were striking. When externalizing was regressed onto internalizing, the change point occurred at an internalizing score corresponding to roughly two or three symptoms. Below that threshold, a one-point increase in internalizing was associated with a 32 percent increase in externalizing. Above it, the same increase predicted only a 7 percent rise, a slope 4.6 times weaker.

The pattern reversed direction exactly as the nomorbidity hypothesis predicted: associations were strongest among the largely asymptomatic and weakest among those with meaningful symptom burden. The findings replicated when the regression direction was flipped, with a pre-change point slope indicating a 43 percent increase in internalizing per point of externalizing compared with just 6 percent afterward. They also held across all four waves of data, with change points consistently located between internalizing scores of three and five, and the pattern extended to attention problems and thought problems, where pre-change point slopes were uniformly several times steeper than post-change point slopes. At moderate to clinically severe levels, the dimensions were so differentiated that their associations approached negligibility.

Perhaps the most consequential implication concerns the p-factor. If the general factor of psychopathology is largely a product of nomorbid cases, then it may be irrelevant to the very population it is meant to serve, people experiencing clinically significant distress. The authors note a provocative parallel with intelligence research, where Spearman’s law of diminishing returns shows that the general factor of intelligence, g, exerts more explanatory power at lower ability levels, with cognitive abilities becoming more differentiated as intelligence increases. The p-factor may behave analogously, functioning as a dimension of mental health rather than mental illness, and its apparent universality may dissolve once attention shifts to symptomatic individuals.

The study also exposed how badly conventional methods distort the picture. Ordinary least squares regression, the workhorse of psychopathology research, produced substantial prediction errors in these data, overestimating the association between dimensions at nonclinical levels and, critically, at clinically severe levels. Simulation studies conducted by the team showed that when two genuinely different slopes exist in a population, the single-slope linear model yields a biased average with no psychological meaning, systematically overstating comorbidity. Factor analysis makes even stronger assumptions, positing a latent normal distribution and linear relationships that the data violated outright, with factor scores proving even more skewed and kurtotic than the raw sum scores.

The authors anticipated and addressed several objections. Skeptics might invoke Berkson’s bias, arguing that conditioning on severity artificially attenuates associations, but that critique holds only if a single linear relationship exists in the population, which the data contradict. Nor did change point models manufacture nonlinearity artificially: simulations showed the models recover linear estimates when no nonlinearity exists, and sensitivity analyses using caregivers’ own Adult Self-Report data and generalized additive models produced the same results. A recent meta-analysis further corroborates the pattern, finding that the externalizing-internalizing correlation is dramatically stronger in nonenriched samples (0.48) than in psychopathology-enriched samples (0.20), and stronger for current than lifetime diagnoses, precisely the conditions that maximize the proportion of asymptomatic cases.

As the framers of the next DSM grapple with incorporating dimensionality and severity into psychiatric nosology, the message of this research is unambiguous: correlation does not imply comorbidity, just as it does not imply causation. Dimensional structures estimated from community samples may serve population screening well, but they should not be read as evidence of shared etiology or treatment-relevant co-occurrence among patients. The researchers call for the field to embrace nonlinearity and population heterogeneity, report the distributional properties of data, and prioritize symptomatology over statistical correlation. Failing to do so, they warn, risks reifying artifactual transdiagnostic dimensions and abandoning the search for disorder-specific mechanisms, ultimately impeding the discovery of the causes and treatments that patients with genuine mental illness need most.

Subject of Research: Statistical drivers of covariation among higher-order psychopathology dimensions in youth

Article Title: Covariation among higher-order psychopathology dimensions is driven by nomorbidity and not comorbidity

Article References: Watts, A. L., Rosen, A. F. G., Greene, A. L., King, K. M., Meyer, F. A. C., Trull, T. J., Sher, K. J., & Joyner, K. J. (2026). Covariation among higher-order psychopathology dimensions is driven by nomorbidity and not comorbidity. Nature Mental Health. https://doi.org/10.1038/s44220-026-00727-0

Image Credits: AI Generated

DOI: 10.1038/s44220-026-00727-0

Keywords: psychiatry, comorbidity, nomorbidity, p-factor, internalizing, externalizing, HiTOP, psychopathology, Bayesian change point models, ABCD Study, DSM, statistics