arXane › Statistics › Statistics
Wednesday, 4 November 2026: 15 new papers, 7 cross-lists and 8 replacements in Applications (stat.AP), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
Wildlife--vehicle collisions (WVCs) impose a large toll on U.S. highways, yet state crash databases often fail to record animal involvement, leaving agencies uncertain of the true missing count. This study evaluates whether existing crash records can identify individual WVCs and estimate overall unrecorded rates. We analyzed 4.9 million crash records from Colorado, Utah, Iowa, and Illinois (2007-2026). Each state's schema underwent a label-leakage screen to exclude explicit animal fields before harmonization into a shared vocabulary. Calibrated gradient-boosted classifiers were trained per state, interpreted using Shapley additive explanations, and evaluated for prevalence estimation via Adjusted Classify-and-Count and Maximum-Likelihood techniques across in-domain, cross-state, and synthetic reporting-gap scenarios. Detection performance depends heavily on record completeness rather than collision rarity. At ~4% prevalence, feature-rich Utah achieved an average precision of 0.88 versus 0.64 for feature-poor Colorado, and outperformed Iowa despite Iowa's 3x higher WVC rate. Within-state richness curves confirm feature depth drives accuracy. While classifiers ranked records accurately across states, probability calibration did not transfer directly. However, in-domain prevalence estimation recovered true collision rates within 0.001. This work shifts WVC analysis from spatial clustering to record-level detection and missing-data estimation using legacy datasets. Transportation agencies can retrospectively flag unrecorded WVCs, quantify total collision burden to support mitigation funding, and identify high-value reporting fields prior to revising crash-report manuals.
The urban heat island (UHI) effect amplifies heat stress in cities, increasing heat-related illness, mortality, sleep disruption, and energy demand. Because UHI intensity varies at neighborhood scales, intra-city temperature mapping is essential for assessing public health impacts, yet existing monitoring networks are sparse. Crowdsourced weather stations provide dense, hourly observations but suffer from noise and systematic biases, including preferential sampling driven by where residents install sensors. We introduce two scalable Gaussian process frameworks which adjust for preferential sampling and enable statewide, high-resolution temperature prediction. The first integrates sampling correction directly within a sparse variational Gaussian process (SVGPR+PS). The second uses a two-stage estimator involving a log-Gaussian Cox process (LGCP+GP) that estimates the sampling intensity field and incorporates it into temperature prediction. Both methods rely on inducing-point approximations and variational inference to scale beyond traditional Gaussian processes. Applied to approximately 10,000 citizen stations across North Carolina, the models generate hourly temperature fields within minutes. Validation against independent urban heat campaign data shows that the preferential sampling correction improves predictive performance, increasing average afternoon correlations across four cities from 0.26 to 0.43. This scalable framework enables neighborhood-level UHI assessment and supports studies of heat exposure disparities statewide.
Bitcoin perpetual futures trade continuously with shallow liquidity and high price impact, making them prone to millisecond-scale flash crashes. Agent-based limit order book simulators are a natural tool for studying such events, but their behavioral parameters are usually hand-crafted or require full order book histories that are rarely available at scale. We propose a four-stage pipeline that constructs a reproducible 100 ms BTCUSDT flash-crash event panel from 66 detected events, elicits behavioral priors for four agent archetypes using an offline large language model conditioned on empirical microstructure anchors, instantiates a heterogeneous limit order book simulator with the validated priors, and applies causal discovery plus counterfactual analysis to the resulting synthetic panel. Across 500 simulation runs, LLM-elicited priors produce a crash rate of 0.176 versus 0.008 under uninformative uniform priors and generate heav- ier return tails. In the frozen counterfactual analysis, reducing leverage amplification by one within-sample standard deviation lowers the predicted crash rate from 0.176 to 0.136, whereas reducing directional pressure yields only a marginal change. These find- ings suggest that empirically anchored LLM elicitation can improve simulator fidelity and help identify plausible crash-amplification mechanisms in a controlled synthetic environment
Probabilistic forecasts of day-ahead electricity prices are increasingly used to manage price risk, yet competing models are usually ranked on aggregate scores that average over the price regimes in which uncertainty matters most. This study evaluates probabilistic forecasts of hourly EPEX SPOT GB day-ahead prices over a full held-out calendar year, applying a common pre-auction information boundary and rolling-origin design to linear quantile regression, a quantile regression forest (QRF), a LEAR-QRA benchmark and an encoder-decoder quantile long short-term memory (LSTM) network. Two routes to more reliable intervals are then compared: conformal recalibration and Quantile Regression Averaging (QRA). Aggregate scores separate the LSTM and QRF only weakly, with a non-significant 4.4% difference in continuous ranked probability score (CRPS), but their conditional behaviour differs sharply. Above 200 GBP/MWh the LSTM covered 0.12 of outcomes and QRF 0.71, consistent with the forest retaining realised spikes in its leaf distributions while the network learned a smooth upper tail. Conformal recalibration corrected marginal coverage but did not improve the interval score or materially repair spike coverage. QRA combining the LSTM, QRF and LEAR-QRA forecasts reduced CRPS to 5.14 GBP/MWh and raised coverage above 200 GBP/MWh to 0.65 at unchanged interval width. Recalibration and combination therefore address different failures and are not substitutes.
Understanding how transmission varies across age groups is important for epidemic surveillance and targeted intervention, but estimating age-specific transmission in near real time is challenging when infections are only partially observed, observations are delayed, and transmission varies across age groups. We develop a Bayesian age-stratified renewal model that jointly estimates latent infections, time-varying age-specific susceptibility, and age-specific contributions to transmission within an empirically specified contact structure. To enable sequential inference under these processes, we use a block particle filtering approach embedded within a sequential Monte Carlo squared framework, with fixed-lag smoothing to account for temporal dependence and delayed observations. From the inferred transmission process, we derive a next-generation matrix, effective reproduction number, and reproduction contributions. Applied to age-stratified COVID-19 surveillance data from Ireland during the Omicron dominant period, the framework reveals heterogeneity in susceptibility and transmission, with older adults exhibiting higher susceptibility, while younger and working-age groups make larger contributions to transmission because of their higher contact rates. These results demonstrate how statistical inference can provide age-specific transmission estimates to support targeted epidemic monitoring and intervention.
Aggregate lexical frequencies reflect both what speakers do and how a corpus records it. We develop a stochastic framework for lexical adoption, abandonment and reactivation on a temporal multilayer network, together with a count observation model separating speaker prevalence, use intensity and detectability, and ask what such data identify. We give a necessary and sufficient condition for the never-active and dormant states to be merged exactly, collapsing the three-state chain to two, and show that the condition constrains the exposures a given network can deliver, not the response function as a whole. No count design can distinguish use intensity from detectability, an exact invariance distinct from the merely practical loss of information in sparse series. And we prove that in a low-prevalence community approximation the rates enter only through the net growth $\beta-\mu$ and the coupling product $\beta\kappa$, so that a one-parameter family of triples has identical trajectories, the only separating information lying in a term quadratic in prevalence whose size depends on the emission scale. Simulations characterise recovery, prediction and sensitivity to misspecification. An exploratory analysis of 144 candidate forms in CREA and CORPES XXI press subcorpora illustrates the consequences: under the chosen emission scale and a symmetric contact graph, very different rate triples give nearly identical fitted trajectories, and in leave-one-country-out comparison with training-only proxies and seeds on a retrospectively selected cohort, a constant-rate count baseline beats the evaluated dynamic specifications on 84 to 94% of forms. These findings neither establish nor refute contact-driven diffusion. They delimit what this model and panel can support, and name the calibration, geographical contrast and repeated speaker observations that would make the question answerable.
Heart failure is a serious medical condition associated with risk of acute deterioration, recurrent hospitalizations and high mortality making accurate mortality prediction potentially valuable for patient care and healthcare planning. Numerous prognostic models have been developed using conventional statistics (CS), machine learning (ML) and deep learning (DL), but variation in study populations, heart failure definitions, prediction horizons and development practices may limit interpretation of applicability. We conducted a systematic review of mortality prediction models published between 2009 to the start of 2026 searching three databases (PubMed, IEEE and Scopus) for studies predicting all-cause mortality over a 1-60 months prediction horizon among patients with heart failure. Data extracted were cohort characteristics, heart failure definitions, model development, cohort size, validation practices, mortality, computational model design and reported performance. The risk of bias and applicability were assessed using the Prediction Model Risk of Bias Assessment Tool (PROBAST). Of 1516 publications identified, 56 met the inclusion criteria. Publication numbers increased over the observation period, alongside increasing use of ML/DL models and decreasing use of CS approaches. Most development cohorts (64%) were classified as Unknown/Undefined heart failure, reflecting inconsistent reporting and terminology that did not correspond with established heart failure guidelines. External validation was reported in 23% of studies. Overall, research in modeling heart failure mortality has grown alongside increasing adoption of ML/DL approaches. Greater standardization of study design and reporting is needed for meaningful comparison, reproducibility and evaluation of models for clinical application.
Many researchers believe that human lifetime on the interval (30,80) years is described by the Gompertz-Makeham distribution. In this work, the task is set to test this hypothesis. We consider a number of distributions: Gompertz-Makeham, Gompertz-Weibull, Logistic Kannisto-Makeham, Logistic Beard-Makeham and Logistic Beard-Weibull, some of which are partially known, for which comparative calculations on real mortality data are performed using the $\chi^2$ criterion. The data were selected for three countries: England \& Wales, Norway and Sweden, cohorts born in 1900. As it turned out, on the interval (30,80) years the Gompertz-Makeham distribution is far from being the best among those listed above. In addition, for the same data, a similar problem was studied for the interval (80,120) years.
Heat-related mortality varies among individuals under similar environmental conditions, yet environmental exposure and genetic susceptibility are typically modelled separately. We propose a signal-processing cascade linking satellite-derived land-surface temperature to sequence-dependent heat-shock response and mortality risk. The framework combines distributed-lag filtering of thermal exposure, nonlinear HSF1 activation, cross-correlation with an HSF1 position-weight-matrix kernel, and Hill-model mapping of sequence-dependent binding changes to regulatory response. Applied to 52 heat-response genes and 157 naturally occurring variants, the framework identifies 21 heat-shock-element arrays across 17 genes. Variants in canonical arrays are significantly enriched for predicted binding disruption ($p=3\times10^{-4}$). Propagating these effects through the cascade yields a peak predicted mortality-risk multiplier of $1.68\times$ at $40$--$42\,^{\circ}\mathrm{C}$. The framework demonstrates how environmental and genomic signals can be integrated to model inter-individual variation in heat-related risk.
We develop ML models that predict when cross-factor predictability will erode, enabling prospective risk management. A decay prediction model achieves C-index $= 0.93$ on held-out factor pairs, providing early warning of signal erosion---the key predictor is initial signal strength: stronger signals decay faster (``regression to the mean''). An online regime detector enables real-time classification with 6.6-day average detection delay. Prior work explains why factors decay (arbitrage, publication effects); we predict when decay will occur. Limitation: The primary HML$\to$SMB signal does not replicate in post-break OOS (2013--2024); this null result is consistent with genuine decay but limits confirmatory claims. Motivation: Among 30 directed Fama-French factor pairs (1990--2024), predictability targeting the Size factor (SMB) decays fastest. Of 7 pairs showing exponential decay ($R^2 > 0.3$), 4 target SMB (Mkt-RF$\to$SMB, CMA$\to$SMB, HML$\to$SMB, RMW$\to$SMB; half-lives 2.4--4.1 years). This SMB-concentration pattern motivates the predictive models. Methodology: Using a regime-conditional Granger framework with Student-$t$ HMMs, we document structural breaks clustering around June 1998 ($p < 10^{-10}$). A pre-break OOS test (HMM trained 1990--1995, tested 1996--2007) confirms signals existed: HML$\to$SMB shows $p = 0.013$ (Elevated) and $p < 0.001$ (Crisis). The primary HML$\to$SMB signal does not replicate in post-break OOS (2013--2024), consistent with genuine decay rather than overfitting---after ${\sim}6$ half-lives, the expected signal is $<$1% of its 1990s peak. International analysis finds 2/4 non-US markets with Bonferroni-surviving OOS effects; correction for full specification search was not applied, so results remain exploratory.
Groundwater inversion is commonly built on Gaussian assumptions for both network weights and output errors. The assumptions are convenient, but it is unclear which one should be relaxed when hydraulic conductivity is heavy tailed. Here, Gaussian and q-Gaussian distributions were assigned independently to variational weights and the conditional output likelihood in a $2\times2$ Bayesian neural design. Hydraulic conductivity, porosity, and dispersion were inferred jointly from sparse head and transport observations. Four q regimes ($q=1.0$, 1.2, 1.5, and 1.8) were evaluated with five independently generated data sets and matched training seeds, giving 130 held-out cases per regime and 500 posterior draws per case. At $q=1.5$, q-Gaussian weights with a Gaussian likelihood reduced log-conductivity CRPS by 2.85\% (95\% paired CI 0.82--4.88) and calibration error by 3.72 percentage points. Conductivity RMSE was unchanged, while 95\% interval width increased by 9.86\%. At $q=1.8$, assigning q-Gaussian tails to both components produced no stable accuracy gain and increased interval width by 138.46\%. The Gaussian-generated porosity and dispersion controls showed negligible accuracy changes. Moderate weight-side tails can thus improve distributional prediction, whereas an overly heavy output likelihood trades sharpness for coverage. Separating these two roles provides a clearer basis for uncertainty modeling in groundwater inversion.
Digital Twins are evolving from passive virtual representations into closed-loop systems that continuously synchronize with physical assets and drive real-time decisions. Yet predictive modeling, machine learning (ML), uncertainty quantification (UQ), and decision-making have been studied as separate capabilities, leaving limited understanding of their integration and maintenance during online operation. This narrative review, scoped by the functional requirements of real-time decision-making rather than by Digital Twin terminology alone, examines how such decisions are generated and sustained in engineering Digital Twins. We first examine foundational decision-making architectures and representative engineering applications, followed by methods that address their limitations across the decision loop. We identify optimization-based, policy-based, and knowledge-based approaches as the major pathways from virtual representation to action. Across them, ML plays three roles in decision-making: enabling efficient surrogate modeling, transforming heterogeneous physical feedback into decision-relevant information, and accelerating or directly generating decisions. UQ supports uncertainty-aware decisions and model adaptation, while continual validation, drift detection, and adaptation help maintain reliable operation as the physical system evolves. Together, these findings underscore the need for a shift from a model-centric to a system-centric perspective on Digital Twins, where its performance depends on the interactions with sensing, state estimation, computation, decision-making, and adaptation rather than on their standalone performance. Therefore, future research should shift from isolated algorithm development toward system-level co-design, scalable decision-making, and approaches to design, and data-efficient continual adaptation and validation for AI-enabled autonomous systems.
As the semiconductor industry transitions to the post-Moore paradigm, wafer warpage has become a critical quality issue in advanced packaging; particularly for 3D stacking and high-bandwidth memory manufacturing where die-level deformation can affect bonding quality, interconnect reliability, and yield. However, direct high-throughput measurement of individual chip warpage remains difficult in mass-production environments, while existing wafer-level metrology systems routinely provide dense 3D shape data at the wafer scale. This paper proposes a Bezier-surface-based Gaussian Process---known as Bezier-GP---for chips-on-wafer warpage modeling. The proposed framework combines wafer-level point-cloud metrology data with wafer-map layout information to construct chip-region-level Bezier surface patches, imposes continuity constraints between neighboring patches, and represents the resulting chips-on-wafer surface through a compact free-control-point vector. A GP is then introduced in this low-dimensional representation to model wafer-to-wafer variation, chip-region-level spatial dependence, and provide uncertainty quantification. Numerical experiments, using an ASC wafer-map layout, demonstrate that the proposed framework can reconstruct chips-on-wafer surfaces, preserve chip-region-level geometric interpretability, and recover population-level mean and covariance structures under a controlled multi-wafer simulation setting. The results suggest that Bezier-GP provides a measurement-driven statistical modeling foundation for connecting wafer-level metrology data to chip-region-level warpage analysis in semiconductor manufacturing.
Smart heat meter data provide an important basis for monitoring district-heating installations, but fault reports are delayed, incomplete and temporally coarse: a report follows the appearance of a fault, sometimes by weeks, so the onset is unknown. This blurs the distinction between statistical changes and operational faults and prevents the reliable labelling that fault classifiers require. Changepoint detectors such as the Bayesian Estimator of Abrupt Change, Seasonality, and Trend (BEAST) report only the probability that a change occurred, so a large jump and a much smaller one can receive the same probability, and probabilities alone cannot tell a utility which installation to inspect first. We therefore develop a decision score that applies BEAST to temperature difference and flow and scores each detected changepoint by its posterior probability together with its deviation from recent operation, jump size, local behaviour and physical direction. Cases with unfavourable changes in both channels, the pattern of insufficient cooling, receive the highest priority. Of 1,522 cases, 648 had a reported fault; these made up 96% of the 25 highest-priority cases and 90% of the highest 200, and Average Precision was 0.771 against a reported-fault prevalence of 0.426. As cases without a report are not verified to be fault-free, these figures are likely conservative. Without using the report date, the strongest unfavourable flow change in reported-fault cases fell a median of 11 days before the report. Level-based screening of temperature difference, as practised by utilities, ranked the cases comparably but cannot date the change, and the two kinds of evidence were complementary. The method can serve as the first step in a fault-detection workflow, providing a manageable subset of installations for inspection and candidate onset dates for training fault classifiers.
Predicting social network churn before it becomes visible in aggregate metrics remains an open challenge, particularly in enterprise settings where heterogeneous usage patterns, sparse data, and deployment constraints preclude standard supervised approaches. We formalize this problem as finite-step engagement projection over contributor-role Markov chains, with a stationary-distribution interpretation for ergodic chains in the long-run limit. For each engagement feature type within a network (e.g., Q&A, communities, articles, etc.), users are classified monthly into four behavioral states and a transition matrix is estimated from six months of history. Six-step propagation yields a label-free projection of the contributor mix; for ergodic chains, the Perron-Frobenius theorem establishes convergence under repeated propagation. Comparing projected future engagement to current engagement produces the Health Ratio, a single score requiring no trained model, no labels, and no infrastructure beyond SQL. Validated across seven rolling prediction windows on 11,500+ tenant-level networks, the Health Ratio achieves mean AUC 0.917 with a 156 times churn-rate gradient across risk tiers, outperforming all single-signal baselines and the growth-adjusted variant previously deployed in production. An ablation study shows that six-step propagation achieves similar churn discrimination to the eigenvector-based score. Deployed on Microsoft Engage since October 2025, the framework powers customer health monitoring and has enabled proactive intervention on at-risk networks before decline becomes visible in traditional metrics.
Accurate forecasting and temporal downscaling of solar irradiance is critical for reliable renewable energy integration and grid management. Traditional methods often struggle to capture rapid irradiance variability. In this work, we develop a Transformer-based architecture for simultaneous forecasting and temporal downscaling. The model takes input data at arbitrary resolutions and generates outputs at any resolutions represented within the training data, leveraging both global and local contextual information. To improve training efficiency, a genetic algorithm-based optimization framework is implemented to identify suitable model hyperparameters, while reducing the computational cost of exhaustive grid search. The effectiveness of the proposed model is shown by analyzing real data in Dallas, Texas. The proposed model achieved root mean square error (RMSE) values of 28.785, 29.544, 30.157, 32.132~W/m\(^2\) for 15-, 30-, 60-minute, and irregularly spaced global input and producing forecast at 5-minutes resolution, respectively. Furthermore, this model produced reliable uncertainty estimates, exhibiting wider prediction intervals for high-resolution inputs during volatile solar conditions, whereas coarser-resolution inputs result in narrower intervals and significantly lower training time and computational cost. Our approach provides a scalable and efficient framework for multi-resolution solar irradiance forecasting and temporal downscaling, suitable for practical energy forecasting and grid management applications.
Modern program evaluation prioritizes evidence from randomized controlled trials (RCTs) because prior research found that observational estimates of program impacts often diverge substantially from experimental benchmarks. We revisit this finding --- which was based on small survey datasets --- in the era of large-scale administrative data. Using anonymized income tax records covering all American adults between 1999 and 2025, we estimate the effects of workforce training programs on earnings by using machine learning models to predict counterfactuals from rich data on prior work histories, demographics, and residential locations. Rather than testing whether our observational estimates are unbiased, we use 37 RCTs to estimate the distribution of their bias. We find that our machine learning estimates closely match the RCT estimates, with root mean squared error (RMSE) comparable to that of the RCTs themselves. Our method reduces RMSE by 60% relative to parametric estimators used in prior work because our larger samples and richer covariates permit more flexible, higher-dimensional models of the counterfactual. Applying our method to a broader set of sites and enrollment years beyond the experimental sample, we find that treatment effects on earnings vary substantially across locations and over time, even within a given program. Programs that place more participants into target-sector jobs generate the largest earnings gains, with impacts that persist even after participants leave their initial jobs. These findings provide guidance for improving job training programs and, more broadly, illustrate a scalable approach to program evaluation that uses observational data to construct experimentally validated ``digital twins.''
Canopy cover is normally reported as a fraction of a horizontal map plane. When the domain of inference is the land surface, the appropriate target is the fraction of terrain surface area under canopy. We define this estimand on a C1 graph surface and show that it differs from vertical-projection cover by the planimetric covariance of cover with the area density, divided by the mean area density; the rumple index is a different quantity. A LiDAR pulse is recorded as a canopy return only when detection succeeds, so the naive return fraction estimates cover multiplied by the canopy detection probability. We study an inverse-probability-weighted estimator that uses that probability as the inclusion probability, and a weighted corner-averaged Cram\'er-von Mises lack-of-fit statistic for constant mean surface-area cover under independent canopy returns, calibrated by a parametric bootstrap. Synthetic validation on the flat plane and the Gaussian hill gives a naive bias near -0.40 and a weighted bias near 0.00; at 5000 pulses the test holds size at 0.02-0.06 across the simulated null cells and reaches power 0.79 under surface-uniform and 0.85 under plane-uniform sampling against broad slope-dependent cover, but only 0.12-0.13 against a compact hotspot. The definitions and their exact reductions are machine-checked in Lean 4. No field data yet.
Interval-censored multistate data arise when subjects are observed at irregular visit times, leaving transition times and intermediate states unobserved. Likelihood-based inference for continuous-time Markov models often requires computationally intensive matrix exponential evaluations. We propose a deterministic uniformization expectation-maximization (EM) algorithm for parameter estimation and latent trajectory inference. By representing the continuous-time process through an embedded Markov chain indexed by latent Poisson event counts, the method enables deterministic E-step calculations without repeated matrix exponential evaluations. The M-step reduces to transition-specific Poisson regressions with exposure offsets, accommodating covariate-dependent transition intensities. We establish uniform truncation error bounds and show that the procedure is an asymptotically monotone generalized EM algorithm. Under standard regularity conditions, the estimator is consistent and asymptotically normal. Simulations demonstrate accurate estimation and computational advantages over direct likelihood optimization, particularly for complex transition structures. We also develop an exact dynamic programming method to calculate posterior probabilities of candidate latent pathways and identify the most probable pathway between observations. Posterior expected transition counts and state occupancy times provide additional subject-specific summaries, while expected-count ratios offer a computational shortcut for classification in simple mutually exclusive pathway structures. The framework supports both population-level inference and individualized characterization of disease progression.
The simultaneous determination of Parton Distribution Functions (PDFs) and fundamental physical parameters, e.g. the strong coupling constant $\alpha_s$, the mass of the top quark $m_t$, or Wilson coefficients of an Effective Field Theory operators, is essential for the high-precision physics programme of the Large Hadron Collider. Yet, simultaneous global fits face significant methodological and computational challenges, rooted in the fundamental tension between estimating a finite-dimensional parameter and an infinite-dimensional function. In this paper, we address this problem by introducing a semiparametric estimation framework. The key advantage of our approach is that it avoids the need to refit the PDFs in the presence of either modified SM parameters or BSM contributions. Starting from standard, decoupled estimates of the PDFs and physics parameters, the method computes a bias correction a posteriori via the efficient influence function, yielding a debiased one-step estimator of the finite-dimensional parameter along with uncertainties with valid frequentist coverage. This correction rigorously accounts for the interplay between PDF and physics parameters without requiring a computationally expensive joint fit. As a proof of concept, we apply the method to two toy scenarios preparatory to a realistic global fit: the extraction of a dimension-six SMEFT Wilson coefficient from Deep Inelastic Scattering (DIS) pseudo-data based on BCDMS measurements, isolating the non-singlet PDF combination $T_3$, and to the determination of the proton total valence $V$ from combined HERA measurements. Our results demonstrate that the one-step estimator successfully removes the bias inherent in a preliminary, decoupled estimate and achieves confidence intervals with correct nominal coverage, offering a statistically rigorous and computationally efficient alternative to full simultaneous PDF fits.
Listwise deletion (LWD) appears more common than imputation: our review of leading journals finds that about 50% of articles state or imply LWD, versus 7% describing an imputation model. Assuming oracle regression with all required values observed consistently estimates the population average treatment effect, we ask when complete-case regression remains consistent. With constant effects, we offer two checks: whether covariates and the missing indicator satisfy the adjustment criterion in an augmented causal diagram (DAG), and whether the estimator pools valid within-covariate comparisons appropriately, potentially using inverse treatment-propensity weighting (IPW). For heterogeneous effects, assuming conditional effects carry over to the population, we reweight comparisons to the population covariate distribution. Simulations and empirical illustrations from American politics, comparative politics, and international relations demonstrate the framework's use and show why a missing-at-random (MAR) classification, although useful for assessing imputation, does not by itself establish whether complete-case regression consistently estimates the target population ATE. Thus, we recommend adding the missing indicator and its causes to causal models, then checking adjustment and weighting for LWD.
A system contains an unknown number $N$ of units, each failing at an unknown common rate, each unit is removed once it fails. The failure-rate declines as units are removed, but after only a few failures the decline is too slight to distinguish from a constant rate, and the maximum-likelihood estimate of $N$ is infinite with substantial probability. This is a well-known feature of the model, but its probability has not been quantified. We show that about $N^{2/3}$ failures are needed before a finite population can be distinguished from an inexhaustible one, and that at this scale the profile log-likelihood ratio converges to that of a Gaussian shift experiment, in which an infinite estimate occurs with a calculable probability. The exponent is not a property of the model alone. Profiling annihilates the Taylor terms that the nuisance-parameters can reproduce, and detectability is governed by the first surviving term. For example, unknown drift in testing-effort reproduces the linear term, leaving a quadratic survivor and raising the requirement to $N^{4/5}$; in general the critical scale is $N^{2q/(2q+1)}$ for a survivor of order $q$. We obtain the limiting-law of the estimator, the null likelihood ratio distribution, and confidence sets that may be unbounded.