Papers

Large-scale multipurpose cohort studies and biobanks often omit covariates needed for specific downstream analyses. We study target-population inference for generalized linear regression when key covariates are completely absent from the target data but observed in a related source population. Standard missing covariate methods are not directly applicable because they require at least partial observation of the covariates in the target population. We develop a doubly robust transfer learning framework under a sub-population shift assumption, which allows the distribution of the observed outcome and covariates to differ between populations while requiring the conditional distribution of the missing covariates given the observed variables to be shared. Unlike linear regression, nonlinear target estimating equations require parameter-indexed conditional functionals of the missing covariates rather than a fixed collection of low-order conditional moments. Our estimator combines importance-weighted source estimating equations with imputation of these conditional functionals. Under the identifying assumption, the estimator remains consistent when either the density-ratio model or the conditional-covariate model is correctly specified. Under regularity conditions, it is root-$n$ consistent and asymptotically normal, and attains the semiparametric efficiency bound when both nuisance models are correctly specified.

Comparisons of confounding-control methods are informative only when simulated data contain the treatment-covariate relationship those methods address. We assessed whether Plasmode 0.1.0 preserves that relationship, uses the returned exposure to generate outcomes, and reports the effect implied by its generating model. We inspected the source and ran the generator under identical seeds with source rows as supplied, sorted by observed exposure, or using an alignment correction. We ran 200 null-effect replicates per strategy in a synthetic cohort and the SUPPORT/Right Heart Catheterisation cohort. A sampled subject usually received another subject's exposure probability. In the synthetic cohort, source-model AUC was 0.503 before and 0.841 after alignment. Crude risk-difference bias moved from +0.0051 to +0.3037. Other orders preserved or reversed the association. After alignment, deliberately misspecified estimators retained risk-difference biases of 0.10-0.11. Correctly specified estimators were nearly unbiased. With the unmodified generator, all five appeared similarly unbiased. At an injected odds ratio of 2, the conditional log odds ratio appeared on the observed exposure (+0.696; target 0.693), not the returned exposure (+0.017). Misalignment can weaken, preserve, or reverse designed confounding and thereby distort method comparisons. Alignment correction does not repair outcome-exposure decoupling, disagreement between the reported and generating effects, or marginal miscalibration.

We develop a stochastic nested fixed point (SNFP) estimator for random coefficients logit demand models that updates model parameters using stochastic gradients and performs demand inversion one market at a time. Relative to the conventional nested fixed point (NFP) estimator, SNFP substantially reduces memory requirements and computational cost, making estimation feasible in very large datasets. We establish the large-$T$ (number of markets) asymptotic properties of the estimator under regularity conditions. We also characterize the effect of sharing one block of simulation draws across markets and show how to correct for it. Monte Carlo simulations show that the SNFP estimator achieves statistical accuracy comparable to the NFP estimator, and in our benchmark a single online pass estimates a model with 100 million markets in about 5.5 hours. An empirical application using scanner data further demonstrates the practical advantages of SNFP for large-scale demand estimation.

The temporal dependence inherent in time series models poses a fundamental challenge for distributed Bayesian inference, as it precludes embarrassingly parallel algorithms based on naive independence assumptions in the time domain. We propose a frequency-domain framework for scalable Bayesian inference in stationary time series that exploits the asymptotic independence underlying the Whittle likelihood. To exploit parallel computing resources, we develop a distributed fast Fourier transform and integrate it with embarrassingly parallel Markov chain Monte Carlo (MCMC) algorithms within a modern cluster-computing framework. This enables the analysis of time series that exceed the memory capacity of a single computational node or for which computation time is a bottleneck. The proposed methodology is compatible with a broad class of existing divide-and-conquer algorithms for independent data by applying them to frequency-domain rather than time-domain partitions. We establish that the error of the spectral divide-and-conquer MCMC posterior approximation relative to the exact time-domain posterior converges to zero in probability in a shrinking neighbourhood of the full-data Whittle posterior mode. The corresponding convergence rate is also derived. Across several experiments, we demonstrate that our approach provides accurate approximations to the full-data Whittle posterior. The proposed method is shown to outperform the current state-of-the-art time-domain divide-and-conquer methodology, particularly for highly persistent processes. The methodology is further illustrated by fitting a semi-long range model to a long meteorological time series.

Researchers across academia increasingly base significance claims on LLM judge scores and small-sample AI evaluations. Yet without well-calibrated confidence intervals (CIs), hypothesis tests, and judge-bias corrections, such claims are unreliable. We address these issues in several contributions. First, we find that running statistics over raw LLM judge scores leads to inflated false positives: counterintuitively, for many inter-rater agreement metrics, false positive risk peaks at "almost perfect" human-LLM agreement. To help researchers understand how to run statistics over LLM judges responsibly, we present guidance and tooling for the statistical analysis of mixed human-AI judge designs, and implement nine hypothesis tests via prediction-powered inference (PPI), including the first known PPI corrections for four rank-based tests (Wilcoxon signed-rank, Mann-Whitney U, and omnibus variants). To keep PPI++ stable with small human-labeled calibration sets, we introduce bootstrap-adaptive power tuning, which shrinks the estimated weight toward a target estimated from the labeled data, and accounts for that weight's own sampling variance. Second, through Monte Carlo simulations, we derive recommendations for what CI, p-value, and FWER correction methods to use for small-sample AI evaluations (N<100), and warn researchers against bootstrap CIs. We package these recommendations into evalstats, an open-source Python package that selects calibrated methods automatically, and demonstrate it in three scenarios, including one where a real LLM judge validated at "substantial agreement" would have led a researcher to publish a spurious finding. evalstats is publicly available at https://github.com/ianarawjo/evalstats.

The rare type match problem is a challenging situation faced by a forensic statistician who aims at providing the value of a match between some characteristic of a crime stain and the corresponding characteristic of a suspect's stain when this characteristic has not been observed before. Several methods have been designed in the literature to assess likelihood ratios for the rare type match case when evidence consists of a Y-STR profile found on the crime scene matching the Y-STR profile of a designated suspect. We develop a general Bayesian decision-theoretic framework for quantifying the expected cost of alternative approaches using the logarithmic scoring rule. The framework provides a novel formalization of the posterior cross-entropy, which explicitly enhances the contribution of the method-specific strategy used to extract information from the data. We revisit existing decompositions of posterior cross-entropy and introduce a new complementary decomposition that provides a more interpretable characterization of this contribution. This work compares nine different methods by assessing their performance using empirical validation experiments. Its ultimate goal is to provide forensic experts and triers of fact with methodological insight and a pre-experimental guide to these alternative approaches.

Robust linear fits can resist response contamination yet remain too dense or unstable for useful global explanations. We propose penalized distillation, which fits a smoothly clipped absolute deviation (SCAD) estimator to a robust initial estimator's empirical fitted surface along a safeguarded coordinate-descent path and evaluates candidate states separately for fidelity, parsimony, perturbation stability, and held-out prediction. The new results attach to the states the algorithm actually computes. Conditional on a fixed uncontaminated design, deterministic bounds transfer response-replacement boundedness from the initial fit to every retained path state. Turning to fixed dimension, we characterize the oracle-support branch by its empirical-Gram projection and influence function, give conditions for covariance-weighted least-squares approximation equivalence, and establish a path-conditional generalized information criterion. By contrast, at large dimension-to-sample ratios the full-coordinate robust fit collapses without warning, and screening restores the construction. Under a sure-screening framework, the robustness bound and the support and selection guarantees transfer to the screened fit. Simulations separate robustness transfer from support recovery, efficiency, and computation across the dimension-to-sample ratio, with p up to 240, and the signal density, which isolates what the sparse stage adds once the screen over-selects. In a duplicate-grouped superconductivity study, the distilled estimator remains predictively stable under prespecified training-response shifts but retains 66.8–68.8 of 81 slopes. Stronger sparsification reduces the model to 12.6–14.0 slopes only at visible fidelity and prediction cost. Distillation therefore preserves predictive stability on these data without substantiating a compact coordinate-level explanation.

Randomized perturbations can reveal downstream responses without identifying which causal relationships are direct. Conditioning on intermediate responses may induce associations through unmeasured common causes, even when the source is randomized. We introduce Proxy-Adjusted Balanced Masking (PABM), a nonparametric framework for recovering directed acyclic graphs from targeted interventions, response data, and recorded proxies. PABM uses valid target-specific interventions to identify candidate ancestors. It then compares conditional target distributions with and without a candidate response and, when supported by the design, its intervention variable, adjusting for other ancestors and proxies. Each comparison uses matched observations, adjustment variables, and fitting procedures. Identification requires every included nonparent comparison to have zero conditional gain and each parent to have positive gain in at least one comparison. We establish population identification, finite-sample recovery conditions that accommodate incomplete adjustment and estimation error, and familywise error control under valid held-out p-values. Continuous-response simulations show favorable graph recovery relative to specified comparator pipelines; K562-calibrated count simulations reveal a selection–ranking tradeoff. Proxy ablations assess sensitivity to recorded information. An analysis of K562 Perturb-seq data illustrates descriptive candidate-network construction; proxy adequacy for unmeasured biological variation remains unresolved.

The target trial framework is increasingly used to define the causal estimand for an observational analysis. However, designing time-to-event analyses that align with the causal estimand is challenging in pregnancy because the timescale on which outcomes are often defined, "gestational age", differs from the timescale on which outcomes are measured, "time since study entry". We argue that neither timescale is "best" but that each aligns with a different estimand. In this article, we use the target trial framework to define the causal estimands corresponding to each timescale. We consider a (hypothetical) target trial comparing randomization to 17-alpha hydroxyprogesterone caproate (17-OHPC) versus placebo between 16-20 weeks of gestation to prevent delivery before 37 weeks' gestation, whether by miscarriage, stillbirth, or live birth. We define the estimand of time-to-event analyses on the "time since study entry" timescale as the effect of randomization to 17-OHPC versus placebo between 16-20 weeks of gestation on delivery before 37 weeks'. In contrast, the causal estimand of time-to-event analyses using the "gestational age" timescale corresponds to the effect had, counter to fact, all participants been randomized at one gestational age (e.g., 16 weeks). We review specific challenges to estimation and possible solutions for each timescale.

Mixed Graphical Models (MGMs) provide a flexible framework for structure learning from heterogeneous data by treating sets of both continuous and discrete. Bayesian inference for MGMs remains challenging due to the combinatorial complexity of graph space exploration and posterior computation. In this paper, we model discrete components through latent Gaussian variables and consider two likelihood specifications: a copula-based ranked likelihood, yielding the copula-MGM, and a probit formulation based on cut-off points, yielding the probit-MGM. We then propose the Mixed Graph WWA, a class of MCMC methods for posterior simulation in Bayesian MGMs. Building upon the WWA algorithm, we develop two specialized algorithms: copula-WWA for copula-MGMs and probit-WWA for probit-MGMs. Both methods exploit the latent Gaussian representations to perform posterior inference through a Gibbs sampling scheme that alternates between latent-variable augmentation and graph-structure updates. Through extensive simulation studies we demonstrate that the proposed methods achieve graph recovery accuracy comparable to or better than existing approaches, including copula-BD MCMC and probit-BD MCMC based on the Birth-Death MCMC methodology, while maintaining efficient posterior exploration and favorable effective sample size per unit computational time. We further illustrate the practical utility of our approach through an application to the PAM$50$ breast cancer gene expression dataset, where the inferred MGMs reveal meaningful dependencies between gene expression profiles and cancer subtypes. These results highlight the effectiveness of the Mixed Graph WWA method as a scalable and principled tool for Bayesian structure learning in MGMs.

Early-phase combination oncology trials increasingly seek the optimal biological dose combination (OBDC) rather than a maximum tolerated dose combination, in line with the FDA's Project Optimus initiative. Existing Bayesian OBDC designs span rule-based, model-assisted, and model-based paradigms, but no unified framework exists for choosing among them, and none supports borrowing information across indications sharing a combination regimen. We propose a corrected three-by-two taxonomy of OBDC designs by mechanism and objective, a rule-based design (Ji3+3-Comb) closing a documented gap in transparent, model-free combination dose-finding, and a Bayesian Hierarchical Utility-based Cross-indication (BHUC) design that borrows information across indications via a robust mixture prior while discounting non-exchangeable information. We derive the shared utility function as the Bayes-optimal decision under a linear clinical loss, and prove that BHUC's mixture-prior posterior weight automatically vanishes as two indications' true rates become discordant, formalizing its robustness to non-exchangeable borrowing, and complement this asymptotic guarantee with an exact, sample-size-free ceiling on borrowed influence that holds even before any own-indication data accrue. A roadmap links trial features to design choice, and a 5000-replication simulation study, sensitivity analyses, and a case study built from a published phase Ib trial show that model-assisted designs offer the most robust safety-efficacy trade-off, while BHUC improves correct selection over independent per-indication designs even under discordance. We conclude with concrete, protocol-actionable recommendations for pharmaceutical and trial biostatisticians, and directions for future methodological and computational development.

Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SDR) provides a principled approach to compress these dependencies, traditional SDR frameworks were not formulated for conditional generation. To bridge this gap, we propose Belted Engression, a unified and architecturally parameter-efficient framework for generative distributional regression. Our approach establishes an end-to-end compress-then-generate paradigm driven by sufficient representation learning, embedding a structural bottleneck into the generative architecture. Theoretically, we prove that the standard SDR condition is equivalent to a law-preserving generative factorization, which is achieved at the global optimum of the population Belted Engression objective. Furthermore, by uncovering a localized Bernstein-type control for the energy-score loss, we establish finite-sample convergence rates that are sharper than those of existing results. We also prove that this belted architecture is strictly smaller, operating with an asymptotically vanishing parameter count relative to the unstructured baseline. Extensive simulations and real-world applications demonstrate that Belted Engression achieves superior distributional prediction and SDR recovery with fewer trainable parameters.

Estimating regression models with nonlinear predictor transformations is challenging when data are missing, because nonlinearity typically renders the conditional distribution of the missing values intractable. Previous methods require specific nonlinear forms, such as polynomials or interactions, or rely on approximations that can induce bias. We propose a stochastic EM algorithm that uses sampling-importance resampling (SIR-StEM) to handle missing data under arbitrary nonlinear transformations of predictors, either substantively motivated or incidental, such as spline basis expansions. Unlike approaches that require linearity or closed-form conditionals, SIR-StEM only requires evaluating the complete-data likelihood up to proportionality, making it applicable across a broad class of nonlinear regression models. We construct an algorithm that makes use of missing data pattern information for computational efficiency, and establish asymptotic normality of the estimator. We demonstrate the method in two simulation studies, one with parametric nonlinear transformations and another with a spline basis expansion based on real behavioral measures. Results show that SIR-StEM yields low bias and near-nominal confidence interval coverage, outperforming other common approaches. We conclude with limitations and directions for future research.

Accurate risk prediction is crucial for clinical-decision making, intervention planning, treatment and transplant allocation. However, longitudinal clinical data are often irregular and subject to censoring. We propose PAR2COX, a joint framework that integrates PARAFAC2 decomposition with Cox proportional hazards model, using patient-specific latent factors as covariates in the likelihood. The proposed alternating optimization framework jointly estimates phenotypes and survival parameters, enabling survival-guided representation learning. PAR2COX accommodates both historical patients with observed outcomes and current patients whose outcomes remain unknown. Numerical experiments and a case study based on MIMIC-IV data demonstrate improved risk stratification compared with existing approaches, highlighting the value of survival-informed phenotype learning.

In this paper, we propose a model-free feature screening framework tailored for high-dimensional and heterogeneous datasets, based on a novel distributionally robust dependence measure termed Copula Divergence. The proposed screening method, named CD-Screen, addresses critical limitations of existing feature screening methods, such as restrictive modeling assumptions and sensitivity to heterogeneous feature distributions. CD-Screen ranks features according to their Copula Divergence without relying on a specific regression model or distributional assumptions. Additionally, we introduce CD-FDR, a data-driven procedure to control false discoveries, ensuring accurate and efficient feature selection. Theoretical analyses establish the sure screening and rank consistency properties of CD-Screen, along with asymptotic control of the false discovery rate by CD-FDR. Extensive simulation studies demonstrate the superior performance of our methods compared to traditional screening approaches across diverse scenarios. Furthermore, a real data analysis of the relationship between stock returns and inflation in the United States {illustrates the practical use of our method and provides descriptive evidence on} sector-specific responses to economic changes.

In high-dimensional tabular learning, feature screening provides a lightweight, model-agnostic way to remove irrelevant features before model fitting. However, scoring raw values directly can miss nonlinear or distributional structure. We introduce PACE (Plug-and-Play Contextual Embedding), which inserts a frozen tabular foundation model (TFM) column encoder before an existing feature-scoring rule, expanding each feature into a higher-dimensional contextual representation. Across controlled studies, PACE improves raw-space screening of complex nonlinear dependence with only modest additional encoding cost. These gains translate to downstream prediction on TALENT datasets: PACE-DC improves binary AUC by 0.077 and multiclass macro-AUC by 0.064, with a median normalized RMSE improvement of 0.063 across ten learners. Matched random-weight and random-feature controls show that PACE gains from pretrained structure beyond generic dimensional expansion. PACE further achieves favorable performance–time trade-offs against task-fitted selectors and attribution-based methods, positioning pretrained column geometry as a reusable upstream primitive for tabular learning.

In clinical trials, randomization of treatment and control groups is typically used to ensure the groups have similar covariate distributions on average, resulting in unbiased causal effect estimation. Such balanced covariate distributions are hard to achieve in practice, however, due to recruitment costs, patient dropouts, and more. One possible solution to this problem is to include control patients from external, real world databases. In this paper, we propose DBML, a method that selects control units from a real world database by matching the distribution between the treatment group and the potential control group, instead of matching units between two groups. DBML has three steps. First, we detect anomalous database units (with respect to the treatment distribution) using a variational autoencoder. Second, we re-weight the remaining database units to match the distribution of the treatments. Finally, we use these weights to sample units for our control group. The proposed method is compared to alternative matching-based algorithms and weighted algorithms, achieving superior performance in covariate balance.

Evaluating treatment effects in clinical trials with time-to-event outcomes is complicated by intercurrent events (ICEs), e.g., treatment discontinuation or competing events. While the ICH E9 (R1) addendum outlines five strategies to address these challenges, accessible software implementing these methods is limited. This article introduces the \pkg{tteICE} package for \proglang{R}, which implements five strategies to facilitate valid causal inference in the presence of ICEs. \pkg{tteICE} enables researchers to either nonparametrically or semiparametrically efficiently estimate potential cumulative incidence functions under both treatment and control conditions. The treatment effect is assessed by contrasting these functions, with statistical uncertainty quantified using pointwise confidence intervals and $p$-values. The package supports data from randomized controlled trials and observational studies, including settings with competing risks and semi-competing risks. To reduce barriers for applied researchers, \pkg{tteICE} features integrated plotting functions and an accompanying interactive Shiny application that provides a user-friendly graphical interface with step-by-step instructions.

Conformal prediction intervals are used to construct marginally well-calibrated regions around point predictions. Recent work has focused on extending these ideas to conformal predictive distributions, whose marginal probability integral transform (PIT) follows a Unif[0, 1] distribution. In this work, we investigate how to recover predictive densities from conformal predictive distributions. We extend the theory of conformal predictive distributions by proving asymptotic marginal validity for a tail-corrected version of conformal predictive distributions. We propose a method called quantile matching, which preserves an upper bound on the deviation of the marginal PIT from uniformity. Furthermore, we show that the distribution induced by quantile matching is equivalent to the crisp version of conformal predictive distributions when the number of quantiles equals the size of the calibration set. For the recovery of conformal densities, we construct a fidelity-constrained bandwidth optimization for kernel smoothing that preserves asymptotic marginal validity and has a closed-form solution. We apply and compare our proposed methodology on a large simulated real estate transactions dataset based on the Hierarchical Trend Model.

We study principal component analysis (PCA) under memory constraints, a setting that is increasingly important in large-scale data analysis. Our focus is on Oja's algorithm, which is a one-pass, memory-efficient algorithm requiring only $O(p)$ storage in the rank-one case and $O(pk)$ storage for $k$- PCA. The main goal is to develop a procedure based on Oja's algorithm that is optimal without prior knowledge of the eigengap, which is otherwise needed to tune the learning rates effectively. We do this by first introducing a geometric perspective on the convergence of $k$-PCA: by embedding the Oja iterates into the exterior space, we establish an exact equivalence between $k$-PCA in the ambient space and $1$-PCA in the exterior space. This geometric viewpoint enables us to establish several convergence guarantees, including one based only on a single learning-rate schedule. Building on this geometric perspective, we develop an averaging theory for $k$-PCA and show that the resulting averaged estimator is adaptive: it achieves the nearly optimal convergence rate without prior knowledge of the eigengap. As an application, we construct memory-efficient estimators for elliptical component analysis (ECA) \cite{han2014scale,han2018eca}. Simulation studies and real data analysis are conducted to demonstrate the benefits of our proposed algorithms.

Without interference, cross-fitting enables flexible covariate adjustment while preserving finite-sample unbiasedness under independent unit-level randomization. Under network interference, out-of-sample prediction alone no longer guarantees unbiasedness: assignments entering evaluation-fold Horvitz–Thompson weights may also affect outcomes in the training sample, inducing dependence between fitted predictions and those weights. We develop neighborhood-excluded cross-fitting, which constructs estimand- and design-specific training samples to restore the conditional independence needed for finite-sample unbiasedness without a correctly specified outcome model. We establish asymptotically valid design-based Wald inference for direct and indirect effects under Bernoulli randomization and for the global average treatment effect under Bernoulli cluster randomization. Neighborhood exclusion creates a trade-off in choosing the number of folds: unit-level splitting may require the number of folds to grow with average exclusion-neighborhood size, while cluster-level splitting can substantially relaxes this requirement, permitting a fixed number of folds under partial interference. For linear adjustment under Bernoulli randomization, we derive variance-optimal and confidence-interval-length-optimal procedures, establish explicit rate conditions allowing the covariate dimension to diverge, and show that the variance-optimal procedure is asymptotically no-harm. Simulations illustrate the bias from omitting neighborhood exclusion and the precision gains from adjustment. An application to a social network experiment yields confidence intervals substantially shorter than those from the unadjusted estimator.

Self-calibrating monitors adapt their threshold online to guarantee a prescribed long-run false-alarm rate under arbitrary drift. We compute the price of that guarantee, stating every law with its exact domain of validity. First, the guarantee is an accounting identity, insensitive to what the monitor is meant to detect. Two evidence identities make the cost exact for the online quantile tracker: a persistent step of height $\delta$ yields excess alarm mass within one alarm of $\delta/\eta$, and exactly $\delta/\eta$ pathwise when $\delta$ is a lattice multiple of the gain $\eta$; a ramp of slope $c$ yields a stationary excess rate of exactly $c/\eta$, independent of accumulated size, up to a boundary $c=\eta(1-\alpha)$ coinciding with the alarm-rate cap. Second, the certificate's own fluctuation obeys an exact law: the windowed alarm rate has standard deviation of order $1/L$, not the binomial $1/\sqrt{L}$, since the windowed mass telescopes to a difference of a tight internal state; the closed-form constant is validated with no fitted parameter. Detectors calibrated on the binomial scale are miscalibrated by $\sqrt{\eta\varphi(q_0)L}$, and correct calibration turns detection windows from quadratic to linear in the inverse fault speed. Third, any monitor required to tolerate a drift class $\mathcal{D}$ is blind, at any horizon and for any rule, to every fault in $\mathcal{D}-\mathcal{D}$; the proof is a deliberately elementary two-point argument and the contribution is the object it identifies: for speed-bounded classes the blind set is exactly the doubled-speed class, and the tracker absorbs a speed class fixed by its own gain, so that under a certification regime declaring absorbed drift normal, the monitor manufactures $\mathcal{D}$. An exact Gaussian projection bound, sharper than Pinsker and never vacuous, quantifies power outside it.

Bayesian graph alignment estimates correspondence probabilities, but convergence of an alignment-score trace need not imply accurate correspondence marginals. We audit this gap on 240 new exact graph pairs from four source families, 240 larger pairs with 20-100 vertices, and a separate 60-case exact implementation check. Under an explicit edge-flip likelihood, we compare three samplers and score, marginal, indicator, categorical, and classifier-based diagnostics. Marginal disagreement improves error discrimination over score R-hat for the exact informed sampler, but its improvement for vanilla local sampling is uncertain. Assignment-based R* and short indicator panels are competitive; no diagnostic dominates across samplers and endpoints. At larger sizes, diagnostics predict subsequent marginal changes, not posterior error, and classification performance depends on the drift threshold. Disjoint-window and held-out-chain checks attenuate but preserve positive associations. Only 22 of 240 original reference sets pass an agreement screen. On forty failure-selected cases, eightfold SMC particle escalation does not resolve disagreement, whereas additional rejuvenation helps. Longer informed runs remain unstable. An elementary feasible-alignment bound demonstrates severely unrepresentative SMC and informed-chain scores in concentrated 100-vertex cases, independently of approximate reference consensus. We also exhibit common-start chains with near-zero disagreement despite exact marginal error near .967. These results support assignment-sensitive auditing while identifying limits of finite budgets, diagnostic rankings, and reference agreement as evidence of accuracy.

We provide sufficient conditions for the consistency of penalized least squares procedures that select the order (dimension) of a regression model from a sequence of nested classes, allowing for dependent, martingale-difference errors. The main contribution is to relax the classical identifiability requirement: parameters indexing classes larger than the true order need not be identified, provided the additional, excess directions admit a linear approximation to the truth in a neighbourhood of the true parameter. This relaxation lets the number of candidate models grow with the sample size, removing the usual need for a fixed upper bound. We verify the resulting high-level conditions for two classes of nonlinear regression models used in applied work: multiple-regime smooth transition regression and mixture-of-experts models with generic generalized linear model experts. Under a BIC-type penalty, the resulting order selection rule is consistent in either model class whenever the number of candidate models grows slower than the logarithm of the sample size.

Clinical trials in critical care often evaluate outcomes that are truncated by death, such as time to discharge alive, for which treatment effects are not well defined among patients who would not survive under one or both treatment strategies. Principal stratification provides a natural framework for defining survivor causal effects, but existing approaches often rely on monotonicity assumptions that may be implausible in settings where treatment can affect survival in competing directions. This concern is illustrated by the ARDS Network trial of lower versus higher positive end-expiratory pressure (PEEP), in which higher PEEP may benefit some patients by improving alveolar recruitment while harming others through over-distention or hemodynamic compromise. Moreover, the largely null average findings of the original trial do not rule out the possibility of clinically meaningful subgroups that may benefit from or be harmed by higher PEEP. We propose a monotonicity-free framework for identifying conditional survivor average causal effects (CSACE) using an interpretable sensitivity parameter that characterizes latent principal-stratum membership. We then develop a flexible Bayesian estimation strategy based on BART, a posterior-mean-based variable importance measure, and a distribution-aware conditional inference tree that uses the full posterior draws of individualized CSACEs. In simulation studies, the proposed BART-based approach improves individualized CSACE estimation and variable-importance recovery compared with linear modeling, especially under nonlinear treatment-effect heterogeneity. Applied to the ARDS PEEP trial, our method reveals clinically interpretable heterogeneity among estimated always-survivors, identifying subgroups with posterior evidence of benefit or harm that are obscured by the overall null trial results.

Health and well-being indices are widely used to assess population health outcomes and inform policy decisions. Individual-level assessment of well-being can be used to develop community-level indices that measure wellness for different geographical units. While many existing indices operate at coarse geographic levels such as counties or states, finer spatial resolution can offer more actionable insights. We present a novel Bayesian double generalized beta regression framework to model a bounded individual-level well-being index (WBI) using annual survey data collected from 2021 to 2023 in Massachusetts. Although survey respondents may differ across years, responses are geotagged to ZIP Code Tabulation Areas (ZCTAs), enabling the integration of both spatial and temporal information. Our framework incorporates spatial dependencies via a graph Laplacian matrix that encodes driving time-based ZCTA neighborhood structure, and leverages temporal borrowing by using posterior spatial effect estimates from one year to inform priors in the next. This dual-borrowing strategy within a Bayesian double generalized beta regression framework enhances estimation precision, particularly in areas with sparse data, and improves inference for smaller geographic units. We demonstrate the utility of our method through a realistic simulation study that highlights improved estimation when borrowing spatial and temporal information. In the real data analysis, we model individual-level well-being for residents in Massachusetts and find that income, education status, and marital status are most associated with WBI. Additionally, we observe that ZCTAs in Western Massachusetts, Cape Cod, and those near Boston perform best with the highest spatial effects.

Mechanistic epidemic calibration can be sensitive to short-lived reporting anomalies that give a few observations high leverage under least squares (LSQ). We develop direct forward-solver least absolute deviations (LAD) calibration for time-varying susceptible-exposed-infectious-removed models fitted to reporting-interval incidence, with finite-horizon regularity and large-sample results. A phase-aware Monte Carlo study compares LAD and LSQ across three transmission drivers, four epidemic phases, five reporting mechanisms, and four forecast horizons. All 120,000 primary fits converged. LAD was favored in 56.7% of mean-absolute-error comparisons and 57.9% of weighted-interval-score comparisons overall; under isolated spikes, backlog release, or temporary underreporting, these proportions rose to 73.6% and 72.2%, with strong gains near the epidemic peak. Rolling-origin validation on four synthetic RAPIDD Ebola scenarios also identifies settings where LSQ is preferred, demonstrating the framework's ability to distinguish robustness gains from sustained-trend behavior. Multiple uncertainty and identifiability diagnostics, complete code and data, and an interactive application provide a reproducible computational workflow.

Classical preliminary-test and Stein-type estimators interpolate between restricted and full regression fits, but OLS and chi-squared calibration fail when $p\gg n$ and the restriction is data-adaptive. We propose an honest sample-separated framework built around a common selected-null law. Independent selection data extend a mandatory core; separate estimation data pair a complete-design regularized full-model (FM) fit with a fresh exact-null submodel refit. A maximum residual-association statistic assesses all excluded coordinates. Projected Gaussian draws reproduce its conditional null distribution under homoskedastic Gaussian errors, yielding a finite-sample-valid rank test. The inverse moment of the same design-specific law replaces $q-2$ and calibrates preliminary-test (PT), Stein-type (S), and positive-part Stein-type (PS) rules. We derive exact endpoint-risk formulas, honest conditional validity, null-law concentration, inverse-moment consistency, an explicit selection-failure remainder, and endpoint adaptivity without uniform-dominance claims. Gaussian experiments with 2,000 replications and up to 30,000 predictors compare Ridge and LASSO FMs, tuned by frozen-fold cross-validation, under a common submodel, test, and calibration. PS provides large near-null coefficient-risk gains and approaches the relevant full-model risk under strong departures. A separate CPSS-LASSO/CPSS-MCP audit evaluates data-adaptive selection, while a split-sample DepMap study with 19,152 predictors illustrates prediction gains and sensitivity to error assumptions. The HDMaxShrink R package implements the procedure.

Many applications provide each observation with a meaningful representation in addition to an ordinary response and covariates. When that representation is hierarchical, hub-periphery structured, or network derived, Euclidean or geographic proximity may define the wrong peer groups. We present Lorentz hyperbolic weighted regression (LHWR) as a practical local regression method for this setting. Responses and predictors remain real valued; only locality is defined by distances between observations represented on the Lorentz model of hyperbolic space. We describe coordinate construction, adaptive bandwidth selection, prediction, local coefficient summaries, collinearity checks, and residual autocorrelation diagnostics. Theoretical results explain consistency, bias-variance tradeoffs, curvature effects, and the extra uncertainty caused by estimated representations. Simulations show that the Lorentz geometry is most useful for sharply localized coefficient surfaces, whereas tangent-plane approximations can be competitive for smooth surfaces. In a 141-country World Development Indicators illustration, economic similarity based on income and trade openness defines local peer groups. Representation-based locality predicts GDP growth better than global least squares and geographically weighted regression, although differences among Lorentz, Poincare, and tangent metrics are modest. The main practical lesson is that the representation should be chosen scientifically and the distance geometry should be checked rather than assumed.

In randomized clinical trials with longitudinal continuous outcomes, missing-not-at-random (MNAR) missingness often motivates conservative alternatives to mixed models for repeated measures (MMRM). Such caution is important for estimation, but estimation and testing need not require identical assumptions. Moreover, overly conservative primary analyses may reduce power, increase required sample size, and raise trial costs. We investigated the validity of MMRM-based testing under the global null of identical longitudinal outcome distributions across groups. Because valid testing minimally requires treatment-effect estimators to converge to the null under the null hypothesis, we investigated sufficient conditions for this property. We introduced a proportional observation condition requiring ratios of observation probabilities relative to a reference group, conditional on the full outcome vector, to be outcome-independent, and showed that, with arbitrary post-baseline visits and monotone missingness, this condition is sufficient for convergence to the null value. The condition allows observation to depend on unobserved outcomes and permits between-group differences in overall observation probabilities through outcome-independent dropout, making it clinically interpretable while accommodating outcome-dependent MNAR missingness. Synthetic and data-based bootstrap simulations showed negligible bias and empirical test sizes near 0.05, including nonmonotone missingness. Thus, MNAR missingness does not by itself imply that a more conservative primary testing procedure is required. This result does not justify treatment-effect estimation under alternatives, which still requires estimand-based interpretation and sensitivity analyses.