Papers

Deployed decisions are often optimized once and retained because updates impose operational, regulatory, or switching costs. As operating conditions change, when should such decisions be re-optimized? We study this question for stochastic optimization when the objective's functional form is known but the decision maker's trade-offs are encoded by an unknown preference parameter. Standard distribution-shift tests are poorly aligned with this goal: they can flag detectable yet decision-irrelevant changes without determining whether the incumbent decision has become materially suboptimal. We propose RADAR (Regret-based Assessment of Decision Adequacy and Risk), a decision-focused framework that uses inverse optimization to infer latent preferences and tests the deployed decision's optimality gap under the current distribution. By targeting regret, RADAR ignores decision-irrelevant shifts while detecting changes that warrant re-optimization. We develop two-sample and sequential changepoint procedures and establish asymptotic guarantees for Type-I error and power. Across synthetic optimization problems, a semi-synthetic capacity allocation task, and police-zone planning, RADAR more reliably distinguishes harmful from harmless shifts than decision-agnostic alternatives.

Whether the risk of death keeps climbing at extreme ages or levels off has divided researchers for a century. We show this conflict reflects a moving target. Using cohort data from twelve low-mortality populations, we find that mortality deceleration and plateau onset shift steadily later across cohorts born from the mid-19th to the early-20th century. The data support a plateau across the full cohort range, though evidence weakens for the youngest, incompletely observed cohorts. In these younger cohorts, deceleration begins near age 100, and the fitted plateau begins beyond age 108. Because past studies focused on different cohorts and fixed age ranges, they sampled different phases of the exact same shift. The mortality plateau has no fixed age: it has been rescheduled.

Physics-informed neural networks (PINNs) often face ill-conditioned objectives that limit high-accuracy training. Dense quasi-Newton methods improve local conditioning but require expensive optimizer state, while Kronecker-factored methods such as SOAP scale to larger networks but rely on periodic basis updates. We introduce \method, which augments SOAP-style preconditioning with a scalar secant-energy correction adapted to Kronecker geometry and an adaptive basis update followed by variance-state downscaling. We characterize the directional secant matching induced by the scalar correction and give a bound on variance-state mismatch across basis changes. Across eight PDE benchmarks, \method attains the lowest final residual on six, including Burgers and Boussinesq, while SOAP-family baselines perform better on Gray-Scott and Ginzburg-Landau. On Boussinesq, \method reaches a residual of $10^{-5}$ in 4.1 hours with 9.2 GB peak VRAM, while Adam does not reach this target within 14 hours. Three-seed $L^2$ and $H^1$ errors on four representative PDEs support the link between lower residuals and improved solution accuracy. These results position \method as a scalable option for stiff, high-accuracy physics-informed training, rather than a uniform replacement for existing optimizers.

Industrial recommenders give new content initial views through budgeted exploration, then use early performance to decide further delivery. On many short-video platforms, exploration is the primary way new videos reach viewers. Viewer-side tests measure consumption; the published budget objectives we review omit creator response. We analyze four experiments on a major short-video platform. An eight-month creator ablation finds production exploration raises videos posted per creator by 8.55% and creators posting at least once by 7.10% relative to a minimal floor. A budget-matched reallocation raises creator participation with no detectable short-run viewer-side change. A year-long viewer ablation finds 1.74% more video views but 2.13% less view time. A delivered view creates immediate feed value, can trigger organic take-up, and can induce creator supply. Take-up and supply replenish a shared corpus, creating two measurement limits. Viewer-side A/B tests cancel the corpus effect when both arms consume the same corpus. Giving each arm its own corpus avoids cancellation, but turnover still controls the horizon. If the corpus turns over at rate w per posting cycle, a t-cycle experiment expresses at most wt of the eventual corpus effect. More users reduce noise but do not speed turnover. Before the corpus path visibly bends, data cannot distinguish a modest fast effect from an arbitrarily large slow one, so a valid confidence interval may lack a finite upper endpoint. As predicted, the three-week co-diverted experiment cannot determine the sign of the eventual corpus effect. Within the window, it identifies the direct feed effect, and an exploratory cohort analysis detects organic lift after exploration ends. The experiments establish a positive creator response, measure the gross corpus flow visible within three weeks, and show the design and duration needed to identify total value.

A new approach to robust estimation in generalized linear models is introduced. The idea of the method is to first transform the responses applying the composition of the normal quantile function and the probability integral transformation. Then, using that the transformed responses should follow a standard normal distribution, find the values of the parameters that minimize a robust measure of their size. In practice an approximation of this transformation is used. The proposed estimators are studied theoretically for distributions that depend on a single parameter and through simulations and examples for the particular cases of Poisson and logistic regression.

Kernel density estimation (KDE) is one of the most fundamental statistical estimators of density functions. Its direct implementation on a dataset of $N$ points incurs an $\mathcal{O}(N^{2})$ computational cost, which is prohibitive for large-scale datasets. Kernel approximation techniques can be applied to bring the computational cost down to $\mathcal{O}(N)$. The random Fourier features (RFF) technique, based on sampling from the spectral density of the kernel function, has become popular to speed up kernel estimators for machine learning applications. Unfortunately, it is restricted to positive definite kernels, while the majority of kernel functions popular in KDE, such as the parabolic kernel, do not satisfy this property. To overcome this limitation, this article introduces the signed random Fourier features (SRFF) technique. It is a generalization of RFF compatible with indefinite kernels whose inverse Fourier transform is absolutely integrable. The motivation for introducing this method is to speed up KDE in the case of multivariate compact kernels, which are generally not positive definite. We detail how to implement SRFF for both product kernels and isotropic kernels. For the class of Kuttner-Golubov kernels $K(\boldsymbol{x}_{i},\boldsymbol{x}_{j})=(1-\left\Vert \boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right\Vert ^{\alpha})^{\beta}\mathbf{1}_{\{\left\Vert \boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right\Vert \leq1\}}$ where $\boldsymbol{x}_{i}\in\mathbb{R}^{d}$, $\boldsymbol{x}_{j}\in\mathbb{R}^{d}$, $\alpha>0$, $\beta>0$, which includes the triangular, parabolic, biweight, triweight, and other kernel functions of interest for KDE as particular examples, we provide an explicit acceptance-rejection algorithm to sample from its signed spectral density. Our numerical tests on a dataset of one million points confirm the computational efficiency and accuracy of SRFF for large-scale KDE.

Varmapack is a software package for efficient, exact simulation of VARMA time series without a burn-in period. For stationary models, Varmapack can generate initial states and innovations from their joint stationary distribution. Alternatively, the user can supply initial states, in which case innovations are generated from their conditional distribution. The core C library has interfaces to R, Python, and Matlab. It also offers VARMAX simulation and computation of autocovariances and correlations, spectral radii, and impulse responses. Varmapack automatically selects between vector-Yule-Walker and state-space methods for covariance computation and uses level-3 BLAS operations for efficient generation of multiple replicates. Benchmarks on several platforms show substantial performance gains over existing simulation software, ranging from several-fold to more than three orders of magnitude for the packages and models considered. Varmapack is open source and publicly available through GitHub.

The Bayes factor (BF) is a central tool in Bayesian hypothesis testing and model selection, yet its practical use is often challenged. Classical BFs depend heavily on prior specification, cannot be applied with improper priors, and are typically interpreted through arbitrary evidence scales. Moreover, they fail to capture uncertainty inherent in the data, leading to an analogy with frequentist p-values, and primarily reflect prior-predictive rather than posterior-predictive performance. We introduce the stochastic Bayes factor (SBF), a new framework that extends the BF by explicitly incorporating uncertainty via replicated data. Formally, the SBF is defined as a push-forward measure transferring the BF from the observed data space to that of replications. This approach generalizes previous calibration proposals, while emphasizing posterior-predictive replication as a robust alternative. We establish key theoretical properties, including model consistency, compatibility and dominance, ensuring that SBFs preserve desirable Bayesian guarantees. An algorithmic routine is then proposed to operationalize the SBF, guiding model discrimination in a principled way while naturally providing model calibration. Simulation studies and real applications confirm that the SBF offers improved robustness and predictive reliability compared to the classical BF, by providing a valuable tool for model comparison.

We study the empirical Sinkhorn estimator of the entropic optimal transport potentials under the uniform loss. Since the potentials are only unique up to additive constants, we measure the error using the quotient supremum norm, defined as $d_\infty([u],[v]) = \inf_{a\in\mathbb{R}}\|u-v-a\|_\infty$. For a fixed regularization parameter $\varepsilon>0$, we establish a non-asymptotic statistical rate of $n^{-1/2}$. This is achieved by combining the Birkhoff-Hopf contraction theorem with entropy bounds on normalized kernel sections. However, the constant in this bound grows exponentially with $1/\epsilon$. To improve this, we isolate geometric conditions under which the empirical estimator maintains the $n^{-1/2}$ rate but features polynomial dependence on $1/\varepsilon$. The key requirement is a polynomial residual-stability estimate for the population Sinkhorn map. We provide sufficient criteria for this, including a polynomial contraction property and a local inverse estimate. Furthermore, we introduce two rigorously verifiable model classes an $\varepsilon$-weak residual-interaction class obtained after separable centering and another based on connected tight-edge graphs for fixed discrete costs where the polynomial rate is guaranteed without relying on abstract resolvent assumptions. Finally, we establish matching minimax lower bounds demonstrating that the $\varepsilon n^{-1/2}$ rate cannot be uniformly improved in the bounded-interaction regime.

While modern generative models excel at modeling complex data, precise inference-time control in conditional generation remains a critical challenge. Classifier-free guidance (CFG) is a primary mechanism for such control, yet it is typically treated as a static tuning parameter. In flow-based models, however, the guidance scale fundamentally dictates the velocity field and the resulting probability path, making guidance selection a dynamic path-optimization problem. We introduce PathGuide, a framework that reformulates scalar CFG selection as an on-policy transport problem. Leveraging the weak form of the continuity equation, we derive a selection criterion with a direct path-correctness interpretation: we prove that if the guided field is weakly equivalent to the exact conditional field along the generated rollout, the sampler's path coincides with the target conditional law. For scalar CFG, this criterion yields a strictly quadratic local objective with an efficient, closed-form selector for each solver interval. PathGuide enables optimal guidance scales to be computed and used online during generation or fitted offline as a reusable piecewise-constant schedule. We validate our method on low-resolution image manifolds and controlled settings across various continuous-time flow constructions, demonstrating that this transport-based selector improves path alignment and sample fidelity over both fixed and state-of-the-art adaptive guidance baselines.

We consider the problem of feature selection in linear models with finite-sample control of the false discovery rate (FDR). While existing knockoff-based methods control the directional FDR, which penalises incorrect sign estimates, they do not target discoveries in a pre-specified direction, and their knockoff constructions are entirely response-agnostic. We introduce the response-guided knockoff filter, which leverages a noise-perturbed version of the response to guide knockoff construction toward features likely to have the target sign, while provably controlling the directional FDR. The method operates under a weaker sample-size requirement $n > p + 2$, compared to $n \geq 2p$ required by existing fixed-X generators. Simulations and HIV drug resistance experiments demonstrate power gains over existing methods.

We determine the sharp restricted isometry threshold for recovery at global minima of the rank-restricted matrix LASSO. For target rank $r_{\star}$, if the rank-$k$ RIP constant satisfies $\delta<\delta_{\mathrm{sharp}}(k/r_{\star})$, where $\delta_{\mathrm{sharp}}(t)=t/(4-t)$ for $0<t<4/3$ and $\delta_{\mathrm{sharp}}(t)=\sqrt{(t-1)/t}$ for $t\ge4/3$, then every global minimizer has Frobenius error $\lesssim\sqrt{r_{\star}}\lambda$ for all $\lambda\gtrsim\|\mathcal{A}^{*}(\xi)\|_{\mathrm{op}}$ and at every search rank $r\ge r_{\star}$. The constants depend only on the RIP constant and $t=k/r_{\star}$, and in particular are independent of the search rank. When the rank restriction is inactive, the result specializes to the ordinary convex matrix LASSO. We also obtain the analogous results for sparsity-restricted vector LASSO. Conversely, we show that the threshold $\delta<\delta_{\mathrm{sharp}}(k/r_{\star})$ cannot be improved, due to the existence of counterexamples whose global minimizers fail to recover the ground truth.

Causal representation learning (CRL) aims to recover latent causal variables and their structural relations from high-dimensional observations. Existing CRL methods typically assume that all environments are defined over the same latent variables, or at least share a common latent representation space. We study a fragmented multi-client setting, where multiple clients interact with the same global latent causal system but each client only accesses and intervenes on a subset of the latent variables. In this regime, marginalizing unused latent variables induces bidirected edges, so a single client no longer admits a node-wise latent causal graph, and the global latent causal order must be recovered by assembling client-specific structural fragments. We propose Jigsaw-CRL, a framework for recovering global latent causal order from such fragmented interventions. Under soft interventions, differences between precision matrices across environments exhibit a low-rank structure governed by latent ancestor relations. This enables recovery, for each client, of a block partition, the corresponding block-level ancestral order, and latent subspaces, and then assembly of these fragments into the global node-level latent causal order. We establish identifiability guarantees, develop practical algorithms, and validate the framework on synthetic data. Our codes are available on https://anonymous.4open.science/r/code-for-Jigsaw-CRL-7B26

Mean-tilted intervals (MTIs) provide a fixed-content family of interval targets indexed by retained-mean balance. This paper develops generalized-Bayes computation for using those targets in regression and time-varying endpoint models after content and tilt have been specified. The update combines a prior with an exponentiated residual-product check loss, yielding uncertainty summaries for endpoint functions rather than a response-distribution model. A pseudo-asymmetric-Laplace normal-exponential representation gives generalized-inverse-Gaussian latent-scale updates and Gaussian conditional updates for one root when the other is fixed. The same representation gives deterministic ECM equations for generalized-posterior modes. We present ridge endpoint regression, a conditionally Gaussian shrinkage construction for the zero-tilt case, deterministic fixed-feature readouts, and dynamic linear endpoint states updated by alternating forward-filtering backward-sampling steps. These methods extend the MTI target from iid intervals to regression and dynamic settings; tolerance certification and response prediction require separate calibration or response models.

An analyst should not assume that a design score improves a meta-analysis simply because it is labeled as robustness. This paper treats declining heterogeneity along a prespecified, outcome-separated design score as a falsifiable directional hypothesis. In an 18-study illustration, the constrained model lands at $\gamma = 0$ and becomes numerically identical to conventional random effects, while the unrestricted scale fit points in the opposite direction. Simulations that deliberately violate the restriction show the same graceful fallback under wrong-direction and U-shaped heterogeneity; a stepwise decreasing variance function retains an efficiency gain despite functional-form misspecification. DR-Meta formalizes the hypothesis as $\tau^2(\mathrm{DR}) = \tau_0^2 \exp(-\gamma \mathrm{DR})$, $\gamma \geq 0$, within an established location-scale framework. Exact nesting, conditional weight monotonicity, a fixed-effect upper bound, pseudo-true targets under mean misspecification, and score-rescaling behavior are derived with full proofs. Efficiency gains are negligible around an empirically anchored $\gamma$ near 1 and become material only under stronger gradients; the largest RMSE reduction, about 9.6 percent, occurs in a deliberately extreme condition. Plug-in intervals under-cover relative to random effects, and modified Knapp-Hartung adjustment improves coverage only modestly. Widening the $\gamma$ optimization bound changes $\gamma$ estimates much more than pooled-estimate RMSE. The practical contribution is therefore diagnostic rather than automatic efficiency: a nested directional restriction can be supported, contradicted, or collapse transparently to random effects, provided constrained, unrestricted, location, and sensitivity analyses are reported together.

We study a class of product-reference diffusion algorithms for sampling from a discrete distribution. We show that their sampling performance can be characterized using a path-based measure of data geometry that we call the interaction growth complexity (IGC). We show that a bivariate IGC kernel gives an exact representation of both the KL discretization error and a simple one-step upper bound. The simpler univariate IGC density can be used to study the effect of stepsize choices on the iteration complexity required to obtain $\epsilon$-accurate samples in KL divergence. Samplers that traverse the path with equi-spaced steps in log-squared-reliability-odds have performance that depends on the aggregate IGC mass, whereas refined choices of stepsizes have a lower complexity depending on a square-root functional. In the fine-grid limit, both of these characterizations become sharp. We also allow general product reference distributions and show that the reference law can substantially reshape the IGC profile and the resulting sampling complexity; in particular, references far from both the uniform and the data marginals can yield dimension-dependent improvements. Finally, the aggregate IGC mass admits bounds in terms of total correlation and dual total correlation, thereby connecting the pathwise geometry to classical measures of multivariate dependence.

Cluster randomized trials (CRTs) can exhibit informative cluster sizes (ICS) where cluster size is associated with outcomes and/or treatment effects. Under ICS, the individual and cluster-average treatment effects (iATE, cATE) can diverge, and the conventional linear mixed-effects model (LMM) and generalized estimating equation (GEE) with an exchangeable working correlation can produce data-dependent weighted contrasts that are not consistent for either estimand. In these settings with ICS, we propose easy to implement "cluster-size saturated models with g-computation" (CS-g), which employ a simple two-step adjustment to standard practice: (1.) augment the appropriately weighted working LMM or GEE with a saturated continuous cluster-size main effect and treatment x cluster-size interaction, and (2.) apply g-computation to target an interpretable marginal estimand. We prove that the appropriately weighted cluster-size saturated LMM with g-computation and more general cluster-size saturated GEE with g-computation can consistently target the iATE and cATE, among a broad class of interpretable estimands, while allowing for ICS. Crucially, this consistency holds under arbitrary misspecification of other model components, including the functional form of the saturated cluster-size terms. Furthermore, we demonstrate exact finite-sample equivalence between these consistent CS-g estimators and their model-robust standardization counterparts. Across simulations with continuous and binary outcomes, the proposed CS-g estimators were unbiased, more efficient than other consistent estimators, and returned greater power to detect ICS. A re-analysis of the PPACT P-CRT further illustrates the approach. Altogether, CS-g offers a simple, robust, and efficient route to target interpretable marginal effects in P-CRTs with ICS.

Modeling multivariate extremes using a geometric perspective leverages the shape of the multivariate point cloud to make inference on joint tail probabilities. While the original statistical framework for geometric extremes was fully parametric, relying on a gauge function that uniquely defines the shape for a given density, newer methods have introduced semi- and non-parametric alternatives to increase flexibility. We propose a modeling approach that retains the simplicity of the parametric framework but adds flexibility by using Bayesian model averaging (BMA) to improve prediction of tail risk probabilities. In contrast to previous works that use a truncated radial likelihood, we propose using a censored likelihood, which we find has consistently better performance in terms of predictive mean squared error, particularly in small-sample settings, although at the expense of increased bias. To generate predictions, we use a simple importance sampling scheme that seems to match the accuracy of more bespoke methods. Finally, we apply our approach to two fire weather indices, which are designed to capture somewhat orthogonal aspects of fire risk, to illustrate our method's practical utility in environmental applications.

Prognostic factor evaluation and prediction model development are central to precision oncology, enabling patient risk stratification and individualized treatment selection. Unified predictions that synthesize information from existing models are valuable for comprehensive and consistent risk assessment. Many studies also seek to evaluate the incremental value of new biomarkers beyond established prognostic factors. However, such efforts are often constrained by small-to-moderate sample sizes. Motivated by these challenges, we consider Cox regression analysis in settings where individualized risk predictions from existing models are externally available without a transparent or interpretable structure, for example, through online calculators. We develop a Bayesian discretized survival time inference framework in which individualized predictions from potentially multiple external sources are integrated through a formulation based on Kullback-Leibler divergence, yielding informative priors. The divergence-based formulation serves as a surrogate for the external information likelihood, enabling principled incorporation of individualized predictions without requiring knowledge of the underlying external prediction models. Theoretical results show that the resulting posterior mean estimators are asymptotically more efficient than their internal-only maximum likelihood counterparts. However, using the divergence-based surrogate in place of the unavailable external likelihood renders posterior variance-based inference conservative. We propose a correction to address this overcoverage. We demonstrate the performance of the proposed approach through simulations and an application to prostate cancer trial data.

Curve fitting for physical, biological, and engineering data typically forces a choice between interpretable but rigid parametric forms and flexible but physically opaque smoothers. This paper introduces the Growth-Decay Curve (GDC), a physics-informed basis derived as the product of a lognormal growth cumulative distribution function and an exponential decay term, each traceable to a governing differential equation. GDC's parameters correspond directly to growth and decay timescales, yielding dimensionless ratios and shape descriptors that connect the fit back to the underlying dynamics. Across simulated differential-equation solutions and applications spanning physical, biological, and economic data, GDC matches the fit quality of splines, generalized additive models, radial basis function networks, and Fourier regression, while remaining substantially more parsimonious and physically interpretable.

We study dependent censoring within a generalized Cox first-hitting-time. framework based on compensator reductions. In the genuinely dependent case, we show that max-stability of the associated survival copula is equivalent to a common operational clock, leading to a nonparametric Marshall Olkin family. We establish sharp identification results under complete and binary observation schemes. Under binary observations, the common clock and event loading are point identified, whereas the censoring loading and the associated latent survival and dependence structures are only partially identified. We develop nonparametric estimation and inference for the identifiable components, derive an efficient restricted estimator, and propose an observable test of max-stable compatibility. Simulations and a real-data application illustrate the practical implications of the identification and efficiency results.

Under a model-assisted framework, a penalized logistic generalized regression estimator is developed to estimate a finite population proportion from complex survey data and auxiliary data. The proposed estimator controls the impact of unnecessary auxiliary variables through a lasso or ridge penalty. A central limit theorem is derived for the penalized regression coefficients and for the penalized logistic generalized regression estimator. Through simulations, it is shown that including the penalty increases the efficiency of the estimator when the true model is sparse. An example using United States Forest Service data demonstrates the applicability of the estimator for surveys with many available auxiliary variables.

Incomplete adjudication and endpoint misclassification arise when gold-standard event classification is available only for an internal validation sample. With accurate follow-up times and covariates but error-prone event indicators, naive Cox regression can be biased and inverseprobability weighting inefficient. We develop orthogonal validation-augmented Cox (OVAC) regression, a cross-fitted augmented Cox estimator for incomplete failure indicators. OVAC replaces the missing event indicator with a cross-fitted augmented pseudo-event and explicitly retains the first-order contribution from estimating the Cox risk-set mean. The same term emerges from projection of the full-data influence function through the validation mechanism, linking the score expansion to the observed-data efficient influence function. The score exhibits exact product-form nuisance drift, yielding double-robust identification, Neyman orthogonality, and root-n inference under product-rate conditions. In 1,000 R replications, full-variance SE/SD ratios were 0.997 and 0.992, with 95% coverage of 0.955 and 0.948. A 200-replication diagnostic showed that the risk-set term alone was 77.8% and 81.1% of the full-SE magnitude, although covariance cancellation made its net SE effect smaller than 0.3%. In a 250-replication method comparison, OVAC reduced empirical variance by 38.8% and 37.7% relative to IPW. OVAC provides machine-learning-compatible Cox estimation with explicit risk-set linearization, calibrated inference, and validation-design guidance.

Representation learning begins when training changes the features that define similarity between data. A frozen-kernel model only reweights a fixed geometry. We establish quantum signal processing (QSP) as a solvable quantum model of the representation-learning regime. At arbitrary depth, we compute the exact mean and variance of its quantum neural tangent kernel, revealing an input-dependent angular geometry whose diagonal remains non-self-averaging even when the underlying unitary approaches Haar randomness. We also prove a sparse-data guarantee for the full nonlinear gradient flow without freezing or ensemble-averaging the kernel: the realized dynamics converges to an integrable scalar flow with a time-dependent kernel closure and explicit convergence times. A finite-depth speed limit holds for every data set and trajectory. At higher data density, numerical results show coupled evolution beyond both the scalar and frozen-kernel descriptions. These results give a controlled theory of learned quantum data geometry with provable training dynamics beyond the frozen limit.

We establish quantitative convergence to the target and uniform-in-time propagation of chaos for Langevin-regularized Stein variational gradient descent. The Stein interaction need not be small relative to the confining Langevin drift and does not generally yield a contractive particle coupling. At the mean-field level, the Stein and Langevin components dissipate the same relative entropy in the kernel-induced Stein and $2$-Wasserstein geometries, producing the squared kernel Stein discrepancy and relative Fisher information. Under a log-Sobolev inequality for the target, this yields exponential last-iterate convergence. We also derive a finite-particle entropy identity relative to the product target, giving exponential-in-time convergence of the empirical measure up to polynomial sampling errors. For propagation of chaos, we develop two complementary finite-time approaches. A synchronous coupling, combined with exponential moment estimates for the nonlinear mean-field diffusion, yields explicit single-exponential bounds in Wasserstein distance and kernel Stein discrepancy (KSD). Moving-product entropy gives joint-law relative entropy control relative to the evolving mean-field product law and, through entropy superadditivity and concentration, fixed-marginal relative entropy and total variation bounds and empirical KSD estimates. Under an additional $T_2$ inequality for the initial law, it also yields Wasserstein bounds. Combining these finite-time estimates with target convergence at a logarithmic cutoff time gives polynomial uniform-in-time propagation of chaos rates in expectation for empirical KSD and $W_2^2$, and for fixed-marginal total variation and $W_2^2$. All bounds control the last iterate in physical time. We also compare the two finite-time mechanisms and identify regimes in which each gives the sharper polynomial exponent.

Fifty-seven years of debate have not led to a consensus on Newcomb's problem. I argue that this failure comes from not viewing the problem in concrete terms, for which common-sense intuitions are clearly applicable. If near-perfect predictions are not required - only predictions good enough that Evidential Decision Theory (EDT) recommends taking only one box - Newcomb scenarios without any fantastic elements are actually feasible. I give a detailed account of such concrete scenarios, in which the decision-maker has varying amounts of information about the prediction process. I argue that in these scenarios it is rational to take both boxes, as Causal Decision Theory (CDT) recommends. To make this more convincing, I introduce a simpler impersonal Newcomb problem, also with a concrete realization, to help bridge causal intuitions from everyday decisions to the standard Newcomb scenario. I also argue that Newcomb's problem with nearly perfect predictions can only be realized by a (currently fantastic) process in which the Predictor accurately simulates the thoughts of a Participant. In a functionalist view of consciousness, this simulation will be a conscious entity, whose experience will not be distinguishable from that of a “real” person. In this scenario, CDT recommends taking one box. I conclude that when Newcomb's problem is properly analysed in concrete terms, CDT gives the correct answer in all scenarios.

Borrowing external control data can improve the efficiency of clinical trials, particularly when patient accrual is difficult. A persistent challenge is how to prespecify the degree of borrowing systematically and transparently. In practice, prior weights are often selected heuristically or calibrated through simulation to achieve desired operating characteristics, making them difficult to justify scientifically. Moreover, patient-level covariate data from external sources are rarely available when the new trial is designed, precluding patient-level adjustment methods. We propose CARB (Covariate-Assessed Robust Borrowing), a framework that formalizes prior-weight specification as a design-stage assessment of baseline compatibility. Using only aggregate information, CARB quantifies discrepancies in prespecified baseline covariates between the new trial and each external source, without using outcome data from the new trial. A prespecified mapping translates the resulting dissimilarity measure into a source-specific prior weight on the exchangeable component of a robust borrowing model. Simulation studies show that CARB reduces bias and type I error inflation relative to fixed borrowing under observed and unobserved incompatibility, while improving efficiency when external controls are compatible. An application to advanced melanoma trials illustrates covariate-informed borrowing from multiple historical sources. An apparent discrepancy in reported baseline characteristics serves as a warning signal that reduces borrowing. CARB provides a transparent and reproducible way to borrow cautiously when patient-level covariate data from external sources are unavailable.

Many observational studies evaluate the risks and benefits of time-varying interventions. In these longitudinal settings, the primary outcome of interest is often a clinical event that is precluded by mortality, which acts as a competing risk. Evaluating dynamic treatment regimes (DTRs) is complicated by time-varying confounding, right-censoring, and progressive sample size reduction over time, for which traditional methods such as the g-formula or inverse probability weighting may be misspecified or highly unstable. In this work, we develop the nonparametric efficiency theory and derive the efficient influence function for the cumulative incidence of an event under a DTR in the presence of a competing risk and right-censoring. Building on this result, we propose a sequentially doubly robust estimator that accommodates flexible machine learning for nuisance estimation while retaining root-n consistency and asymptotic normality. We illustrate the utility of our framework by estimating long-term cumulative incidence of clinical fractures under different bisphosphonate "drug holiday" regimes for osteoporosis.

Flow cytometry generates inherently compositional count data: observed cell population counts are constrained to sum to the total number of acquired events, which precludes direct inference about absolute cellular abundance. Despite this constraint, most differential abundance (DA) analyses in cytometry rely on methods originally developed for RNA sequencing, such as edgeR with trimmed mean of M-values (TMM) normalization, without fully acknowledging the conditional nature of the resulting estimates. Here, we offer a critical perspective on the statistical implications of compositionality for flow cytometry DA analysis. We compare the theoretical foundations and interpretational scope of three per-population DA testing methods (edgeR/TMM), centered log-ratio transformation with linear modeling (CLR + limma), and analysis of composition of microbiomes with bias correction-2 (ANCOM-BC2), and evaluate their performance through a comprehensive simulation study spanning seven scenarios at two sample sizes (n = 50 and n = 200 per group). We additionally evaluate compositional data analysis using kernels (CODAK) as a global, omnibus screening test for overall compositional differences, implemented via PERMANOVA on Aitchison distances. Our results show that, considering sample size, zero-inflation, dispersion, and correlation among cell populations in addition to false discovery rate (FDR) and sensitivity, the methods developed for microbiome data analysis, ANCOM-BC2 and CLR + limma, emerge as better-suited methods for per-population DA analysis of flow cytometry data than edgeR/TMM, while CODAK/PERMANOVA offers a robust first-stage screen for overall compositional shifts.

Synthetic data can improve statistical inference when real data are scarce, but naively treating synthetic samples as real data can introduce bias and lead to unreliable inference. We develop a general framework for synthetic-augmented inference across a population of related tasks. It characterizes synthetic augmentation by the number of synthetic observations and their weight. Central to our framework is a size-weight frontier that specifies, for each weight, the largest synthetic sample size for which all smaller sizes attain the target task-marginal coverage. We estimate this frontier from historical tasks, and establish a finite-sample coverage guarantee simultaneously for all size-weight configurations on or below the estimated frontier. In experiments using large language model responses to augment opinion survey data, our procedure achieves target coverage and substantially narrows confidence intervals.