Papers

Policy gradient computes a backward pass for every sample, even though the backward pass is expensive and most samples carry little learning value. The Delightful Policy Gradient (DG) provides a forward-pass signal of learning value: delight, the product of advantage and surprisal (negative log-probability). We introduce the Kondo gate, which compares delight against a compute price and pays for a backward pass only when the sample is worth it, thereby tracing a quality–cost Pareto frontier. In bandits, zero-price gating preserves useful gradient signal while removing perpendicular noise, and delight is a more reliable screening signal than additive combinations of value and surprise. On MNIST and transformer token reversal, the Kondo gate skips most backward passes while retaining nearly all of DG's learning quality, with gains that grow as problems get harder and backward passes become more expensive. Because the gate tolerates approximate delight, a cheap forward pass can screen samples before expensive backpropagation, suggesting a speculative-decoding-for-training paradigm.

Distributed reinforcement learning trains on data from stale, buggy, or mismatched actors, producing actions with high surprisal (negative log-probability) under the learner's policy. The core difficulty is not surprising data per se, but negative learning from surprising data. High-surprisal failures can dominate finite-batch updates through large perpendicular components, while high-surprisal successes reveal opportunities the current policy would otherwise miss. The Delightful Policy Gradient (DG) separates these cases by gating each update with delight, the product of advantage and surprisal, suppressing rare failures and preserving rare successes without behavior probabilities. In a tabular analysis, DG suppresses the perpendicular second moment of high-surprisal failures by a policy-overlap factor that vanishes as the learner improves. The advantage sign is essential for surprisal-based filtering: any learner-probability-only gate that suppresses rare failures also suppresses rare successes. On MNIST with simulated staleness, DG without off-policy correction outperforms importance-weighted PG with exact behavior probabilities. On a transformer sequence task with staleness, actor bugs, reward corruption, and rare discovery, DG often achieves nearly order-of-magnitude lower error. When all four frictions act simultaneously, its sample-efficiency advantage is order-of-magnitude and grows with task complexity.

Simulation-based inference (SBI) with neural networks has accelerated and transformed cognitive modeling workflows. SBI enables modelers to fit complex models that were previously difficult or impossible to estimate, while also allowing rapid estimation across large numbers of datasets. However, the utility of SBI for iterating over varying modeling assumptions remains limited: changes to parameterizations, generative functions, priors, and design variables all necessitate model retraining, thereby diminishing the benefits of amortization. To address these issues, we pilot the CogFormer, a meta-amortized framework for cognitive modeling. Our framework trains a transformer-based architecture that remains valid across a combinatorial number of structurally similar models, allowing for changing data types, parameters, design matrices, and sample sizes. We present promising quantitative results across families of decision-making models for binary, multi-alternative, and continuous responses. Our evaluation suggests that CogFormer can accurately estimate parameters across model families with minimal amortization offset, making it a potentially powerful engine that catalyzes cognitive modeling workflows.

Demographers rely on a variety of tools and methods to work with mortality schedules - model life tables, fitting methods, summary-indicator prediction, and forecasting - largely developed independently and not providing structurally coherent sex-specific outputs. The multi-dimensional mortality model (MDMx) unifies all four within one Tucker tensor decomposition demonstrated using the Human Mortality Database (HMD). Period life tables from the HMD are organized as a four-way tensor of logit(1qx) indexed by sex, age, country, and year. Shared factor matrices for sex and age make every output schedule structurally coherent by construction. From this decomposition four capabilities emerge: model life tables via clustering and smooth within-regime trajectories; life table fitting via a three-stage algorithm with Bayes-factor disruption detection; summary-indicator prediction mapping child or adult mortality to complete schedules, reformulating SVD-Comp in tensor coordinates; and forecasting via a damped local linear trend Kalman filter on PCA-reduced core matrices with hierarchical drift.

We study the effects of center initialization on the performance of a family of distributed gradient-based clustering algorithms introduced in [1], that work over connected networks of users. In the considered scenario, each user contains a local dataset and communicates only with its immediate neighbours, with the aim of finding a global clustering of the joint data. We perform extensive numerical experiments, evaluating the effects of center initialization on the performance of our family of methods, demonstrating that our methods are more resilient to the effects of initialization, compared to centralized gradient clustering [2]. Next, inspired by the $K$-means++ initialization [3], we propose a novel distributed center initialization scheme, which is shown to improve the performance of our methods, compared to the baseline random initialization.

Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical simulation at scales necessary for quantifying key properties. Surrogate models of the drift function of an SDE, learned from data of the high-fidelity system, are routinely used to increase the efficiency of simulation and prediction of properties. However, standard choices of loss function for learning the surrogate model fail to provide error guarantees in certain path-dependent observables, such as transition times. This paper introduces an error bound for path-space observables and employs it as a novel variational loss for the goal-oriented learning of the drift function of a SDE. We show the error bound holds for a broad class of observables, including mean first hitting times on unbounded time domains. We derive an analytical gradient of the goal-oriented loss by leveraging the formula for Fréchet derivatives of expected path functionals, which remains tractable for implementation in stochastic gradient descent schemes. We demonstrate that surrogate models of overdamped Langevin systems developed via goal-oriented learning achieve improved accuracy in predicting the statistics of a first hitting time observable and robustness to distributional shift in the data.

Panel data methods are widely used in empirical analysis to address unobserved heterogeneity, but causal inference remains challenging when treatments are endogenous and confounding variables high-dimensional and potentially nonlinear. Standard instrumental variables (IV) estimators, such as two-stage least squares (2SLS), become unreliable when instrument validity requires flexibly conditioning on many covariates with potentially non-linear effects. This paper develops a Double Machine Learning estimator for static panel models with endogenous treatments (panel IV DML), and introduces weak-identification diagnostics for it. We revisit three influential migration studies that use shift-share instruments. In these settings, instrument validity depends on a rich covariate adjustment. In one application, panel IV DML strengthens the predictive power of the instrument and broadly confirms 2SLS results. In the other cases, flexible adjustment makes the instruments weak, leading to substantially more cautious causal inference than conventional 2SLS. Monte Carlo evidence supports these findings, showing that panel IV DML improves estimation accuracy under strong instruments and delivers more reliable inference under weak identification.

The potential system is a nonparametric time series model for assessing the causal impact of moving an assignment at time $t$ on an outcome at future time $t+h$, accounting for the presence of features. The potential system provides nonparametric content for, e.g., time series experiments, time series regression, local projection, impulse response functions and SVARs. It closes a gap between time series causality and nonparametric cross-sectional causal methods, and provides a foundation for many new methods which have causal content.

Probabilistic circuit (PC) structure learning is hampered by greedy algorithms that make irreversible, locally optimal decisions. We propose SymCircuit, which replaces greedy search with a learned generative policy trained via entropy-regularized reinforcement learning. Instantiating the RL-as-inference framework in the PC domain, we show the optimal policy is a tempered Bayesian posterior, recovering the exact posterior when the regularization temperature is set inversely proportional to the dataset size. The policy is implemented as SymFormer, a grammar-constrained autoregressive Transformer with tree-relative self-attention that guarantees valid circuits at every generation step. We introduce option-level REINFORCE, restricting gradient updates to structural decisions rather than all tokens, yielding an SNR (signal to noise ratio) improvement and >10 times sample efficiency gain on the NLTCS dataset. A three-layer uncertainty decomposition (structural via model averaging, parametric via the delta method, leaf via conjugate Dirichlet-Categorical propagation) is grounded in the multilinear polynomial structure of PC outputs. On NLTCS, SymCircuit closes 93% of the gap to LearnSPN; preliminary results on Plants (69 variables) suggest scalability.

We derive the asymptotic risk function of regularized empirical risk minimization (ERM) estimators tuned by $n$-fold cross-validation (CV). The out-of-sample prediction loss of such estimators converges in distribution to the squared-error loss (risk function) of shrinkage estimators in the normal means model, tuned by Stein's unbiased risk estimate (SURE). This risk function provides a more fine-grained picture of predictive performance than uniform bounds on worst-case regret, which are common in learning theory: it quantifies how risk varies with the true parameter. As key intermediate steps, we show that (i) $n$-fold CV converges uniformly to SURE, and (ii) while SURE typically has multiple local minima, its global minimum is generically well separated. Well-separation ensures that uniform convergence of CV to SURE translates into convergence of the tuning parameter chosen by CV to that chosen by SURE.

Probability theory has become the predominant framework for quantifying uncertainty across scientific and engineering disciplines, with a particular focus on measurement and control systems. However, the widespread reliance on simple Gaussian assumptions–particularly in control theory, manufacturing, and measurement systems–can result in incomplete representations and multistage lossy approximations of complex phenomena, including inaccurate propagation of uncertainty through multi stage processes. This work proposes a comprehensive yet computationally tractable framework for representing and propagating quantitative attributes arising in measurement systems using Probability Density Functions (PDFs). Recognizing the constraints imposed by finite memory in software systems, we advocate for the use of Gaussian Mixture Models (GMMs), a principled extension of the familiar Gaussian framework, as they are universal approximators of PDFs whose complexity can be tuned to trade off approximation accuracy against memory and computation. From both mathematical and computational perspectives, GMMs enable high performance and, in many cases, closed form solutions of essential operations in control and measurement. The paper presents practical applications within manufacturing and measurement contexts especially circular factory, demonstrating how the GMMs framework supports accurate representation and propagation of measurement uncertainty and offers improved accuracy–compared to the traditional Gaussian framework–while keeping the computations tractable.

Machine learning has opened new frontiers in purely data-driven forecasting of dynamical systems; the resulting methods are showing considerable promise in some application domains. However, in contrast to model-driven algorithms, analysis of these data-driven methods is poorly developed. In this paper we address this issue, developing a theory to underpin data-driven methods to solve forecasting problems. The theoretical framework comprises two key components: (i) establishing the existence of a mapping defining the forecasting problem; (ii) showing that it is possible to approximate this mapping by supervised learning techniques, to arbitrary accuracy. We work in the continuous-time and noise-free setting as this defines a simple canonical setting in which to establish an underpinning theory; the continuous-time setting leads to an operator formulation of the problem in which the underlying forecasting map is defined on pathspace. As a byproduct of our framework we show that analogous existence and approximation results may be obtained for the smoothing problem of recovering unobserved components of dynamical systems, from observed components, using supervised learning. The theoretical results, for both forecasting and smoothing, are illustrated with experiments studying the Lorenz `63, Lorenz `96 and Kuramoto-Sivashinsky dynamical systems.

In pharmaceutical and toxicological research, historical control data are increasingly used to validate concurrent control groups, typically via the construction of historical control limits. While methods have been described for continuous and dichotomous endpoints, approaches for overdispersed multinomial data, common in developmental and reproductive toxicology or histopathology, are currently lacking. This article introduces and compares methods for constructing simultaneous prediction intervals for future multinomial observations subject to overdispersion. We investigate a range of frequentist approaches, including asymptotic approximations and bootstrap techniques (incorporating symmetric, asymmetric, and marginal calibration, as well as rank-based methods), alongside Bayesian hierarchical models. Extensive simulation studies assessing simultaneous coverage probability and the balance of lower and upper tail error probabilities show that standard asymptotic methods and simple Bonferroni adjustments yield liberal intervals, especially for small sample sizes or rare event categories. In contrast, bootstrap methods, specifically the Marginal Calibration and Rank-Based Simultaneous Confidence Sets, provide reliable error control and equal tail probabilities across diverse scenarios involving varying cluster sizes and degrees of overdispersion. These methods fill an important gap for multinomial endpoints and support the validation of concurrent controls using historical control data, in line with the recent European Food Safety Authority scientific opinion on the use and reporting of historical control data.

Hypoglycemia is a severe condition of decreased blood glucose, specifically below 70 mg/dL (3.9 mmol/L). This condition can often be asymptomatic and challenging to predict in individuals with type 1 diabetes (T1D). Research on hypoglycemic prediction typically uses a combination of blood glucose readings and heart rate data to predict hypoglycemic events. Given that these features are collected through wearable sensors, they can sometimes have missing values, necessitating efficient imputation methods. This work makes significant contributions to the current state of the art by introducing two novel imputation techniques for imputing heart rate values over short-term horizons: Controlled Weighted Rational Bézier Curves (CRBC) and Controlled Piecewise Cubic Hermite Interpolating Polynomial with mapped peaks and valleys of Control Points (CMPV). In addition to these imputation methods, we employ two metrics to capture data patterns, alongside a combined metric that integrates the strengths of both individual metrics with RMSE scores for a comprehensive evaluation of the imputation techniques. According to our combined metric assessment, CMPV outperforms the alternatives with an average score of 0.33 across all time gaps, while CRBC follows with a score of 0.48. These findings clearly demonstrate the effectiveness of the proposed imputation methods in accurately filling in missing heart rate values. Moreover, this study facilitates the detection of abnormal physiological signals, enabling the implementation of early preventive measures for more accurate diagnosis.

Integrating dynamical systems models with time series data is a central part of contemporary mathematical biology. With the rich variety of available models and data, numerous methods and computational tools have been developed for these purposes. One such tool is Stan, a freely available and open-source probabilistic programming framework that provides efficient methods for estimating model parameters from data using computational Bayesian inference algorithms. Stan includes built-in mechanisms for working with ordinary differential equation (ODE) models, which are widely used in mathematical biology and related fields to study simulated, experimental, and real-world systems that change over time. Through step-by-step worked examples, including both pedagogical toy models and applications with real data, this article provides a practical, self-contained introduction to performing parameter estimation and model evaluation for first-order linear and nonlinear ODE models in Stan. The article also explains key statistical methods that underpin Stan and discusses computational Bayesian modelling in the context of biological applications.

We study the ill-posed problem of recovering a probability measure flow from finitely many moving localized sensors using a Bayes Hilbert framework. Relative to a fixed reference probability measure, a probability law is represented by its centered log-ratio coordinates, so that an evolving law becomes a path in a Hilbert space of functions. For sufficiently regular Bayes Hilbert paths, we construct a canonical minimum-energy transport realization of the path by solving a weighted Neumann problem at each time, yielding an intrinsic transport form on tangent directions. We then formulate an inverse problem directly on Bayes Hilbert path space. Linearization of an observation operator yields an observability form, and recoverability is governed by its interaction with the transport geometry through a joint transport–observability form. In the ambient infinite-dimensional setting, we develop a regularized variational theory and identify limitations of localized sensing: mobile sensors can make the joint form injective, but they do not in general yield a coercive stability estimate on the full state space. This obstruction leads naturally to finite-dimensional Bayes Hilbert reductions. There the transport form becomes a kinetic tensor and the linearized observations become reduced sensing matrices, so recoverability can be expressed through explicit Gramian conditions. We show that localized bump sensors detect every fixed reduced direction, that finitely many suitably placed static sensors yield uniform reduced observability, and there exist path-dependent sensor trajectories such that even a single moving sensor can recover the reduced path. Finally, we show that these reduced recovery results lift to approximate ambient recovery for paths that are well approximated by the chosen finite-dimensional subspaces, yielding stable reconstruction up to projection error.

Social insect colonies and ensemble machine learning methods represent two of the most successful examples of decentralized information processing in nature and computation respectively. Here we develop a rigorous mathematical framework demonstrating that ant colony decision-making and random forest learning are isomorphic under a common formalism of stochastic ensemble intelligence. We show that the mechanisms by which genetically identical ants achieve functional differentiation – through stochastic response to local cues and positive feedback – map precisely onto the bootstrap aggregation and random feature subsampling that decorrelate decision trees. Using tools from Bayesian inference, multi-armed bandit theory, and statistical learning theory, we prove that both systems implement identical variance reduction strategies through decorrelation of identical units. We derive explicit mappings between ant recruitment rates and tree weightings, pheromone trail reinforcement and out-of-bag error estimation, and quorum sensing and prediction averaging. This isomorphism suggests that collective intelligence, whether biological or artificial, emerges from a universal principle: \textbf{randomized identical agents + diversity-enforcing mechanisms $\rightarrow$ emergent optimality}.

Causal generative models provide a principled framework for answering observational, interventional, and counterfactual queries from observational data. However, many deep causal models rely on highly expressive architectures with opaque mechanisms, limiting auditability in high-stakes domains. We propose KaCGM, a causal generative model for mixed-type tabular data where each structural equation is parameterized by a Kolmogorov–Arnold Network (KAN). This decomposition enables direct inspection of learned causal mechanisms, including symbolic approximations and visualization of parent–child relationships, while preserving query-agnostic generative semantics. We introduce a validation pipeline based on distributional matching and independence diagnostics of inferred exogenous variables, allowing assessment using observational data alone. Experiments on synthetic and semi-synthetic benchmarks show competitive performance against state-of-the-art methods. A real-world cardiovascular case study further demonstrates the extraction of simplified structural equations and interpretable causal effects. These results suggest that expressive causal generative modeling and functional transparency can be achieved jointly, supporting trustworthy deployment in tabular decision-making settings. Code: https://github.com/aalmodovares/kacgm

It is currently difficult to distill discrete diffusion models. In contrast, continuous diffusion literature has many distillation approaches methods that can reduce sampling steps to a handful. Our method, Discrete Moment Matching Distillation (D-MMD), leverages ideas that have been highly successful in the continuous domain. Whereas previous discrete distillation methods collapse, D-MMD maintains high quality and diversity (given sufficient sampling steps). This is demonstrated on both text and image datasets. Moreover, the newly distilled generators can outperform their teachers.

We consider the problem of constructing sequential power-one tests where the null and alternative classes are specified indirectly through historical or offline data. More specifically, given an offline dataset consisting of observations from $L+1$ distributions $\{P_0, P_1, \ldots, P_L\}$, and a new unlabeled data stream $\{X_t: t \geq 1\} \overset{i.i.d}{\sim} P_\theta$, the goal is to decide between the null $H_0: \theta = 0$, against the alternative $H_1: \theta \in [L]:=\{1,\ldots,L\}$. Our main methodological contribution is a general approach for designing a level-$\alpha$ power-one test for this problem using a multi-class classifier trained on the given offline dataset. Working under a mild "separability" condition on the distributions and the trained classifier, we obtain an upper bound on the expected stopping time of our proposed level-$\alpha$ test, and then show that in general this cannot be improved. In addition to rejecting the null, we show that our procedure can also identify the true underlying distribution almost surely. We then establish a sufficient condition to ensure the required separability of the classifier, and provide some converse results to investigate the role of the size of the offline dataset and the family of classifiers among classifier-based tests that satisfy the level-$\alpha$ power-one criterion. Finally, we present an extension of our analysis for the training-and-testing distribution mismatch and illustrate an application to sequential change detection. Empirical results using both synthetic and real data provide support for our theoretical results.

In this paper, we propose a triple (or double-debiased) Lasso estimator for inference on a low-dimensional parameter in high-dimensional linear regression models. The estimator is based on a moment function that satisfies not only first- but also second-order Neyman orthogonality conditions, thereby eliminating both the leading bias and the second-order bias induced by regularization. We derive an asymptotic linear representation for the proposed estimator and show that its remainder terms are never larger and are often smaller in order than those in the corresponding asymptotic linear representation for the standard double Lasso estimator. Because of this improvement, the triple Lasso estimator often yields more accurate finite-sample inference and confidence intervals with better coverage. Monte Carlo simulations confirm these gains. In addition, we provide a general recursive formula for constructing higher-order Neyman orthogonal moment functions in Z-estimation problems, which underlies the proposed estimator as a special case.

We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise interaction models such as the Ising model, we consider a framework to accommodate more general tensor structures that capture higher-order dependencies. We develop a two-step procedure for low-dimensional linear and quadratic functionals. The first step constructs a regularized maximum pseudolikelihood estimator, for which we establish consistency under high-dimensional features. However, as in other classical high-dimensional regression problems, this estimator is biased and cannot be directly used for valid statistical inference. The second step introduces a bias-correction that yields an asymptotically normal estimator from which one can construct confidence intervals and test hypotheses. Our results move beyond the existing literature, where only estimation guarantees were available or only for pairwise interaction models. We complement our theoretical analysis with simulation studies confirming the effectiveness of the proposed method.

This paper is concerned with the construction of prior free posterior distributions which rely on the use of one step ahead predictive distribution functions. These are typically more straightforward to motivate than prior distributions. Recent interest has been with Hill's $A_n$ prediction model through what has become known as conformal prediction. This model predicts the next observation to lie with equal probability in the intervals created by the observed data. The prediction model generates complete data sets which can be used to provide posterior inference on any statistic of interest.

Over the last decades, two distinct approaches have been instrumental to our understanding of the computational complexity of statistical estimation. The statistical physics literature predicts algorithmic hardness through local stability and monotonicity properties of the Franz–Parisi (FP) potential \cite{franz1995recipes,franz1997phase}, while the mathematically rigorous literature characterizes hardness via the limitations of restricted algorithmic classes, most notably low-degree polynomial estimators \cite{hopkins2017efficient}. For many inference models, these two perspectives yield strikingly consistent predictions, giving rise to a long-standing open problem of establishing a precise mathematical relationship between them. In this work, we show that for estimation problems the power of low-degree polynomials is equivalent to the monotonicity of the annealed FP potential for a broad family of Gaussian additive models (GAMs) with signal-to-noise ratio $\lambda$. In particular, subject to a low-degree conjecture for GAMs, our results imply that the polynomial-time limits of these models are directly implied by the monotonicity of the annealed FP potential, in conceptual agreement with predictions from the physics literature dating back to the 1990s.

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these approximate posteriors so that they appropriately capture uncertainty. vWe introduce two methods that extend simulation-based calibration checking (SBC) to widen approximate posterior uncertainty intervals to aim for marginal calibration. We demonstrate these methods in several experimental settings, and we discuss the challenge of calibration using posterior inferences and the potential for posterior recalibration of hierarchical models.

Ensembles of regional-global climate model combinations show substantial spread in projected wind and solar resources. Using 31 RCM-GCM pairs, we quantify the sources of this spread with a spatially and seasonally resolved variance decomposition, separating contributions from RCMs and GCMs. For both wind speed and solar radiation, RCMs dominate the variability in the absolute historical fields. In contrast, projected changes in wind speed are largely controlled by the driving GCMs, except in mountainous regions where RCM-induced variance becomes larger than that induced by GCMs. For solar radiation, contributions are strongly season-dependent, with RCMs dominating in summer and GCMs in winter. Our findings support that GCM and RCM variability together define the uncertainty of wind and solar climate projections. This provides guidance for designing climate model ensembles that better support uncertainty-aware energy system decisions under climate change.

We study adversarial learning when the target distribution factorizes according to a known Bayesian network. For interpolative divergences, including $(f,\Gamma)$-divergences, we prove a new infimal subadditivity principle showing that, under suitable conditions, a global variational discrepancy is controlled by an average of family-level discrepancies aligned with the graph. In an additive regime, the surrogate is exact. This closes a theoretical gap in the literature; existing subadditivity results justify graph-informed adversarial learning for classical discrepancies, but not for interpolative divergences, where the usual factorization argument breaks down. In turn, we provide a justification for replacing a standard, graph-agnostic GAN with a monolithic discriminator by a graph-informed GAN (GiGAN) with localized family-level discriminators, without requiring the optimizer itself to factorize according to the graph. We also obtain parallel results for integral probability metrics and proximal optimal transport divergences, identify natural discriminator classes for which the theory applies, and present experiments showing improved stability and structural recovery relative to graph-agnostic baselines.

Designing clinical trials requires evaluating multiple operating characteristics (OCs), such as the likelihood of an early stopping decision, the probability of detecting a treatment effect, and the Type I error rate. In most cases, these evaluations are based on computationally intensive Monte Carlo simulations. As the complexity of clinical trials and the use of adaptive designs increase, the computational burden can quickly become prohibitive. We introduce a strategy for rapidly approximating OCs, called the Q-approximation. Our approach is based on quadratic approximations of the log-likelihood and asymptotic arguments. The main idea is to replace simulation of full trial datasets with simulation of the approximate likelihood functions that determine the trial's interim and final decisions. The Q-approximation approach can be applied to any trial design that uses data analysis methods coherent with the likelihood principle, including multistage designs with early stopping, adaptively randomized designs, and designs that leverage external data. We illustrate the approach with several examples and show that it provides an accurate approximation of important OCs while reducing the computation time compared to Monte Carlo simulations. In particular, in our experiments, the standard Monte Carlo approximation of OCs requires 150 to 1,900 times greater computing budget than Q-approximations to achieve comparable levels of accuracy. By enabling fast OC evaluations, Q-approximations can support the broader use of innovative trial designs in both applied trial planning and methodological development.

Recently, the U.S. Food and Drug Administration (FDA) released draft guidance \citep{FDA2026} signaling a paradigm shift that facilitates the use of Bayesian methodology as the primary analysis and decision framework for drug approval. The cornerstone and fundamental challenge of this framework is the specification and calibration of Bayesian success criteria to control decision errors, ensuring reliable clinical and regulatory outcomes. In this work, we systematically investigate various Bayesian decision-error metrics, their theoretical interrelationships, and their alignment with conventional Frequentist counterparts. This investigation provides critical theoretical insights and practical guidance on calibrating Bayesian success criteria and operating characteristics to ensure robust decision-making and the integrity of public health decisions. We illustrate this framework using a clinical trial evaluating revascularization strategies for cardiogenic shock. A Shiny application will be available at www.trialdesign.org to assist sponsors and regulators in evaluating calibration strategies consistent with recent regulatory perspectives.

Estimating the number of migrants who die or go missing along dangerous routes such as the Central Mediterranean remains challenging as available records are incomplete. Some incidents are never documented, and fatalities associated with such unobserved incidents are absent from observed totals. We propose a Bayesian approach for probabilistic estimation of total migrant fatalities in such settings. Building on recent developments in multiple-systems estimation, we develop a time-stratified latent-class framework that accommodates missing fatality counts for unobserved incidents. We apply the method to recoded incident-level data from the Missing Migrants Project for the Central Mediterranean route from 2014 to 2025, encompassing 25,712 fatalities across 1,562 incidents. Our model yields 95% credible intervals of 31,922-41,413 fatalities and 2,170-2,952 deadly incidents, indicating that approximately 62%-81% of fatalities and 53%-72% of incidents are reflected in the available data. We estimate that unreported fatalities were concentrated between 2014 and 2016. Furthermore, we document that reporting likelihood increases with incident severity, implying that smaller incidents are most likely to remain undetected. While contingent on modeling assumptions and incomplete data, our method provides a broadly applicable and principled alternative to naive data adjustment methods.