Papers

Uncertainty quantification (UQ) is essential to experimental mechanics, but has become particularly relevant in computational mechanics, manifesting in two fundamental problem types: forward and inverse problems. The former addresses how input uncertainties propagate to the quantities of interest, whereas the latter aims to infer unknown parameters from experimental observations or simulations. Since efficient propagation typically requires a prohibitive number of evaluations to compute marginal output distributions, the development of fast, data-driven surrogate models becomes necessary. Thus, we can distinguish between two inverse tasks: (i) the identification and calibration of input uncertainties, and (ii) the construction of surrogates, a methodology collectively referred to as surrogate-based UQ. Building on probabilistic reasoning and the concept of partial belief, we demonstrate that Bayesian probability theory provides a unified theoretical framework for addressing both problem types. We further show that Bayesian inference allows for the seamless incorporation of essential subproblems, including model selection for identifying the most probable model specifications and experimental design for optimizing data collection by identifying experiments or simulations that maximize expected information gain about parameters, among others such as connections to sensitivity analysis or the use of special priors like random fields. While this theoretical framework is presented for general mechanical problems, particular emphasis is placed on biomechanics, where variability and uncertainty is especially pronounced due to inherent biological heterogeneity, patient-specific variability, and noisy data.

Given observations $\mathbf x=(x_1,\dots,x_n)$, Gaffke (2005) defined \[ K_n(\mathbf x)=\mathbb{P}_{\mathbf D}\!\left\{\sum_{i=1}^n x_iD_i\le 1\right\}, \qquad (D_0,D_1,\ldots,D_n)\sim\mathrm{Dirichlet}(1,\ldots,1), \] and conjectured that it is a $p$-value whenever the inputs are independent e-values. Recently, Vlassis and Thomas (2026) proved this conjecture. Inverting the tests for observations in $[0,1]$ gives the confidence interval studied by Learned-Miller and Thomas (2020), which reduces to Clopper–Pearson for Bernoulli data. We give a finite- and large-sample account of Gaffke's test and interval. First, for every $\mathbf x\in[0,\infty)^n$ and every elementary symmetric polynomial $e_k$, \( K_n(\mathbf x)e_k(\mathbf x)\le {n\choose k}, \) so the Gaffke $p$-value never larger than the SymPol $p$-value of Ming et al. (2026). However, Gaffke's p-value is inadmissible. For $n=2$, we construct a valid rule that is strictly smaller on mixed configurations and is the unique admissible rule that dominates $K_2$. A neutral-face extension proves inadmissibility of $K_n$ for every $n\ge2$. If one independent uniform random variable is allowed, there is an even simpler full-dimensional improvement: on the upper orthant, where $K_n(\mathbf x)=1/\prod_i x_i$, replace it by $U/\prod_i x_i$. The equal-tail Gaffke confidence interval $I_n$ is nevertheless first-order asymptotically efficient: for iid observations on $[0,1]$ with unknown variance $\sigma^2>0$, \[ \sqrt n\,\operatorname{Width}(I_n)\longrightarrow 2\sigma z_{1-\alpha/2}\qquad\text{almost surely}. \] Our simulations also find that, among a variety of bounded-mean intervals considered, the Gaffke interval is the shortest, including comparisons with a recent empirical Berry–Esseen procedure having the same first-order Gaussian target.

We establish improved lower bounds on the minimax expected regret of stochastic bandit convex optimization for $1$-Lipschitz functions on the $d$-dimensional Euclidean ball. For time horizons $n\ge d^{10/3}$, we prove a lower bound of $\Omega(d^{4/3}\sqrt{n})$, the first nontrivial bound that exceeds the $d\sqrt{n}$ dependence of linear bandits, showing that stochastic bandit convex optimization is fundamentally harder than linear bandits. For $d^2\le n\le d^{10/3}$, we obtain a lower bound of $\Omega(\sqrt{d}n^{3/4})$, matching the regret of the algorithm of Flaxman et al. (2005), establishing its optimality in this regime. The hard class of convex functions we construct takes the following form in dimension $2d$: for an action $a=(a^1,a^2)\in \mathbb{B}^{2d}$, each function is the scaled soft maximum of a "tube", $r^{-1}\|W^\star a^1-\frac{r}{8\varepsilon}a^2 \|$ (hyperparameterized by $\varepsilon,r$), and a squared distance function, $\frac12\|a^1-u^\star\|^2-\frac12\|u^\star\|^2$. Here $u^\star\in\mathbb{R}^d$ is the unknown target determining the minimizer, while $W^\star\in\mathbb{R}^{d\times d}$ hides the region in which the quadratic curvature is observable. Indeed, observations reveal substantial information about $u^\star$ only when the learner acts near the hidden tube $a^2\approx \frac{8\varepsilon}{r}W^\star a^1$; away from it, the tube branch masks the quadratic branch. Thus the learner must pay to uncover the geometry encoded by $W^\star$ before it can effectively exploit the curvature that identifies $u^\star$. Formalizing this tradeoff yields a sample complexity lower bound of $\Omega(\frac{d^{5/2}}{\varepsilon^2}\wedge\frac{d^2}{\varepsilon^4})$ for finding an $\varepsilon$-optimal action, and ultimately the $\Omega(d^{4/3}\sqrt{n}\wedge\sqrt{d}n^{3/4})$ regret lower bound. The proof was developed by GPT-5.5 Pro and GPT-5.6 Sol Pro under the authors' guidance.

Let $f$ be the density of the Chernoff random variable $\mathrm{argmax}_{t\in\mathbb{R}}\{W(t)-t^2\}$, where $W$ is a two-sided Brownian motion. This note proves the conjecture of Balabdaoui and Wellner (2014) that $f$ is strongly log-concave. The proof was generated in its entirety by GPT-5.6 Sol.

Conditional generative models, including diffusion models and ensemble forecasters, often produce predictive samples without a tractable likelihood representation. Such sample-based predictive distributions can be systematically biased and poorly calibrated. We propose bias-corrected conformal probability integral transform (PIT) calibration, a split-sample post-processing framework that outputs a calibrated predictive distribution rather than a single fixed-level prediction interval. The method first estimates an affine location-scale correction on a held-out bias split, then calibrates randomized PIT values using a conformal calibrator. The resulting predictive law is represented as a weighted empirical distribution on the generator order statistics, enabling the direct computation of threshold-coherent exceedance probabilities, arbitrary quantiles, highest-density intervals, expected tail losses, and calibrated resamples. In contrast, standard conformal prediction primarily provides fixed-level prediction sets or threshold decisions and does not directly estimate predictive probabilities or high-density regions. We establish finite-sample calibration in probability under exchangeability and show how an optional split-conformal wrapper based on a PIT-centrality score gives nested prediction intervals with finite-sample marginal coverage at user-specified levels. Simulation studies with controlled misspecification and a WeatherBench-2 precipitation-forecasting application demonstrate substantial improvements in probabilistic calibration and downstream distributional summaries relative to uncalibrated sample-based forecasts and interval-only conformal baselines.

Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process. We study exact recovery of the graph from one trajectory of random-scan Gaussian Glauber dynamics. Existing techniques for this problem either inherit the mixing time of the chain, which can be super-polynomial in the dimension $p$ without strong assumptions, or are suboptimal in the minimum normalized edge strength $\kappa$. We propose two algorithms that are mixing-free and attain the $\kappa^{-2}$ dependence of the information-theoretic lower bounds. Both instantiate a shared dueling-neighborhood search meta-algorithm with a local statistic built directly from the update sequence. For every fixed precision matrix and deterministic initialization, the first algorithm fits a least-squares regression at the updates of each node and has pointwise recovery horizon $\widetilde O(pd^{2}/\kappa^{2})$, where $d$ is the maximum degree. Its horizon depends logarithmically on a local conditioning quantity and on the initialization potential. The second algorithm is based on counting occurences of a specific update pattern and requires $\widetilde O(pd^{4}/\kappa^{2})$ updates, with no dependence on any condition number. The central technical challenge is that both statistics are built from dependent, non-stationary observations. Our analysis tackles this by demonstrating how to extract fresh Gaussian innovations from the update sequence, which yields mixing-free control of appropriate quantities. Neither the algorithms nor their analyses invoke stationarity, a spectral gap, or mixing conditions.

Researchers often select top-performing options or winners, based on a data-driven criterion, such as treatments, models, or model features and then report effect estimates for the selected winners. Naive post-selection estimates, however, are known to suffer from the winner's curse, producing systematically overoptimistic results. We introduce a flexible conditional inference method that corrects for this overoptimism through an adaptive exponential randomization scheme. Our method achieves selection quality that closely matches that of standard top-k selection, while also yielding shorter confidence intervals than existing approaches. Furthermore, our approach applies broadly to nonparametric settings with asymptotically linear selection statistics, covering wide-ranging applications such as inference for the efficacy of the most promising treatments in clinical trials, the abilities of top-ranked models on leaderboards, and the importance of the most predictive features in a model.

We construct a vector space whose defining characteristics are rooted in univariate regular variation of random variables. Specifically, the base vector space $\mathbb{V}_b$ consists of random variables whose limiting tail probabilities, when scaled by regularly varying functions of the form $b(s)=s^\alpha L(s)$, are finite. Defining a subspace ${\cal N}_b$ corresponding to random variables in $\mathbb{V}_b$ whose limiting tail probabilities are zero when normalized by $b(s)$ allows the base space $\mathbb{V}_b$ to be partitioned into equivalence classes. We define a vector space $\mathbb{W}_b$ consisting of these equivalence classes, and show its nonzero elements are equivalence classes of regularly varying random variables. We show that a natural norm exists for $\mathbb{W}_b$ if $\alpha > 1$. We show that the equivalence classes and convergence in norm are different than more familiar vector spaces of random variables. Turning our attention to extreme value modeling, we consider finite-dimensional subspaces of $\mathbb{W}_b$ whose basis vectors are jointly regularly varying. We show that in the case $\alpha = 2$, the previously defined tail pairwise dependence measure serves as an inner product. As any finite-dimensional space is complete, we can use the projection theorem to perform linear prediction.

Two-sample Mendelian randomization (MR) uses genetic variants as instrumental variables to estimate causal effects from observational data using summary association statistics. However, horizontal pleiotropy can invalidate standard MR estimators and lead to biased causal inference. Pleiotropy-robust methods have been proposed to address this issue, including regularization-based approaches such as MR-Lasso. However, MR-Lasso may fail to identify invalid instruments consistently, and its post-selection inference can be unreliable. In this paper, we develop two lasso-type procedures for two-sample MR with summary-level data. The first, MR-ALasso, extends MR-Lasso by introducing adaptive penalty weights for pleiotropic effects in order to improve the identification of valid and invalid instruments. The second, MR-ALasso-B, combines adaptive lasso selection with bootstrap smoothing to improve post-selection inference. We establish theoretical results for MR-ALasso under the two-sample summary data framework, including invalid instrument identification consistency and oracle-type post-selection behavior. Simulation studies show that MR-ALasso generally improves upon MR-Lasso in estimation accuracy and invalid-instrument identification, whereas MR-ALasso-B substantially improves coverage and type-I error control relative to naive post-selection inference. A real-data application based on bidirectional analyses of multiple complex traits further illustrates the practical usefulness of the proposed methods. We provide an R package, MRAlasso, to facilitate implementation.

Clinical trials for neurodegenerative diseases must identify sensitive endpoints – outcomes that change rapidly enough to detect treatment effects. In Huntington disease, this requires measuring how outcomes change as participants approach Stage 1. Yet many participants exit studies before reaching this stage, making their time to Stage 1 right-censored. Estimating how outcomes change requires models for both time to Stage 1 and time to study exit. When participants with worse outcomes exit earlier, this outcome-dependent censoring causes existing estimators to produce contradictory results: for the same cognitive outcome, one estimator suggests improvement while another shows decline. Existing estimators either ignore outcome-dependent censoring or require one model to be correctly specified, with no protection when it is not. We introduce SPYCE, a doubly robust estimator (consistent when either model is correctly specified) that achieves the smallest possible variance and allows both models to be estimated nonparametrically without sacrificing efficiency. Applied to data from PREDICT-HD, an observational Huntington disease study, SPYCE resolves current contradictions, identifies caudate and putamen volume ratios as the most promising sensitive endpoints, and shows that as few as 241 participants per arm are needed to detect treatment effects, versus hundreds of thousands under estimators that cannot handle outcome-dependent censoring.

Gold-standard phenotype labels are often unavailable at scale in electronic health record (EHR) studies because they require manual chart review. Weakly supervised phenotyping methods instead use silver-standard labels, such as diagnosis-code counts, natural language processing (NLP) mentions, medication indicators, or laboratory thresholds. PheNorm is widely used for this purpose, but its original formulation was designed for count-valued silver labels and relies on log transformation, utilization normalization, and Gaussian mixture modeling. These steps are not directly suited to binary silver labels, which are common and may be highly informative. We propose Binary PheNorm, an extension that uses binary silver labels directly in the corruption-and-regression denoising step and produces a continuous phenotype score without EM calibration. We also consider a lasso-regularized version for high-dimensional EHR settings and combined models using both binary and count labels. In simulations, Binary PheNorm achieved strong discrimination using binary labels alone and often improved performance when combined with count labels. In anaphylaxis, AUC increased from 0.793 for an epinephrine-mention indicator to 0.891-0.892 after Binary PheNorm. In acute pancreatitis, AUC increased from 0.736 for a lipase-threshold indicator to 0.805-0.819. These results support Binary PheNorm as a practical weakly supervised approach when informative binary silver labels are available.

We show that MI connects subtly and elegantly the two best-known state-of-the-art independence test statistics: the $G^2$ and the Pearson's chi-square statistic $\chi^2$. Furthermore, we show that the MI connects directly those statistics by an elegant formula arising from a stochastic Taylor expansion of MI ($\delta$-method). MI second order term is precisely $\chi^2$ up to a scale factor. As a consequence, by this connection, the difference between $G^2$ and $\chi^2$ can be explicitly quantified.

Overparameterized models often have continuous parameter symmetries, so different parameters define the same predictor. We show that PAC–Bayesian analysis should be performed on the quotient predictor space: pushing a prior and posterior to the quotient preserves the empirical and population Gibbs risks while removing the nonnegative KL contribution caused solely by how the two distributions differ among parameterizations of the same predictor. Quotienting alone does not determine which prior to use. We construct a canonical choice of one parameterization for each predictor and account for the geometric volume of its equivalent parameterizations. This transforms a neutral reference prior into a data-independent prior that reflects the model's implicit bias. It approximates the ideal but inadmissible posterior-matched prior, which would minimize the KL term by depending on the training data. The resulting certificate is tighter exactly when this geometry-induced prior has smaller KL divergence from the learned quotient posterior than the neutral prior. We test this prediction in Fourier regression with a Hadamard parameterization and in Query-Key attention, using ordinary SGD without an explicit regularizer. The implicit-bias prior reduces the mean quotient-space KL by \(40.69\%\) and the mean PAC–Bayes certificate by \(21.40\%\) in the Fourier-Hadamard experiment. The smaller, prior-scale-dependent improvement in Query-Key attention confirms the predicted conditional nature of the effect.

We develop an exact finite-population stochastic framework for SIR epidemics evolving under Markovian switching between intervention regimes. The epidemic state is augmented by a finite phase component, allowing transmission, recovery, and direct immunity-acquisition rates to depend on the active regime. Phase-transition intensities may depend on the current epidemic state, so that policy escalation can react to the number of infectious individuals. Exploiting the monotonicity of the susceptible compartment, we derive level-wise recursions for the joint Laplace–Stieltjes transform and probability generating function of the extinction time and the number of infections generated before extinction. These recursions yield the infection-count distribution, conditional extinction-time transforms, and mixed moments linking epidemic duration and infection burden, while replacing a large global linear system with small phase-level solves. The framework is illustrated using weekly mpox incidence data from Luxembourg. A baseline one-phase SIR model is calibrated by maximum likelihood under a Poisson observation model. The calibrated baseline is then used for conditional comparisons of fixed control regimes, early versus delayed strict intervention, vaccination-supported control, and state-dependent escalation. The results show how switching mechanisms affect both the total number of infected individuals and the extinction time, including their dispersion. Since the switching mechanisms are specified rather than estimated from the intervention history, the results are conditional model-based comparisons rather than estimates of the historical effects of interventions in Luxembourg.

Causal discovery methods have shown strong performance in temporal systems, but they typically rely on regular and discrete lag structures, limiting their applicability to regularly sampled data. However, many real-world tasks require dealing with irregularly sampled streams of events, such as sensor streams, healthcare data, and financial transactions. In this work, we propose an extension of PCMCI+, a state-of-the-art method for causal discovery on regular multivariate time series, to allow for handling irregular time series. Instead of modelling causal relations through fixed-lag dependencies, our method aggregates causal influence over predefined temporal windows. We evaluate our method on synthetic irregular event streams with known causal structures under different signal-to-noise ratios, showing that it consistently recovers the underlying causal graph and substantially outperforms the standard PCMCI+ on irregularly sampled data.

We propose one-step and two-step methods for policy learning with retrieval-augmented generation (RAG). We formulate RAG-based action selection under the potential outcome framework. In the two-step method, vector search retrieves action-specific neighboring evidence in an embedding space, the generator estimates conditional expected outcomes or their contrasts, and a plug-in rule selects an action. This formulation connects action-specific vector search with nearest-neighbor matching in causal inference. We decompose the regret of the two-step method into candidate-generation regret and within-candidate choice regret, and we bound the latter using prediction-error guarantees for nearest-neighbor estimators and transformers. We evaluate the one-step method directly as a policy because its intermediate computation is unobserved.

This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, whereas the latent structure is decomposed into invariant factors with shared loadings and heterogeneous factors with environment-specific loadings. Such a model is motivated by transfer learning and latent factor regression, where one seeks stable low-dimensional representations for both interpretation and robust out-of-sample prediction of the response $Y$. Leveraging the invariance principle, we show that the invariant and heterogeneous factors are disentangled under a minimal structural condition. Based on this, we propose ATLAS, an Auxiliary-label and invariance-guided Transfer via Latent Alignment across heterogeneous environmentS. ATLAS is a unified procedure that leverages the invariance principle to separate aligned invariant and unaligned heterogeneous factors, and further exploits supervision from auxiliary labels to extract prediction-invariant and transferable factors from those unaligned heterogeneous factors. ATLAS yields near-oracle performance for downstream latent factor regression, enables transferable prediction in new environments through the full latent signal when auxiliary labels are available, and reduces to robust invariant-factor-only prediction otherwise. We establish sharp non-asymptotic error bounds for recovering invariant and heterogeneous factors, identifying all the response-invariant factors, and estimating the invariant signal in $Y$.

Digital Twins rely on surrogate models to mirror physical systems in real time, yet these models can degrade as operating conditions evolve, a phenomenon known as concept drift. Maintaining surrogate fidelity under drift, particularly when models must also capture aleatoric uncertainty, remains an open challenge. Existing adaptive frameworks lack principled mechanisms for detecting when updates are needed, for efficiently adapting models from limited streaming data, and for certifying that updates genuinely improve predictive performance. Here we present an adaptive Digital Twin framework that integrates a Fisher score–based multivariate drift detector, Low-Rank Adaptation (LoRA) for parameter-efficient continual learning, and a Mann–Whitney $U$ test for online statistical validation. The framework monitors surrogate-model confidence via Fisher score vectors, triggers targeted fine-tuning of fewer than 1% of model parameters upon drift detection, and statistically certifies predictive improvement before deploying the updated surrogate. Applied to a stochastic linear system and a directed energy deposition additive manufacturing process as case studies, the framework successfully detects distributional shifts with short delays and restores both predictive accuracy and uncertainty quantification under abrupt and incremental drift. These results establish a statistically rigorous and computationally tractable pathway for sustaining the trustworthiness of neural-network–based Digital Twins throughout their operational life cycle.

Fair clustering aims to make cluster assignments independent of sensitive attributes, but this goal becomes challenging when multiple sensitive attributes jointly define many subgroups. In such settings, directly extending existing fair clustering algorithms is computationally expensive or numerically unstable, especially when the number of subgroups grows exponentially and some subgroups contain only a few instances. To address these challenges, we define a subgroup-fairness gap for clustering and derive a covariance-based surrogate that exactly matches this gap. We then introduce a continuous relaxation of the surrogate, enabling efficient gradient-based optimization and yielding our proposed algorithm, COVA-FC. We also show that subgroup fairness alone does not imply marginal fairness, and extend our framework to capture a subgroup-marginal-fairness gap. Experiments on benchmark datasets show that COVA-FC achieves competitive cost-fairness trade-offs and improves computational efficiency over existing baselines in both subgroup and higher-order marginal settings.

A simple alternative to the binomial distribution that places more probability weight on the tails is considered. Its derivation only requires the weighted arithmetic mean of two discrete probability mass functions, one being the binomial itself and the other being the bi-uniform introduced here. Some properties are derived, and an application to a classical data set is discussed. The presentation can be seen as an exemplary treatise on how to construct a statistical model, derive statistical properties, fit models to actual data by employing estimation methods, and verify appropriateness by using elements from statistical hypothesis testing.

A Bayesian network framework is proposed for modelling unit-bounded continuous variables using conditional beta-distributed nodes within a fully Bayesian inference setting. The model captures conditional dependencies and propagates uncertainty through the network, with inference performed via Markov Chain Monte Carlo methods implemented in WinBUGS. The framework is applied to an experimental study of emotional and facial responses, focusing on rage intensity and facial gestures. Results show that brow lowering is strongly associated with rage intensity and is more frequent in men, whereas upper lid raising decreases under provocation independently of rage or sex. The model also predicts rage severity from informative facial gestures.

Statistical modeling for goals scored in football is typically achieved using the Poisson distribution and its variants. Here we propose a Bayesian framework for modeling under- and over-dispersion in count data by combining the Conway-Maxwell-Poisson (CMP) likelihood with a spikeand-slab (SAS) prior on unit-specific dispersion parameters. The proposed methodology generalizes Poisson-based count data models by treating equidispersion as an explicit baseline, and offering probabilistic quantification of departures from this regime, while simultaneously estimating their magnitude. Posterior inference is performed through a tailored Metropolis-within-Gibbs sampler that handles the doubly-intractable likelihood and provides efficient posterior exploration. The new method is examined using simulated data to confirm its ability to capture non-equidispersion, and applied to English Premier League (EPL) data. Dispersion is modeled at the team level and linked to goal-scoring behavior, and allows for thresholding mechanisms to distinguish teams based on their posterior probability of non-equidispersion. The results reveal heterogeneities in team-specific dispersion in the EPL, and demonstrate improvements in both model fit and predictive performance with respect to the standard Poisson model.

TabPFN is a transformer-based foundation model for tabular prediction that performs inference without task-specific training by conditioning on a support set and query inputs. Despite its strong empirical performance, its internal behavior on structurally difficult tabular geometries remains poorly understood. We study this behavior using zigzag persistent homology, treating TabPFN layer representations as evolving point clouds. We construct a controlled benchmark of synthetic tabular tasks with known true probabilities and varied intrinsic topology, including warped circles, tori, spheres, Hopf links, trefoil knots, and Swiss rolls. Across these tasks, we find that the topology of TabPFN's internal representation geometry is strongly associated with dataset-level reliability; for example, the zeroth homology group $H_0$ fragmentation count correlates positively with mean absolute residual across controlled tasks, and this association strengthens in a high-resolution warped circle case study at large sample size. Harder geometries induce a dual topological signature: increased $H_1$ loop activity and increased $H_0$ fragmentation, while the $H_1$ persistence becomes shorter-lived. These descriptors correlate with Bayes error, mean absolute residuals, and overconfidence. Our results suggest that zigzag persistence diagnoses the reliability of the inferred in-context task geometry and provides a context-level view of when TabPFN operates in topologically stressed regimes.

Electronic health record (EHR) networks provide unprecedented opportunities to study treatment mechanisms at scale, but mediation analyses across institutions are often hindered by privacy and governance constraints that restrict sharing of patient-level data. We developed a privacy-preserving federated mediation framework that enables estimation of natural direct and indirect effects without exchanging individual-level records across participating sites. The proposed approach integrates renewable learning with counterfactual causal mediation analysis, allowing institutions to collaboratively investigate treatment mechanisms using only low-dimensional summary statistics. Both simulation studies and the real-world application demonstrated that the federated estimator closely reproduced pooled-data results while preserving patient privacy. We applied the method to 32,146 patients in the Indiana Network for Patient Care to evaluate the extent to which body mass index (BMI) mediates the effect of GLP-1 receptor agonist on glycated hemoglobin (HbA1c) reduction. The BMI-mediated pathway accounted for only a small proportion of the overall treatment effect, suggesting that most glycemic improvement occurred through mechanisms other than weight loss.

Importance splitting (ISPLIT) evaluates the probabilities of rare events in non-Markovian models. It requires a heuristic importance function (IFUN) that estimates the distance to the target. While including timer evaluations in the IFUN can substantially improve the effectiveness of ISPLIT, the existing time-sensitive IFUNs evaluate simulation states with respect to single sampled timer values. Thus, reaching highly important states requires simultaneously sampling specific combinations of timer values, yielding many unproductive simulation runs. In this paper, we revisit time-sensitive ISPLIT with the goal of steering simulation runs towards important states. First, we study how timer values can be resampled conditioned on the elapsed time. The importance can be evaluated by considering the set of feasible timer values, decoupling importance estimation from timer samples. Second, we exploit the global age of a simulation to identify and prune the executions that can no longer reach the target within the remaining time budget. Together, these ideas lead to a taxonomy of distance metrics clarifying the role of timer bounds, resampling, and the global age. In particular, for models with unbounded timers, we show that time-sensitive IFUNs collapse to ordinary IFUNs under resampling. Experiments demonstrate that the proposed formulations substantially improve the accuracy of ISPLIT estimators.

High-stakes decisions in oncology clinical trials must often be made while survival data remains immature: progression-free survival (PFS) and overall survival (OS) are heavily censored, few events have accumulated, and the primary endpoint may be months or years from reading out. What is available at interim data cut-offs is information-rich longitudinal tumour measurements and baseline covariates. We present PIONEER, a Bayesian joint modelling framework that couples a mechanistic two-component state-space submodel of longitudinal tumour size dynamics to a multistate proportional-hazard submodel for competing clinical events, fitted simultaneously under a single posterior. The mechanistic submodel infers latent per-patient tumour trajectories - decomposed into treatment-responsive and refractory compartments with Gompertz-attenuated growth - from sparse, noisy sum-of-longest-diameter (SLD) observations. These latent trajectories feed the multistate hazard as time-varying covariates, while the event data simultaneously refines the tumour dynamics through the joint likelihood. All clinical endpoints (PFS, OS, objective response rate) are derived from the joint posterior in a single forward simulation pass, propagating full parameter uncertainty without any two-stage plug-in. Applied to a case study in extensive-stage small-cell lung cancer (two trials, N = 497), leave-future-out cross-validation demonstrates that at month 4 of enrolment (9 patients) the model produces calibrated PFS forecasts covering the mature month-19 Kaplan-Meier curve, and at month 11 (39 patients) the OS forecast converges - representing at least 8 months of advance forecasting with properly quantified uncertainty. We hope this work paves the way for broader adoption of Bayesian mechanistic state-space frameworks in clinical development, enabling earlier and more informed decision-making from immature trial data.

Many prediction and decision-making problems in operations research involve path-valued covariates – data that evolve over time – for which path signatures have become a canonical feature representation. Their use is justified by a universal approximation theorem, but this is an existence result: it guarantees that a finite-level signature can approximate any continuous path functional, without quantifying how fast the approximation error decreases as the truncation level grows. This paper develops approximation and statistical theory for signature-based path regression. We establish an \(L^2\) approximation rate for smooth functionals of Itô diffusions and show that it is minimax optimal. We then propagate the truncation error through three statistical learning procedures – Signature-OLS, Signature-LASSO, and Signature-Logistic – and establish their consistency. Three real-data applications show that signatures provide informative finite-dimensional representations of path-valued covariates and can improve prediction relative to handcrafted features, in the context of finance – foreign exchange realized volatility forecasting from intraday price paths; energy – battery end-of-life prediction from early diagnostic current-voltage pulse paths; and medicine – epileptic seizure detection from short electroencephalogram windows.

The conditional randomization test (CRT) provides a principled approach to conditional independence (CI) testing, guaranteeing exact type-I error control when the true conditional distribution is known. In practice, however, this distribution must be estimated, and estimation errors can inflate type-I errors, while high dimensionality and limited sample sizes can reduce power. Although external and unlabeled data offer the potential to improve CI testing, naive integration that ignores distributional heterogeneity can compromise type-I error control and fail to enhance power. We propose CRT*, a novel framework that robustly integrates external and unlabeled datasets to enhance CI testing in heterogeneous scenarios. CRT* employs smooth residual-bootstrap (SRB) with transfer learning for conditional distribution estimation, combined with adaptive data fusion via an optimal convex combination of test statistics. We theoretically establish that the SRB-based estimator converges to the true conditional distribution in expected total variation distance. Furthermore, even in high-dimensional regimes, CRT* maintains valid type-I error control and achieves strictly higher power than standard CRT without external data. Simulations and RNA-seq breast cancer data analyses demonstrate that CRT* substantially improves power while maintaining type-I error control in heterogeneous settings.

Nonlinear state estimation under structural model uncertainty remains a fundamental challenge in autonomous Guidance, Navigation, and Control (GNC) systems. Conventional Bayesian filtering separates state propagation from measurement correction, allowing model mismatch to accumulate during propagation, resulting in proposal–likelihood inconsistency, particle degeneracy, and degraded estimation accuracy. Existing approaches primarily improve proposal distributions or weighting strategies without explicitly incorporating measurement geometry into state propagation. This paper introduces a geometry-consistent Bayesian filtering framework that incorporates measurement geometry directly into the propagation process. The nominal drift is projected onto the measurement-consistent subspace, yielding a geometry-consistent proposal while preserving the Bayesian posterior through a rigorous change-of-measure formulation. A Geometric Projection Particle Filter (GPF) is developed together with a geometric co-state that quantifies instantaneous dynamics–measurement inconsistency. Theoretical analysis establishes existence and uniqueness of the projected dynamics, posterior preservation, standard Monte Carlo convergence of the particle approximation, and robustness under structural model uncertainty. The framework is validated using lunar descent navigation under partial observability and persistent model uncertainty. Compared with the bootstrap particle filter and conventional Gaussian filtering methods, GPF consistently achieves higher effective sample size and lower estimation error. These results demonstrate that geometry-consistent propagation provides a principled, computationally efficient, and theoretically grounded framework for robust nonlinear Bayesian filtering.

Missing data and confounding are common in real-world statistical applications, yet few studies have examined how imputation methods perform under time-varying confounding in binary variables, or how missingness mechanism, missing rate, missingness location and sample size jointly affect performance and the underlying identifiability conditions. We generated synthetic data and conducted a simulation study comparing missing data methods across scenarios varying these factors. Missingness was introduced in both treatment and outcome variables, and we applied stratified hot deck imputation, single mode imputation, multiple imputation with chained equations (MICE), and complete-case analysis. Average treatment effect (ATE) estimates were obtained using logistic regression with propensity score weighting, and we measured coverage, absolute bias and empirical standard errors across 48 scenarios with 500 replications each. Performance was primarily driven by the missingness mechanism and choice of method, with multiple imputation generally achieving better coverage and lower bias than other methods. Missingness location was also important, while missing rate and sample size primarily affected positivity violations, which were most pronounced under MNAR, high missingness and low sample sizes. Exchangeability violations from mild to moderate confounding were adequately controlled for by propensity score models, whereas strong confounding produced a modest decrease in coverage. Further research should examine additional ways identifiability conditions can be violated under missingness, using more advanced methods and more complex missingness scenarios.