Papers

Comparing the relative explanatory power of two dependent predictors regarding a common target variable is a fundamental challenge across scientific disciplines. Classical asymptotic procedures, such as Vuong's closeness test or the Hotelling-Williams test, frequently collapse under pathological data conditions, including heavy-tailed distributions and extreme categorical sparsity. To bypass these limitations, practitioners often turn to non-parametric resampling. However, naive permutation tests destroy the natural covariance structure of dependent predictors, while the paired bootstrap evaluating variance around the alternative hypothesis and introducing artificial ties suffers from metric space compression and categorical omission, rendering it highly unreliable in finite samples. In this paper, we introduce the Paired Swap Permutation Test, a novel and exact non-parametric methodology. Grounded in the principle of functional exchangeability under the null hypothesis, our algorithm utilizes a symmetric within-subject swapping mechanism for categorical data, and introduces an Empirical Cumulative Distribution Function (ECDF) mapping step for continuous domains. This copula-based transposition perfectly preserves marginal densities and the empirical support without introducing resampling ties. Through extensive Monte Carlo simulations, we demonstrate that the proposed test strictly maintains the nominal significance level and maximizes statistical power under conditions where standard methods become catastrophically liberal or pathologically conservative. Finally, we apply the framework to a high-dimensional linguistic dataset of Italian noun-noun compounds, proving its capacity to deliver robust, exact inference in environments where conventional analytical methods inherently fail.

Linear structural equation models on directed mixed graphs encode causal relationships among variables subject to latent confounding. The half-trek criterion (HTC) provides a graphical sufficient condition for the structural coefficients to be rationally identifiable from the observable covariance matrix, and yields a corresponding closed-form rational estimator. Despite this, the asymptotic distribution of the HTC estimator, and hence valid standard errors and confidence regions, have not been derived. We derive the semiparametric influence function of this estimator for all HTC-identified directed mixed graphs, including cyclic ones. The influence function combines the structural residual at the target node with the identification instruments, recursively corrected for uncertainty from earlier estimation stages. The HTC estimator is asymptotically normal with variance computable in closed form, yielding confidence regions, marginal intervals, and Wald tests for individual structural coefficients. Applied to the Fulton Fish Market dataset, our theory delivers a complete inferential summary for the causal effect of supply on demand.

We study learning in prophet inequalities with i.i.d. rewards drawn from an exponential-type parametric family with an unknown parameter $\theta$, a class that includes exponential, Pareto, and bounded-support power-family distributions. We first characterize the optimal full-information asymptotic competitive ratio for this family. In the unbounded-support case, the limit is $ {\left({\theta}/({\theta-c_+})\right)^{c_+/\theta}}/ {\Gamma(1-c_+/\theta)},$ while in the bounded-support case, the limit is $1$. We then propose a confidence-based dynamic-programming policy for online learning. By exploiting the explicit parametric structure, the policy achieves the same optimal asymptotic competitive ratio using only online observations, without external offline samples. We further derive distribution-specific convergence rates for canonical examples. Finally, numerical experiments on synthetic instances illustrate the performance of our algorithm.

We introduce an accelerated Langevin-based sampling method that is based on two complementary devices: SamAdams adaptive timestepping, which automatically shrinks the effective integration step in stiff regions of phase space using a relaxed stiffness monitor, and position-adaptive Langevin (PAL) dynamics, which concentrates friction along the local force direction while preserving the canonical distribution as the exact invariant measure. The resulting combined scheme (SA-PAL) is implemented in a palindromic integrator which requires only one force evaluation per iteration through suitable organisation of the integration steps and by exploiting the rank-one-plus-scalar structure of the PAL friction tensor. We test the method on various model problems: the Rosenbrock function, a thin entropic channel, the Mueller-Brown potential, and a Bayesian parameterisation problem with a sparsity-inducing shrinkage prior. On the Rosenbrock and Mueller-Brown potentials mixing rates are improved by 1.5-3 times compared to fixed stepsize integration. Efficiency gains of more than an order of magnitude are documented in the other examples.

This article presents a new estimation scheme for the reliability-oriented Shapley effects when there is a large number of correlated input variables in the model, using a unique sample of failure points. To do so, we first propose a new writing of the reliability-oriented closed Sobol indices involving the marginal densities conditionally to the failure, which may be high-dimensional. Then, we propose to estimate these densities with the available failing samples using Normalizing Flows, powerful tools from generative modeling that enable the estimation of complex high-dimensional densities. In addition, we provide an error estimation procedure relying on the same sample of failing points, which constitutes a new contribution for the estimation of target Shapley effects. Finally, we illustrate our methodology on numerical use-cases, discuss insightful features of our approach and provide prospects for the future.

Instrumental variable regression quantifies causal effects between a possibly confounded treatment variable $ X_2 $ and a response variable $ X_3 $ by leveraging an instrument $ X_1 $. Our work considers the setting where some prior information of the joint distribution of $ X_{123} $ is given, potentially through an initial dataset. However, further samples must be gathered to improve the accuracy of the estimation. We show that under specific parameter configurations in a Gaussian graphical model, taking partial samples from, e.g., $ X_{12} $ can reduce the asymptotic variance of a consistent estimator. This idea is developed by adding a budget constraint over the cost per (partial) sample. The optimization problem is analytically solvable over the real numbers and gives the optimal number of requested partial and complete samples. We provide significance level, power, and sample-size calculations for detecting a non-zero causal effect under optimal budget allocation. Our method can considerably reduce the necessary budget and the number of complete samples. Finally, we showcase the advantages and applicability of adaptive causal effect estimation for automotive analytics and pharmaceutical research.

This paper compares different methods for forecasting the term structure of U.S. and European zero-coupon government bonds using both traditional econometric and Machine Learning (ML) approaches. We compare classical models (e.g., Dynamic Nelson-Siegel (DNS) and Principal Component Analysis (PCA)) with different Neural Network (NN) architectures, including those inspired by the classical models, on the U.S. Treasury market and bonds issued by the European Central Bank (ECB). To enhance predictive performance, macroeconomic variables are incorporated. The findings for both markets are separately analyzed and compared. To this end, we propose a robust model evaluation framework combining statistical accuracy metrics - such as RMSE, MAE, and directional accuracy - with the economic relevance of a quantitative bond trading strategy. Results show that NNs consistently outperform traditional models in both forecasting accuracy and portfolio performance. For the U.S., the most effective approach is a direct-forecasting NN that incorporates DNS factors to reduce the dimensionality of zero-rate data and an Autoencoder (AE) to extract macroeconomic features, while for Europe, the optimal model is a factor-based NN using PCA-derived zero-rate factors without the integration of macroeconomic variables. Overall, the paper demonstrates how combining traditional modeling approaches with modern ML techniques and evaluation can improve yield curve forecasts and support applications in fixed-income portfolio construction.

General smooth models replace parameters of a regular likelihood with additive models. The models can include parametric terms, Gaussian random effects, and smooth functions of covariates. The latter are parameterized via a reduced-rank spline basis and regularized via weighted quadratic penalties placed on the basis coefficients. Estimates for these weights (i.e., smoothing parameters) can be obtained by optimizing the Laplace-approximate Bayesian marginal likelihood. Existing (second-order) methods require the Hessian of the log-likelihood to solve this optimization problem approximately - exact optimization requires up to fourth order derivatives - which can be difficult to derive and expensive to evaluate. To address these problems, we present a quasi-Newton variant of the second-order Extended Fellner-Schall (EFS) optimization method. Our qEFS method relies on structured limited-memory secant approximations to the Hessian of the log-likelihood and is principally first-order. However, the approximation can also be accumulated for a sub-block of the Hessian, with the remaining columns being constrained to match those of the actual Hessian. The exact columns then provide additional structure for the sub-block approximation, which becomes more accurate as a result. We show that the qEFS method converges to the EFS method under certain conditions and continues to provide good estimates beyond these circumstances, which we illustrate in simulation studies. Secondary tasks involving the Hessian (confidence interval coverage & model selection) require partial approximations to achieve close to nominal performance. We provide Hidden Markov and Tweedie model examples, for which the qEFS method is substantially easier to implement than alternative methods.

This text provides an introduction to multiple hypothesis testing. It covers various error criteria and testing procedures, and includes references to relevant R packages. An earlier version of this text served as the lecture notes for a PhD-level course on multiple testing.

Retail and supply chain operations rely on demand forecasts to drive decisions, from replenishment at the product level to capacity planning at the store level. These forecasts should be probabilistic, to allow risk-aware decisions, and coherent across the aggregation hierarchy, so that decisions taken at different levels are not based on conflicting demand forecasts. Producing such forecasts is computationally demanding; at retail scale, with hierarchies of hundreds of thousands of time series, this cost becomes a primary concern. Existing two-step forecast-then-reconcile procedures and end-to-end neural models scale poorly, rely on restrictive assumptions, or require specialized hardware and engineering effort. We propose e2eTD, a scalable method for coherent probabilistic forecasting of large hierarchical and grouped time series. e2eTD directly forecasts only a small subset of aggregate series (about 0.3% of the hierarchy in our experiments), which are smoother and thus more predictable than the intermittent bottom series. The resulting forecast samples are propagated to the bottom level through a novel probabilistic top-down sampling algorithm, in which the historical disaggregation proportions are modeled as joint distributions, estimated in-sample. Since the bottom samples retain the cross-series dependence, summing them yields coherent forecasts for all aggregation levels. On the M5 and Favorita datasets, e2eTD achieves the lowest weighted scaled pinball loss across aggregation levels among all competing methods; it would have ranked 11th of 892 teams in the M5 Uncertainty competition. On a standard laptop, e2eTD runs in about five minutes on M5 ($\sim$40K series) and twenty minutes on Favorita ($\sim$300K series).

Differentially private (DP) training of neural networks is often hindered by the large amount of noise required by gradient-based methods such as DP-SGD, which repeatedly inject high-dimensional noise in parameter space throughout training. In this paper, we propose a new framework for DP learning that avoids iterative optimization in parameter space. Instead of updating the target model using privatized gradients, we employ a hypernetwork trained on public datasets to map a private dataset to the parameters of the target model. Specifically, each example is embedded into a low-dimensional representation, the embeddings are aggregated and perturbed to obtain a DP dataset embedding, and the hypernetwork generates the target model parameters from this noisy embedding. Because privacy noise is injected only once into a low-dimensional dataset representation, our approach can significantly reduce the adverse effect of noise. We theoretically show in a synthetic setting that, under a fixed privacy budget, models produced by our approach achieve higher utility than those trained with DP-SGD. Moreover, we apply our approach to LoRA fine-tuning of diffusion models and show that it achieves lower FID than LoRA models trained with DP-SGD and other public-data-guided methods.

In this paper, we study Nyström subsampling for vector-valued regression in vector-valued reproducing kernel Hilbert spaces. Standard kernel methods often suffer from prohibitive computational costs due to the construction and inversion of large kernel matrices, which limits their scalability to large datasets. To overcome this bottleneck, we propose an efficient operator learning algorithm based on Nyström subsampling that accommodates functional outputs. Under general source conditions characterized by index functions-extending beyond the classical Hölder-type and operator-monotone frameworks-we establish minimax-optimal convergence rates for the proposed estimator. As an application of the proposed framework, we consider function denoising problems. Unlike classical denoising methods, which are typically tailored to specific signal representations or noise models, our approach formulates denoising within a general operator learning framework. Numerical experiments on signal denoising, real-time audio denoising, image denoising, inverse Radon transform reconstruction, and energy-efficiency prediction confirm that the proposed method achieves performance comparable to full kernel methods while substantially reducing computational cost.

Weak instruments are a well known limitation for valid causal inference in Mendelian randomization studies. In the single exposure setting, weak instrument bias can be mitigated by selecting genetic instruments which are strongly associated with the exposure according to p-value and/or F-statistic thresholds. However, in the multi-exposure setting, genetic instruments may be strongly associated with an exposure but weakly associated with it conditional on all other exposures in the analysis. It is therefore more difficult to guarantee conditionally strong instruments in multivariable Mendelian randomization. Weak instrument bias can be mitigated using modelling approaches, however there are fewer methods for doing this in the multivariable case compared with the single exposure case. In this paper, we consider a method for mitigating weak instrument bias in multivariable Mendelian randomization using a Bayesian framework: MVMR-Pony. We compare this method with existing frequentist methods. We show using simulation studies that the MVMR-Pony method outperforms the frequentist approaches with respect to bias, coverage, type I error rates, and power, across settings where weak instrument bias arises due to correlated genetic effects, measurement error, and mediation.

Quadratic inference functions (QIF) provide a robust and efficient alternative to generalized estimating equations (GEE) for marginal regression with correlated data, particularly in cluster randomized trials (CRTs). However, existing QIF methodology does not account for confounding due to covariate imbalance between treatment arms, a common concern in observational CRTs or CRTs with prognostic covariate adjustment. We propose a doubly robust QIF (DR-QIF) estimator that combines doubly robust pseudo-outcomes, constructed from propensity score and outcome regression models, with the QIF extended score equations. The DR-QIF estimator is consistent for the average treatment effect when either the propensity score model or the outcome regression model is correctly specified, but not necessarily both. We show that DR-QIF is more efficient than doubly robust GEE (DR-GEE) when the working correlation structure is misspecified, and we characterize the asymptotic efficiency gain analytically. For cross-sectional CRTs the two estimators are algebraically identical; efficiency gains emerge in longitudinal CRTs with strong temporal correlation, reaching 3.5% at N=120 and T=8 repeated measures. Finite-sample properties are evaluated via Monte Carlo simulation, and the method is illustrated using data from the WASH Benefits Kenya cluster randomized trial.

Polynomial Stein discrepancies (PSD) provide a scalable alternative to kernel Stein methods for measuring sample quality and goodness-of-fit testing, but their statistical properties remain poorly understood. We show that increasing polynomial degree primarily amplifies signal without adequately controlling variance, rather than directly optimising the signal-to-noise ratio (SNR). Under suitable assumptions, this might lead to a failure mode in which the $\text{SNR}^2$ can provably decay exponentially with polynomial degree. Motivated by this observation, we reformulate Stein discrepancy construction as an explicit $\text{SNR}^2$ maximisation problem, yielding a Rayleigh quotient over Stein features. This perspective motivates $\lambda$-PSD, an approximate scalable covariance-aware reweighting scheme defined in a low-dimensional subspace. Under Gaussian settings, we show that $\lambda$-PSD avoids the exponential $\text{SNR}^2$ collapse and achieves a stable $\text{SNR}^2$. Empirically, $\lambda$-PSD substantially improves test power while retaining linear-time complexity in the number of samples, highlighting the importance of SNR-aware design for scalable Stein discrepancies.

Robust regression methods, particularly MM-estimators, are essential for analyzing datasets where heavy-tailed noise or high-leverage outliers may be present. Algorithms to compute these estimators are iterative and rely on having a good initial point. A widely-used probabilistic approach to obtaining an initial regression estimator that is not affected by outliers consists of fitting linear regression models to many random subsets of the training data. Unfortunately, the number of subsets that need to be considered in order to have a high probability of finding one that is clean of outliers grows exponentially with the number of predictors. This renders the approach unfeasible for models with a moderate to large numbers of variables. Alternative non-stochastic strategies that have been proposed recently also fail to scale well when the number of parameters and observations are large. To overcome this problem, we propose a highly scalable algorithm based on block-coordinate descent. Our Robust Orthogonal Block Updates (ROBU) algorithm uses lower-dimensional blocks of explanatory variables, which require much fewer sub-samples to find a good initial point with high probability. Extensive simulations and a proteogenomics data application illustrate the robustness properties of the estimators computed with ROBU and demonstrate that they compare favourably to those calculated with existing algorithms.

Case-control studies are widely used in epidemiology and biomedical research because they provide substantial efficiency gains when outcomes are rare or prospective follow-up is impractical. However, retrospective outcome-dependent sampling distorts the population outcome distribution, creating fundamental challenges for causal inference. We propose a unified three-stage weighting (3S-weighting) framework for causal inference and causal mediation analysis from case–control studies. The proposed approach first estimates the unknown population outcome prevalence using density-ratio learning and label-shift correction combined with externally available covariate information. Next, prevalence-based design weights are used to reconstruct the target population distribution from the retrospective sample. Finally, stabilized causal and mediation weights are applied within a marginal structural modeling framework to estimate total and pathway-specific causal effects, including the pure direct effect, pure indirect effect, and interaction effect. Simulation studies demonstrate that conventional analyses that ignore retrospective sampling can produce substantial bias in both total and mediation effect estimates, whereas the proposed approach consistently recovers the target population causal parameters across a range of sampling scenarios. An application of data from the National Health and Nutrition Examination Survey further illustrates the practical implementation and utility of the proposed framework.

Bayesian filtering of partially and noisily observed dynamical systems seeks to infer the evolving conditional distribution of the state of a dynamical system given observations, in an online fashion. This Bayesian filtering distribution is rarely available as a supervised learning target. However, one can often use the forecast model to generate synthetic trajectories, with corresponding synthetic observations. We introduce the proper scoring ensemble filter (PSEF), an ensemble data assimilation method trained using only synthetic trajectories. The analysis step is represented as a permutation-equivariant, transformer-based map. Training is based on strictly proper scoring rules—with the energy score used in our implementation—so that probabilistic accuracy is rewarded over the whole probability distribution. Under a realizability assumption, the population mean-field objective is minimized by the true Bayesian filtering distribution. Our methodology allows the same learned parameters to be shared between different ensemble sizes, subject to an ensemble-dependent fine-tuning. Numerical experiments show that the learned filter accurately approximates challenging filtering distributions, including highly non-Gaussian and multi-modal posteriors, and achieves stronger performance in data assimilation tasks than classical methods or learning-based methods with mean-squared-error objectives.

The general Bayesian approach provides a flexible framework by introducing a loss-based likelihood with a learning rate controlling the relative weight of the likelihood and prior. This flexibility creates an important calibration problem under model misspecification, where the conventional Bayesian information identity fails and uncalibrated Gibbs posteriors may not provide reliable uncertainty quantification. We propose a method for selecting the learning rate by minimizing a weighted Fisher divergence between the asymptotic general posterior and a normal distribution with sandwich-type covariance, yielding a closed-form calibrated learning rate. The proposed framework includes Fisher information matching as a special case and, for an important choice of the weight matrix, yields a learning rate no larger than the Fisher information matching rate. This leads to a more dispersed posterior and can reduce the risk of undercoverage. The framework also includes a learning rate based on Kullback–Leibler divergence as a special case. Numerical examples show that the proposed method tends to mitigate undercoverage under model misspecification, while real-data analyses illustrate its practical applicability.

Large language models (LLMs) are increasingly used as components of agentic systems that observe, plan, and act. In finance, even "assistive" systems become decision-relevant once their outputs are used to size trades or allocate risk. A key failure mode is the confidence–competence gap: a model that is only slightly better than chance but consistently overconfident will, under typical bet-sizing rules, generate negative long-run growth. Existing benchmarks emphasize semantic understanding or point accuracy, but do not directly test probabilistic calibration under the temporal constraints and non-stationarity that define real markets. We introduce FinBench, a benchmark designed to evaluate calibration and uncertainty quality for financial forecasting in a setting that is (i) strictly time-gated to avoid look-ahead bias and (ii) evaluated with strictly proper scoring rules that penalize hallucinated confidence. FinBench tasks require models to output (a) a probability of positive return and (b) an 80% prediction interval for realized log return; evaluation uses the Brier score and the Winkler interval score, along with skill scores against hard baselines. This paper describes the benchmark specification and reports a small pilot run (one trading day; three liquid tickers; 33 forecasts) as a sanity check of the pipeline. The pilot illustrates how calibration-sensitive metrics distinguish between "confident but fragile" behavior and uncertainty-aware forecasting.

Non-coherent Grassmannian (unitary space-time) signaling detects on the received subspace, which is invariant to a branch-side (polarization or mode-coupling) rotation and to a phase that is constant over the coherence block. It therefore needs no carrier-phase or polarization recovery within the block and is robust to phase noise when the per-block phase drift is small, while a multi-branch (polarization or spatial) front end harvests diversity without channel estimation or pilots. However, the Grassmannian-constellation literature usually assumes a distortion-free, linear channel and transmitter and already-acquired symbol timing. This paper closes both gaps while reusing off-the-shelf Grassmannian packings. First, we impose a constant-modulus (low peak-to-average-power-ratio, PAPR) constraint on the constellation and quantify the PAPR/chordal-distance trade-off: a constant-modulus design lowers the 0.1% PAPR from 6.1 dB (unconstrained) to 3.6 dB – 1.6 dB below 16-QAM (5.2 dB) – easing the optical modulator linear range and the fiber Kerr-nonlinearity penalty, at a ~1.8 dB cost in high-SNR coding gain. Second, we derive a phase-blind subspace timing-error detector (TED) that exploits the invariance of the GLRT projection energy to the unknown carrier phase, plus a feedforward acquisition metric, supplying clock recovery without prior carrier or polarization recovery. The TED yields a clean S-curve with a stable lock point for roll-offs down to beta=0.1. Under block fading the proposed estimator attains genie-timing SER within a fraction of a dB and recovers full diversity, whereas an uncorrected 0.35-symbol timing offset floors the error rate near 0.4. Results use a symbol-rate block-fading abstraction; full fiber, modulator, and phase-noise modeling is future work. The scheme combines low PAPR with the diversity and phase-recovery-free operation of non-coherent reception.

This paper presents a probabilistic framework for online test-time adaptation problems. In them, a model is trained on labeled data but must adapt to unlabeled data at test time under the assumption that training and test distributions potentially differ, that is, there might have been a distributional shift. The framework is based on a state-space modelling architecture from which parameter learning, parameter time evolution, prior tuning, and prediction can be characterized.

The dependence of evolutionary rate estimates on the timeframe of sampling poses a fundamental challenge for reconstructing evolutionary histories from molecular sequence data, which is central to evolutionary biology and infectious disease research. We present a novel and flexible approach to accommodate time-varying evolutionary rates by modeling the sequence substitution process using inhomogeneous continuous-time Markov chains (ICTMCs) acting along the branches of the phylogeny, and parameterizing the log transformed rate as a smooth function of time using a cubic B-spline basis expansion. Following the parlance of phylogenetics that refers to rates of molecular substitutions as molecular clocks, we call this a spline clock model. Integrals of the rate function over all branches, required for likelihood evaluation, are approximated efficiently using Gauss-Legendre quadrature, and smoothness is enforced by assigning a Gaussian Markov random field prior to the spline coefficients. Through a simulation study, we demonstrate that the spline clock model recovers the true time-varying rates more accurately and with tighter credible intervals than competing clock models. We apply the spline clock model to examine the evolutionary rate of foamy virus and the rate of spatial diffusion of SARS-CoV-2 across Europe, recovering strong time-varying signal in both settings.

Standard maximum likelihood estimation of polychoric correlations is highly sensitive to contamination in survey data, including response errors, interviewer effects, and careless responding, yet assigns equal weight to all observations regardless of data quality. We develop robust estimators for polychoric correlation under complex survey designs based on two minimum divergence criteria – Hellinger distance (HD) and negative exponential disparity (NED) – incorporating survey weights through Horvitz–Thompson adjusted cell frequencies. For HD, we propose penalized Ridge and Lasso variants that regularize nuisance parameters while leaving the correlation unpenalized, and establish consistency and asymptotic normality with a sandwich covariance reflecting the sampling design. The influence function is finite but not uniformly bounded, reflecting Hellinger's sensitivity to sparse cells. Simulations under Poisson proportional-to-size sampling examine three contamination geometries – concordant upper, concordant lower, and discordant mixed corner – crossed with standard and non-standard latent marginals. The two estimator classes offer complementary advantages: penalized HD methods achieve the lowest mean squared error under concordant contamination, while NED performs best under discordant contamination and under compound misspecification–contamination effects. We provide practical guidelines for method selection based on anticipated contamination patterns in survey practice.

Matrix completion seeks to recover a low-rank matrix from a sparse and noisy subset of its entries. In many applications, such as recommendation systems and urban mobility, the observed matrix is accompanied by auxiliary covariates on its rows and columns and exhibits dependence across them. We propose Incomplete Matrix Regression (IMR), a distribution-free penalized regression framework that integrates such information into matrix completion. The target matrix is modeled as the sum of intercepts, covariate effects regularized by a Lasso penalty, and a low-rank latent component that captures structure unexplained by the covariates. Known similarity structures, such as spatial and temporal kernels, are incorporated through ridge-type penalties on the latent factors. For estimation, we provide a scalable alternating least-squares algorithm whose modular form allows us to include or exclude individual model components without rederiving the updates. We establish non-asymptotic error bounds for both the Lasso and matrix completion estimators that are consistent with standard rates in their respective literature. Through simulation studies and two real-data applications, we demonstrate that the proposed method attains predictive accuracy competitive with more complex methods at a small fraction of their computational cost. The methodology is implemented in the R package IMR.

We present an outlier identification method for mixed type data sets comprising continuous and ordinal variables. We define outliers based on using a multivariate Gaussian distribution as reference distribution for non-outliers, with a latent Gaussian assumed for ordinal variables. The proposed algorithm is based on the robust Minimum Covariance Determinant estimator for estimating the parameters of the multivariate Gaussian for the non-outliers. This is extended to account for the fact that the full Gaussian information underlying the ordinal variables is not observed. A breakdown theorem shows that replacing observations will noty stop extreme enough outliers from being identified. The effectiveness of our approach is demonstrated via simulations on synthetic data with various types of contamination, achieving high detection and low false positive rates. Practical relevance is illustrated through an application to Airbnb listing data containing both continuous and ordinal attributes.

Monitoring species occurrence is essential for understanding biodiversity change, informing conservation decisions, and assessing the impact of environmental pressures on ecosystems. Species occurrence data arise from different survey designs, and the statistical literature has developed distinct corresponding modelling approaches, namely occupancy models, species distribution models, and presence-only methods, whose fundamental connections have remained largely unrecognised. We argue that these are all special cases of a single hierarchical observation process. To make these connections explicit, we introduce a unified terminology centred on two data types: detection/non-detection data with T visits (DN-T) and detection-only data (DO), where DN-T with T>1 corresponds to traditional occupancy modelling, DN-1 to species distribution modelling, and DO to what the literature commonly, but we argue inaccurately, calls presence-only data. Within this framework, we study the identifiability of DO models and propose a novel hierarchical model for DO data that, for the first time, explicitly accounts for both false positive and false negative detection errors. Identifiability is achieved through prior distributions that express the natural belief that a species is more likely to be recorded where it is present than where it is absent. ...

This work proposes a framework for sampling from the Gibbs distribution of a given potential using hybrid stochastic dynamics. In this framework, two distinct sampling dynamics are run in different regions of the state space. The two dynamics are coupled across the interface through natural transmission conditions that preserve the target distribution. Using a specially constructed regularization scheme, we establish an exponential rate of convergence for the hybrid dynamics to equilibrium. We also analyze the metastability properties of the hybrid dynamics in a radially symmetric landscape, showing that the hybrid scheme can improve the mean exit time. This advantage is further confirmed by the numerical experiments.

In observational settings, where the data generating process and possibly the sample size are not controlled, it is typically impossible to guarantee a priori that quantities of interest will be estimated with sufficient precision. However, even when the data do not determine the quantities of interest, they may still allow determination of what is missing – unobserved information which, if observed, would meaningfully reduce uncertainty. We propose an interactive visualization system, termed variance deltas, to enable the discovery of such missing information from a Bayesian posterior distribution. This system, which we provide as a software package, represents missing information as subsets of unobserved model quantities, organized into a tree based on how well each subset explains uncertainty about the quantity of interest. This system both automates the construction of candidate subsets from minimal user input and implements interactive operations for the division and combination of subsets, allowing the efficient discovery of interesting and useful explanations. We demonstrate this system by using it to discover nonobvious explanations of uncertainty for (1) a treatment effect parameter in a simulated causal inference problem and (2) a population proportion in a forecasting model of real polling data with many sources of bias.

Explainability is increasingly recognized as a key aspect of outlier detection. However, for complex data structures such as interval-valued data, it remains largely unexplored. Building on an outlier detection framework based on the Interval Minimum Covariance Determinant estimator, we propose a novel approach to explain the outlyingness of interval-valued observations using the concept of the Shapley value. We derive a closed-form expression for the Shapley value of the squared robust Interval-Mahalanobis distance, enabling efficient computation of variable contributions. This formulation allows for a fine-grained interpretation of outliers, providing a detailed decomposition into contributions from centers, ranges, and cross-terms of the interval-valued observations. Moreover, the Shapley value is closely connected to the concept of cellwise outliers, as it can help identify variable-specific outliers that may not be evident at multivariate level. We further extend the framework through the Shapley interaction index to capture pairwise variable interactions driving atypical behavior. The practical utility of the proposed approach is illustrated through two real-world datasets.