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Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of…
Frequentist robust variable selection has been extensively investigated in high-dimensional regression. Despite success, developing the corresponding statistical inference procedures remains a challenging task. Recently, tackling this…
Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability…
Large Language Models (LLMs) are increasingly deployed across diverse domains, raising the need for rigorous reliability assessment methods. Existing benchmark-based evaluations primarily offer descriptive statistics of model accuracy over…
We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…
Approximate Bayesian Computation (ABC) methods often require extensive simulations, resulting in high computational costs. This paper focuses on multifidelity simulation models and proposes a pre-filtering hierarchical importance sampling…
We propose and illustrate a hierarchical Bayesian approach for matching statistical records observed on different occasions. We show how this model can be profitably adopted both in record linkage problems and in capture--recapture setups,…
Factorial hidden Markov models (FHMMs) are powerful tools of modeling sequential data. Learning FHMMs yields a challenging simultaneous model selection issue, i.e., selecting the number of multiple Markov chains and the dimensionality of…
A major focus of causal inference is the estimation of heterogeneous average treatment effects (HTE) - average treatment effects within strata of another variable of interest such as levels of a biomarker, education, or age strata.…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest.…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
We introduce a novel ensemble approach for feature selection based on hierarchical stacking for non-stationarity and/or a limited number of samples with a large number of features. Our approach exploits the co-dependency between features…
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as…
Few Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing…
In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation…