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The real-world testing of decisions made using causal machine learning models is an essential prerequisite for their successful application. We focus on evaluating and improving contextual treatment assignment decisions: these are…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of…
Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…
Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been…
The problem of estimating the mean of a normal vector with known but unequal variances introduces substantial difficulties that impair the adequacy of traditional empirical Bayes estimators. By taking a different approach, that treats the…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
Experimental design techniques such as active search and Bayesian optimization are widely used in the natural sciences for data collection and discovery. However, existing techniques tend to favor exploitation over exploration of the search…
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal…
In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
In medical research, a scenario often entertained is randomized controlled $2^2$ factorial design with a binary outcome. By utilizing the concept of potential outcomes, Dasgupta et al. (2015) proposed a randomization-based causal inference…
Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected…
We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…
We study stochastic gradient descent for solving conditional stochastic optimization problems, in which an objective to be minimized is given by a parametric nested expectation with an outer expectation taken with respect to one random…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…
Monte Carlo integration becomes prohibitively expensive when each sample requires a high-fidelity model evaluation. Multi-fidelity uncertainty quantification methods mitigate this by combining estimators from high- and low-fidelity models,…
The hybrid approach to experimental design aims to control frequentist operating characteristics of Bayesian decision procedures. These operating characteristics are assessed by simulating sampling distributions of posterior summaries under…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…