Related papers: Optimal Multiple Testing Under a Gaussian Prior on…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…
We consider large-scale studies in which it is of interest to test a very large number of hypotheses, and then to estimate the effect sizes corresponding to the rejected hypotheses. For instance, this setting arises in the analysis of gene…
We consider a problem of recovering a high-dimensional vector $\mu$ observed in white noise, where the unknown vector $\mu$ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family…
One of the primary goals of statistical precision medicine is to learn optimal individualized treatment rules (ITRs). The classification-based, or machine learning-based, approach to estimating optimal ITRs was first introduced in…
In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…
Many scientific questions in biomedical, environmental, and psychological research involve understanding the effects of multiple factors on outcomes. While factorial experiments are ideal for this purpose, randomized controlled treatment…
This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
When characterizing materials, it can be important to not only predict their mechanical properties, but also to estimate the probability distribution of these properties across a set of samples. Constitutive neural networks allow for the…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
Power and sample size analysis comprises a critical component of clinical trial study design. There is an extensive collection of methods addressing this problem from diverse perspectives. The Bayesian paradigm, in particular, has attracted…
Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of…
In the management of most chronic conditions characterized by the lack of universally effective treatments, adaptive treatment strategies (ATSs) have been growing in popularity as they offer a more individualized approach, and sequential…
We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…
Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world…
Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of…
Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with…
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…