Related papers: Large-Scale Multiple Hypothesis Testing with the N…

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…

This paper explores the multiple testing problem for sparse high-dimensional data with binary outcomes. We propose novel empirical Bayes multiple testing procedures based on a spike-and-slab posterior and then evaluate their performance in…

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…

This paper outlines a framework for quantifying the prior's contribution to posterior inference in the presence of prior-likelihood discordance, a broader concept than the usual notion of prior-likelihood conflict. We achieve this dual…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…

We investigate the credible sets and marginal credible intervals resulting from the horseshoe prior in the sparse multivariate normal means model. We do so in an adaptive setting without assuming knowledge of the sparsity level (number of…

We consider the problem of comparing two Poisson parameters from the Bayesian perspective. Kawasaki and Miyaoka (2012b) proposed the Bayesian index $P(\lambda_1 < \lambda_2 | X_1,X_2)$ and expressed it using the hypergeometric series. In…

One of the core facets of Bayesianism is in the updating of prior beliefs in light of new evidence$\text{ -- }$so how can we maintain a Bayesian approach if we have no prior beliefs in the first place? This is one of the central challenges…

We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish…

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

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…

We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and…

We consider Bayesian multiple statistical classification problem in the case where the unknown source distributions are estimated from the labeled training sequences, then the estimates are used as nominal distributions in a robust…

Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients…

Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…

The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures…

In a bivariate meta-analysis the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Bayesian inference is attractive as informative priors that add small amount of information can…

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…

Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…