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In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are…

The classic frequentist theory of hypothesis testing developed by Neyman, Pearson and Fisher has a claim to being the twentieth century's most influential piece of applied mathematics. Something new is happening in the twenty-first century:…

Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…

Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient…

Suppose that we wish to estimate a vector $\mathbf{x}$ from a set of binary paired comparisons of the form "$\mathbf{x}$ is closer to $\mathbf{p}$ than to $\mathbf{q}$" for various choices of vectors $\mathbf{p}$ and $\mathbf{q}$. The…

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…

Analogues of the frequentist chi-square and F tests are proposed for testing goodness-of-fit and consistency for Bayesian models. Simple examples exhibit these tests' detection of inconsistency between consecutive experiments with identical…

When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…

A staple of Bayesian model comparison and hypothesis testing, Bayes factors are often used to quantify the relative predictive performance of two rival hypotheses. The computation of Bayes factors can be challenging, however, and this has…

A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…

As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…

We consider situations in Bayesian analysis where we have a family of priors $\nu_h$ on the parameter $\theta$, where $h$ varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity…

Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN…

Variational inference is a general framework to obtain approximations to the posterior distribution in a Bayesian context. In essence, variational inference entails an optimization over a given family of probability distributions to choose…

We examine necessary and sufficient conditions for posterior consistency under $g$-priors, including extensions to hierarchical and empirical Bayesian models. The key features of this article are that we allow the number of regressors to…

We develop a new method for frequentist multiple testing with Bayesian prior information. Our procedure finds a new set of optimal p-value weights called the Bayes weights. Prior information is relevant to many multiple testing problems.…

Many penalized maximum likelihood estimators correspond to posterior mode estimators under specific prior distributions. Appropriateness of a particular class of penalty functions can therefore be interpreted as the appropriateness of a…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…

The paper proposes a linesearch for a primal-dual method. Each iteration of the linesearch requires to update only the dual (or primal) variable. For many problems, in particular for regularized least squares, the linesearch does not…

When combining apparently inconsistent experimental results, one often implements errors on errors. The Particle Data Group's phenomenological prescription offers a practical solution but lacks a firm theoretical foundation. To address…