Related papers: Computational approaches for empirical Bayes metho…

Consider a Bayesian situation in which we observe $Y \sim p_{\theta}$, where $\theta \in \Theta$, and we have a family $\{ \nu_h, \, h \in \mathcal{H} \}$ of potential prior distributions on $\Theta$. Let $g$ be a real-valued function of…

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…

We propose a cautious Bayesian variable selection routine by investigating the sensitivity of a hierarchical model, where the regression coefficients are specified by spike and slab priors. We exploit the use of latent variables to…

Bayesian aggregation lets election forecasters combine diverse sources of information, such as state polls and economic and political indicators: as in our collaboration with The Economist magazine. However, the demands of real-time…

For in vivo research experiments with small sample sizes and available historical data, we propose a sequential Bayesian method for the Behrens-Fisher problem. We consider it as a model choice question with two models in competition: one…

Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…

Determining the sensitivity of the posterior to perturbations of the prior and likelihood is an important part of the Bayesian workflow. We introduce a practical and computationally efficient sensitivity analysis approach using importance…

The measurement of the efficiency of an event selection is always an important part of the analysis of experimental data. The statistical techniques which are needed to determine the efficiency and its uncertainty are reviewed. Frequentist…

Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice.…

This paper presents a Markov chain Monte Carlo method to generate approximate posterior samples in retrospective multiple changepoint problems where the number of changes is not known in advance. The method uses conjugate models whereby the…

Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…

While observational data are routinely used to estimate causal effects of biomedical treatments, doing so requires special methods to adjust for observed confounding. These methods invariably rely on untestable statistical and causal…

Bayesian model comparison implements Occam's razor through its sensitivity to the prior. However, prior-dependence makes it important to assess the influence of plausible alternative priors. Such prior sensitivity analyses for the Bayesian…

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

Databases often contain corrupted, degraded, and noisy data with duplicate entries across and within each database. Such problems arise in citations, medical databases, genetics, human rights databases, and a variety of other applied…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…

In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes…