Related papers: Prior Sensitivity Analysis without Model Re-fit
This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a…
Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
The rising interest in Bayesian deep learning (BDL) has led to a plethora of methods for estimating the posterior distribution. However, efficient computation of inferences, such as predictions, has been largely overlooked with Monte Carlo…
Bayes factor sensitivity analysis examines how the evidence for one hypothesis over another depends on the prior distribution. In complex models, the standard approach refits the model at each hyper-parameter value, and the total…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a…
Simultaneous predictive distributions for independent Poisson observables are investigated. A class of improper prior distributions for Poisson means is introduced. The Bayesian predictive distributions based on priors from the introduced…
Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria…
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…
Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…
Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process,…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are…
The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. We rigorously derive…
We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer…
In many applications in biology, engineering and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical…
Sensitivity analysis of a numerical model, for instance simulating physical phenomena, is useful to quantify the influence of the inputs on the model responses. This paper proposes a new sensitivity index, based upon the modification of the…
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…
This paper deals with a new Bayesian approach to the standard one-sample $z$- and $t$- tests. More specifically, let $x_1,\ldots,x_n$ be an independent random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. The…