Related papers: Joint Specification of Model Space and Parameter S…
A transformation group approach to the prior for the parameters of the beta distribution is suggested which accounts for finite sets of data by imposing a limit to the range of parameter values under consideration. The relationship between…
We introduce a Bayesian prior distribution, the Logit-Normal continuous analogue of the spike-and-slab (LN-CASS), which enables flexible parameter estimation and variable/model selection in a variety of settings. We demonstrate its use and…
Two Bayesian models with different sampling densities are said to be marginally equivalent if the joint distribution of observables and the parameter of interest is the same for both models. We discuss marginal equivalence in the general…
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…
Spatially dependent data arises in many applications, and Gaussian processes are a popular modelling choice for these scenarios. While Bayesian analyses of these problems have proven to be successful, selecting prior distributions for these…
Prior sensitivity analysis is a fundamental method to check the effects of prior distributions on the posterior distribution in Bayesian inference. Exploring the posteriors under several alternative priors can be computationally intensive,…
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
We study probit regression from a Bayesian perspective and give an alternative form for the posterior distribution when the prior distribution for the regression parameters is the uniform distribution. This new form allows simple Monte…
In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…
We show that a language model's ability to predict text is tightly linked to the breadth of its embedding space: models that spread their contextual representations more widely tend to achieve lower perplexity. Concretely, we find that…
The use of improper priors in the context of Bayesian hierarchical linear mixed models has been studied under the assumption of normality of the random effects. We study the propriety of the posterior under more flexible distributional…
A central characteristic of Bayesian statistics is the ability to consistently incorporate prior knowledge into various modeling processes. In this paper, we focus on translating domain expert knowledge into corresponding prior…
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…
Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…
This paper studies the influence of perturbations of conjugate priors in Bayesian inference. A perturbed prior is defined inside a larger family, local mixture models, and the effect on posterior inference is studied. The perturbation, in…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
Bayesian inferences in high energy physics often use uniform prior distributions for parameters about which little or no information is available before data are collected. The resulting posterior distributions are therefore sensitive to…
We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the "true" solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and…
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…