Related papers: Bayesian Hierarchical Models and the Maximum Entro…

In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…

Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…

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…

Hierarchical models are increasingly used in many applications. Along with this increased use comes a desire to investigate whether the model is compatible with the observed data. Bayesian methods are well suited to eliminate the many…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…

There are many issues that can cause problems when attempting to infer model parameters from data. Data and models are both imperfect, and as such there are multiple scenarios in which standard methods of inference will lead to misleading…

Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…

In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulation. A variety of model formulations for the latent level…

The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach…

Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…

High-dimensional Bayesian procedures often exhibit behavior that is effectively low dimensional, even when the ambient parameter space is large or infinite-dimensional. This phenomenon underlies the success of shrinkage priors,…

Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…

We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution…

In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is…

The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly,…

Data containing human or social attributes may over- or under-represent groups with respect to salient social attributes such as gender or race, which can lead to biases in downstream applications. This paper presents an algorithmic…

The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant…

A principle of hierarchical entropy maximization is proposed for generalized superstatistical systems, which are characterized by the existence of three levels of dynamics. If a generalized superstatistical system comprises a set of…

Multi-level normal hierarchical models, also interpreted as mixed effects models, play an important role in developing statistical theory in multi-parameter estimation for a wide range of applications. In this article, we propose a novel…