Related papers: Objective Bayesian approach to the Jeffreys-Lindle…

We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of…

In practical situations, most experimental designs often yield unbalanced data which have different numbers of observations per unit because of cost constraints, or missing data, etc. In this paper, we consider the Bayesian approach to…

For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution…

The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…

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…

Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…

We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically…

Motivated by the statistical evaluation of complex computer models, we deal with the issue of objective prior specification for the parameters of Gaussian processes. In particular, we derive the Jeffreys-rule, independence Jeffreys and…

We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise,…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…

We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…

Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same…

Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also…

An important aspect of Bayesian model selection is how to deal with huge model spaces, since exhaustive enumeration of all the models entertained is unfeasible and inferences have to be based on the very small proportion of models visited.…

Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…

A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…

We are entering an era where progress in cosmology is driven by data, and alternative models will have to be compared and ruled out according to some consistent criterium. The most conservative and widely used approach is Bayesian model…

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…