Related papers: On The Distribution of Bayesian Evidences

The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…

Bayesian modeling provides a principled approach to quantifying uncertainty in model parameters and model structure and has seen a surge of applications in recent years. Within the context of a Bayesian workflow, we are concerned with model…

A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…

A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…

We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss…

One of the big challenges in astrophysics is the comparison of complex simulations to observations. As many codes do not directly generate observables (e.g. hydrodynamic simulations), the last step in the modelling process is often a…

Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…

Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…

We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To…

Model selection for regression problems with an increasing number of covariates continues to be an important problem both theoretically and in applications. Model selection consistency and mean structure reconstruction depend on the…

We collect in this note some observations on the role of symmetries in Bayesian inference problems, that can be useful or detrimental depending on the way they act on the signal and on the observations. We emphasize in particular the need…

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…