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Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a…

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset…

The present paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and…

In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in…

The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the…

This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…

Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…

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…

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

The importance of interpretability of machine learning models has been increasing due to emerging enterprise predictive analytics, threat of data privacy, accountability of artificial intelligence in society, and so on. Piecewise linear…

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…

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…

Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces…

The well-known Bayes theorem assumes that a posterior distribution is a probability distribution. However, the posterior distribution may no longer be a probability distribution if an improper prior distribution (non-probability measure)…

Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and the data are drawn from the prior and the model…

Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…

Following the critical review of Seaman et al. (2012), we reflect on what is presumably the most essential aspect of Bayesian statistics, namely the selection of a prior density. In some cases, Bayesian inference remains fairly stable under…