Related papers: Generalization of Jeffreys' divergence based prior…

In reliability engineering, data about failure events is often scarce. To arrive at meaningful estimates for the reliability of a system, it is therefore often necessary to also include expert information in the analysis, which is…

The recently developed semi-parametric generalized linear model (SPGLM) offers more flexibility as compared to the classical GLM by including the baseline or reference distribution of the response as an additional parameter in the model.…

An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…

We look at the distribution of the Bayesian evidence for mock realizations of supernova and baryon acoustic oscillation data. The ratios of Bayesian evidences of different models are often used to perform model selection. The significance…

Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…

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…

In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are…

Deep Bayesian neural networks (BNNs) are a powerful tool, though computationally demanding, to perform parameter estimation while jointly estimating uncertainty around predictions. BNNs are typically implemented using arbitrary…

The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated…

While diffusion priors generate high-quality posterior samples across many inverse problems, they are often trained on limited training sets or purely simulated data, thus inheriting the errors and biases of these underlying sources.…

Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over…

In social and biomedical sciences testing in contingency tables often involves order restrictions on cell-probabilities parameters. We develop objective Bayes methods for order-constrained testing and model comparison when observations…

This paper studies Bayesian variable selection in linear models with general spherically symmetric error distributions. We propose sub-harmonic priors which arise as a class of mixtures of Zellner's g-priors for which the Bayes factors are…

Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t-test. In contrast, the Bayesian versions of the t-test have languished in obscurity. In recent years, however, the theoretical and practical…

In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…

We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…

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…

Bayesian model selection with improper priors is not well-defined because of the dependence of the marginal likelihood on the arbitrary scaling constants of the within-model prior densities. We show how this problem can be evaded by…

Bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses, taken as a random vector, are quantized. Nearest neighbor and centroid conditions are derived using mean Bayes risk error as a distortion measure…

The Bayes factor, the data-based updating factor from prior to posterior odds, is a principled measure of relative evidence for two competing hypotheses. It is naturally suited to sequential data analysis in settings such as clinical trials…