Related papers: Singular prior distributions and ill-conditioning …
We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional…
Bayesian hierarchical models are frequently used in practical data analysis contexts. One interpretation of these models is that they provide an indirect way of assigning a prior for unknown parameters, through the introduction of…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…
We develop singular value shrinkage priors for the mean matrix parameters in the matrix-variate normal model with known covariance matrices. Our priors are superharmonic and put more weight on matrices with smaller singular values. They are…
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…
The Bradley-Terry model assigns probabilities for the outcome of paired comparison experiments based on strength parameters associated with the objects being compared. We consider different proposed choices of prior parameter distributions…
In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated…
We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…
Structural missingness breaks 'just impute and train': values can be undefined by causal or logical constraints, and the mask may depend on observed variables, unobserved variables (MNAR), and other missingness indicators. It simultaneously…
When complex Bayesian models exhibit implausible behaviour, one solution is to assemble available information into an informative prior. Challenges arise as prior information is often only available for the observable quantity, or some…
In statistical problems, a set of parameterized probability distributions is used to estimate the true probability distribution. If Fisher information matrix at the true distribution is singular, then it has been left unknown what we can…
Generalized linear models (GLMs) have been used widely for modelling the mean response both for discrete and continuous random variables with an emphasis on categorical response. Recently Yang, Mandal and Majumdar (2013) considered full…
Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…
We propose a new model selection method, the posterior averaging information criterion, for Bayesian model assessment from a predictive perspective. The theoretical foundation is built on the Kullback-Leibler divergence to quantify the…
We study prior distributions for Poisson parameter estimation under $L^1$ loss. Specifically, we construct a new family of prior distributions whose optimal Bayesian estimators (the conditional medians) can be any prescribed increasing…
The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…