Related papers: The generalized IFS Bayesian method and an associa…
A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…
In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon an asymptotically unbiased…
We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…
Iterated function systems (IFS) can be a surprisingly useful tool for studying structure in data. Here we present results stemming from a 2013 computational study by the author using IFS. The results include fractal patterns that reveal…
Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance…
Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…
Multivariate categorical data are common in many fields. We are motivated by election polls studies assessing evidence of changes in voters opinions with their candidates preferences in the 2016 United States Presidential primaries or…
In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…
This paper describes a decision theoretic formulation of learning the graphical structure of a Bayesian Belief Network from data. This framework subsumes the standard Bayesian approach of choosing the model with the largest posterior…
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…
Inferences that arise from loss functions determined by the prior are considered and it is shown that these lead to limiting Bayes rules that are closely connected with likelihood. The procedures obtained via these loss functions are…
We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…
We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…
We propose a score-based generative algorithm for sampling from power-scaled priors and likelihoods within the Bayesian inference framework. Our algorithm enables flexible control over prior-likelihood influence without requiring retraining…
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…
Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…
Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…
Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…