Related papers: Objective Bayesian analysis for the generalized ex…
Objective priors for sequential experiments are considered. Common priors, such as the Jeffreys prior and the reference prior, will typically depend on the stopping rule used for the sequential experiment. New expressions for reference…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
One of the main approaches used to construct prior distributions for objective Bayes methods is the concept of random imaginary observations. Under this setup, the expected-posterior prior (EPP) offers several advantages, among which it has…
High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an empirical or data-driven prior leading to an empirical…
In Bayesian statistics, the choice of the prior can have an important influence on the posterior and the parameter estimation, especially when few data samples are available. To limit the added subjectivity from a priori information, one…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
Although Bayesian methods are robust and principled, their application in practice could be limited since they typically rely on computationally intensive Markov Chain Monte Carlo algorithms for their implementation. One possible solution…
We propose a novel computationally low-cost method for estimating a general predictive measure of generalised Bayesian inference. The proposed method utilises posterior covariance and provides estimators of the Gibbs and the plugin…
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…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…
Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the…
This paper generalises the exponential family GLM to allow arbitrary distributions for the response variable. This is achieved by combining the model-assisted regression approach from survey sampling with the GLM scoring algorithm, weighted…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
In this paper, we derive a Bayesian model order selection rule by using the exponentially embedded family method, termed Bayesian EEF. Unlike many other Bayesian model selection methods, the Bayesian EEF can use vague proper priors and…
Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…
The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…
The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…