Related papers: Power-Conditional-Expected Priors: Using g-priors …

In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…

This paper investigates Bayesian variable selection when there is a hierarchical dependence structure on the inclusion of predictors in the model. In particular, we study the type of dependence found in polynomial response surfaces of…

Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, and canonical correlation analysis are specific instances of…

In order to represent the preferences of a group of individuals, we introduce Probabilistic CP-nets (PCP-nets). PCP-nets provide a compact language for representing probability distributions over preference orderings. We argue that they are…

In Bayesian machine learning, conjugate priors are popular, mostly due to mathematical convenience. In this paper, we show that there are deeper reasons for choosing a conjugate prior. Specifically, we formulate the conjugate prior in the…

We introduce the implicit processes (IPs), a stochastic process that places implicitly defined multivariate distributions over any finite collections of random variables. IPs are therefore highly flexible implicit priors over functions,…

The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but as shown in this paper, the results can be sensitive to the prior choice for the global shrinkage hyperparameter. We argue that the previous…

In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG…

Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…

Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…

In the Bayesian analysis of contingency table data, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameter is a major challenge. Though the conjugate prior on cell probabilities has…

In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…

Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…

This article addresses issues of model criticism and model comparison in Bayesian contexts, and focusses on the use of the so-called posterior predictive p-values (ppp values). These involve a general discrepancy or conflict measure and…

Projected priors were originally introduced to accommodate parameter constraints, but have recently regained popularity due to their ability to assign probability mass to low-dimensional parameter sets, such as the spaces of sparse vectors,…

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…

This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

Significance testing based on p-values has been implicated in the reproducibility crisis in scientific research, with one of the proposals being to eliminate them in favor of Bayesian analyses. Defenders of the p-values have countered that…

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…

Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…