Belief Networks in the Bayesian approach provide a wellestablished methodology to fuse prior knowledge and statistical observations for an enriched decision support. In this paper we investigate one of the advantages of the Bayesian approach the provided additional uncertainty information for predictions in a medical classification problem. We perform a Bayesian analysis using Belief Network mo...

In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or more argument. We make the case that shape constraints are often appropriate in at least two important application areas of Bayesian optimization: (1) hyperpar...

In this paper we provide an algorithm allowing to solve the variational Bayesian issue as a functional optimization problem. The main contribution of this paper is to transpose a classical iterative algorithm of optimization in the metric space of measures involved in the Bayesian methodology. Once given the convergence properties of this algorithm, we consider its application to large dimensio...

Animal models are generalized linear mixed model (GLMM) used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast non-sampling based Bayesian inference for hierarchical Gaussian Markov models. In this paper we demonstrate that the INLA methodology can be used for many versions of Bayes...

In this paper we present an active learning procedure for the two-class supervised classification problem. The utilized methodology exploits the Bayesian modeling and inference paradigm to tackle the problem of kernel-based data classification. This Bayesian methodology is appropriate for both finite and infinite dimensional feature spaces. Parameters are estimated, using the kernel trick, foll...

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are constructed based upon second-order conditional independence, in order to facilitate posterior updating and prediction of required distributional quantities. ...

We propose a flexible hierarchical Bayesian nonparametric modeling approach to compare the spiking patterns of neurons recorded under multiple experimental conditions. In particular, we showcase the application of our statistical methodology using neurons recorded from the supplementary eye field region of the brains of two macaque monkeys trained to make delayed eye movements to three differen...

We propose a fully Bayesian methodology for generalized kernel mixed models (GKMMs), which are extensions of generalized linear mixed models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of a generalized kernel model (GKM). This mixture prior allows a fraction of the components of the regres...