Posterior expectation is a well-accepted method for data analysis via Bayesian inference based on parametric likelihoods. In this paper we propose utilizing empirical likelihood (EL) methodology to develop novel nonparametric posterior expectation. The parametric Bayesian methodology contains the empirical Bayes approach for the purpose of using the observed data to estimate parameters, or even...

This paper introduces online Bayesian network learning in detail. The structural and parametric learning abilities of the online Bayesian network learning are explored. The paper starts with revisiting the multi-agent self-organization problem and the proposed solution. Then, we explain the proposed Bayesian network learning, three scoring functions, namely LogLikelihood, Minimum description le...

We present a competitive analysis of some non-parametric Bayesian algorithms in a worst-case online learning setting, where no probabilistic assumptions about the generation of the data are made. We consider models which use a Gaussian process prior (over the space of all functions) and provide bounds on the regret (under the log loss) for commonly used non-parametric Bayesian algorithms — incl...

1 SUMMARY Kernel models for classification and regression have emerged as widely applied tools in statistics and machine learning. We discuss a Bayesian framework and theory for kernel methods, providing a new rationalisation of kernel regression based on non-parametric Bayesian models. Functional analytic results ensure that such a non-parametric prior specification induces a class of function...

In this paper, minimal conditions under which a semi-parametric binary response model is identified in a Bayesian framework are presented and compared to the conditions usually required in a sampling theory framework. Running headline: Semi-parametric Binary Response Models.

Super-resolution of signals and images can improve the automatic detection and recognition of objects of interest. However, the uncertainty associated with this process is not often taken into consideration. This is important because the processing of noisy signals can result in spurious estimates of the scene content. This paper reviews a variety of super-resolution techniques and presents two...

This paper proposes a new Bayesian non-parametric approach for clustering. It relies on an infinite Gaussian mixture model with a Chinese Restaurant Process (CRP) prior, and an eigenvalue decomposition of the covariance matrix of each cluster. The CRP prior allows to control the model complexity in a principled way and to automatically learn the number of clusters. The covariance matrix decompo...

We describe a statistical model over linguistic areas and phylogeny. Our model recovers known areas and identifies a plausible hierarchy of areal features. The use of areas improves genetic reconstruction of languages both qualitatively and quantitatively according to a variety of metrics. We model linguistic areas by a Pitman-Yor process and linguistic phylogeny by Kingman’s coalescent.