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Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…
We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…
We derive explicit Bayesian nonparametric analysis for a species sampling model with finitely many types of Gibbs form of type $\alpha= -1$ recently introduced in Gnedin (2009). Our results complement existing analysis under Gibbs priors of…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems…
Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…
The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables…
Gibbs random fields play an important role in statistics. However they are complicated to work with due to an intractability of the likelihood function and there has been much work devoted to finding computational algorithms to allow…
We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…
We investigate the efficiency of a marginal likelihood estimator where the product of the marginal posterior distributions is used as an importance-sampling function. The approach is generally applicable to multi-block parameter vector…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper demonstrates that such weighting can indeed improve the…
A Bayesian nonparametric approach to the study of species diversity based on choosing a random discrete distribution as a prior model for the unknown relative abundances of species has been recently introduced in Lijoi et al. (2007, 2008).…
In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not…
Bayesian and other likelihood-based methods require specification of a statistical model and may not be fully satisfactory for inference on quantities, such as quantiles, that are not naturally defined as model parameters. In this paper, we…
We propose a general method for distributed Bayesian model choice, using the marginal likelihood, where a data set is split in non-overlapping subsets. These subsets are only accessed locally by individual workers and no data is shared…
Model selection is an important activity in modern data analysis and the conventional Bayesian approach to this problem involves calculation of marginal likelihoods for different models, together with diagnostics which examine specific…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…