Related papers: A Note on the Posterior Inference for the Yule-Sim…

Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…

This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects,…

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to uniquely identify the parameters of the model. This paper proposes a novel identification…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

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).…

This paper provides bayesian analysis of singular Marshall-Olkin bivariate Pareto distribution. We consider three parameter singular Marshall-Olkin bivariate Pareto distribution. We consider two types of prior - reference prior and gamma…

In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…

In this paper we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalised logistic regression model. We propose a P\'olya-Gamma sampler algorithm that allows us to sample from the exact…

I present all the details in calculating the posterior distribution of the conjugate Normal-Gamma prior in Bayesian Linear Models (BLM), including correlated observations, prediction, model selection and comments on efficient numeric…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…

Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…

The present paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…

We study parameter inference in large-scale latent variable models. We first propose an unified treatment of online inference for latent variable models from a non-canonical exponential family, and draw explicit links between several…