The DA-T Gibbs sampler is proposed by Maris and Maris (2002) as a Bayesian estimation method for a wide variety of Item Response Theory (IRT) models. The present paper provides an expository account of the DAT Gibbs sampler for the 2PL model. However, the scope is not limited to the 2PL model. It is demonstrated how the DA-T Gibbs sampler for the 2PL may be used to build, quite easily, Gibbs sa...

Parsimonious Markov models have been recently developed as a generalization of variable order Markov models. Many practical applications involve a setting with latent variables, with a common example being mixture models. Here, we propose a Bayesian model averaging approach for learning mixtures of parsimonious Markov models that is based on Gibbs sampling. The challenging problem is sampling o...

We demonstrate the use of auxiliary (or latent) variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate and hierarchical models by using a Gibbs sampler. Their strategic use can result in a Gibbs sampler having easily sampled full conditionals. We propose such a procedure to simplify or speed up the Markov chain Monte Carlo algorithm. T...

Recently, the null category noise model has been proposed as a simple and elegant solution to the problem of incorporating unlabeled data into a Gaussian process (GP) classification model. In this paper, we show how this binary likelihood model can be generalised to the multi-class setting through the use of the multinomial probit GP classifier. We present a Gibbs sampling scheme for sampling t...

Inference in general Ising models is difficult, due to high treewidth making treebased algorithms intractable. Moreover, when interactions are strong, Gibbs sampling may take exponential time to converge to the stationary distribution. We present an algorithm to project Ising model parameters onto a parameter set that is guaranteed to be fast mixing, under several divergences. We find that Gibb...

The Indian Buffet Process (IBP) is a stochastic process on binary features that has been applied to modeling communities in complex networks [4, 5, 6]. Inference in the IBP is challenging as the potential number of possible configurations grows as 2 where K is the number of latent features and N the number of nodes in the network. We presently consider the performance of three MCMC sampling app...

The generalized inverse Gaussian distribution has become quite popular in financial engineering. The most popular random variate generator is due to Dagpunar (1989). It is an acceptance-rejection algorithm method based on the Ratio-of-uniforms method. However, it is not uniformly fast as it has a prohibitive large rejection constant when the distribution is close to the gamma distribution. Rece...

Gibbs sampling is a well-known Markov Chain Monte Carlo (MCMC) technique, widely applied to draw samples from multivariate target distributions which appear often in many different fields (machine learning, finance, signal processing, etc.). The application of the Gibbs sampler requires being able to draw efficiently from the univariate full-conditional distributions. In this work, we present a...

We provide provably privacy-preserving versions of belief propagation, Gibbs sampling, and other local algorithms — distributed multiparty protocols in which each party or vertex learns only its final local value, and absolutely nothing else.

Consider a system with n components (different types of molecules) with r phases in equilibrium. The state of each phase is defined by P, T and then (n− 1) concentration variables in each phase. The phase equilibrium at given P, T is defined by the equality of n chemical potentials between the r phases. Thus there are n(r − 1) constraints on (n− 1)r + 2 variables. This gives the Gibbs phase rul...