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In this paper, a highly effective slice sampling algorithm is proposed to estimate the graded response model that has been widely used in educational psychological assessments. The new algorithm not only avoids the Metroplis–Hastings algorithm boring adjustment the turning parameters to achieve an appropriate acceptance probability, but also overcomes the dependence of the traditional Gibbs sampling algorithm on the conjugate prior distribution. Three simulation studies are conducted and a detailed analysis of sexual compulsivity scale (SCS) data is carried out to further illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

One of the major challenges in modern day statistics is to formulate models and develop inferential procedures to understand the complex multivariate relationships present in high-dimensional datasets. In this paper, we address the issue of model determination for DAGs, with respect to a given ordering of the variables, together with the corresponding parameter estimation. For this, we use a hierarchical mixture prior and develop a Gibbs sampling algorithm to carry out the posterior computations. We first focus on the Gaussian DAG models and calculate the posterior probability of being the edge between two nodes. We then extend our idea to construct a DAG for discrete data under the assumption that the data generated by discretization of the marginal distributions of a latent multivariate Gaussian distribution via a set of predetermined threshold values. Results show that the proposed method has high accuracy. The source code is available at [ABSTRACT FROM AUTHOR]

Feature selection arises in many areas of modern science. For example, in genomic research, we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal). One approach is to fit regression/classification models with certain penalization. In the past decade, hyper-LASSO penalization (priors) have received increasing attention in the literature. However, fully Bayesian methods that use Markov chain Monte Carlo (MCMC) for regression/classification with hyper-LASSO priors are still in lack of development. In this paper, we introduce an MCMC method for learning multinomial logistic regression with hyper-LASSO priors. Our MCMC algorithm uses Hamiltonian Monte Carlo in a restricted Gibbs sampling framework. We have used simulation studies and real data to demonstrate the superior performance of hyper-LASSO priors compared to LASSO, and to investigate the issues of choosing heaviness and scale of hyper-LASSO priors. [ABSTRACT FROM AUTHOR]

In this paper the issue of making inferences with misclassified data from a noisy multinomial process is addressed. A Bayesian model for making inferences about the proportions and the noise parameters is developed. The problem is reformulated in a more tractable form by introducing auxiliary or latent random vectors. This allows for an easy-to-implement Gibbs sampling-based algorithm to generate samples from the distributions of interest. An illustrative example related to elections is also presented. [ABSTRACT FROM AUTHOR]

In this paper zero-inflated distributions (ZID) are studied from the Bayesian point of view using the data augmentation algorithm. This type of discrete model arises in count data with excess of zeros. The zero-inflated Poisson distribution (ZIP) and an illustrative example via MCMC algorithm are considered. [ABSTRACT FROM AUTHOR]