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Full-Text Articles in Statistical Models
Evaluating The Efficiency Of Markov Chain Monte Carlo Algorithms, Thuy Scanlon
Evaluating The Efficiency Of Markov Chain Monte Carlo Algorithms, Thuy Scanlon
Graduate Theses and Dissertations
Markov chain Monte Carlo (MCMC) is a simulation technique that produces a Markov chain designed to converge to a stationary distribution. In Bayesian statistics, MCMC is used to obtain samples from a posterior distribution for inference. To ensure the accuracy of estimates using MCMC samples, the convergence to the stationary distribution of an MCMC algorithm has to be checked. As computation time is a resource, optimizing the efficiency of an MCMC algorithm in terms of effective sample size (ESS) per time unit is an important goal for statisticians. In this paper, we use simulation studies to demonstrate how the Gibbs …
Bayesian Skew Selection For Multivariate Models, Michael S. Smith, Anastasios Panagiotelis
Bayesian Skew Selection For Multivariate Models, Michael S. Smith, Anastasios Panagiotelis
Michael Stanley Smith
We develop a Bayesian approach for the selection of skew in multivariate skew t distributions constructed through hidden conditioning in the manners suggested by either Azzalini and Capitanio (2003) or Sahu, Dey and Branco~(2003). We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether there is symmetry, or skew, in each dimension. We adopt a proper beta prior on each non-zero skew coefficient, and derive the corresponding prior on the skew parameters. In both distributions we show that as the degrees of freedom increases, …
Spatially Adaptive Bayesian P-Splines With Heteroscedastic Errors, Ciprian M. Crainiceanu, David Ruppert, Raymond J. Carroll
Spatially Adaptive Bayesian P-Splines With Heteroscedastic Errors, Ciprian M. Crainiceanu, David Ruppert, Raymond J. Carroll
Johns Hopkins University, Dept. of Biostatistics Working Papers
An increasingly popular tool for nonparametric smoothing are penalized splines (P-splines) which use low-rank spline bases to make computations tractable while maintaining accuracy as good as smoothing splines. This paper extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially adaptive smoothing parameter. These extensions have been studied before, but never together and never in the multivariate case. This combination is needed for satisfactory inference and can be implemented effectively by Bayesian \mbox{MCMC}. The variance process controlling the spatially-adaptive shrinkage of the mean and the variance of the heteroscedastic error process are modeled as log-penalized …