Above are papers related to the following paper: [Paper_ID] Paper #1131189. 	[Title] MARKOV CHAIN MONTE CARLO SAMPLING FOR EVALUATING MULTIDIMENSIONAL INTEGRALS WITH APPLICATION TO BAYESIAN COMPUTATION [Abstract] Recently, Markov chain Monte Carlo (MCMC) sampling methods have become widely used for determining properties of a posterior distribution. Alternative to the Gibbs sampler, we elaborate on the Hit-and-Run sampler and its generalization, a black-box sampling scheme, to generate a time-reversible Markov chain from a posterior distribution. The proof of convergence and its applications to Bayesian computation with constrained parameter spaces are provided and comparisons with the other MCMC samplers are made. In addition, we propose an importance weighted marginal density estimation (IWMDE) method. An IWMDE is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w. The asymptotic properties for the IWMDE and the guidelines for choosing a weighting conditional density w are also considered. The generalized version of IWMDE for estimating marginal posterior densities when the full joint posterior density contains analytically intractable normalizing constants is developed. Furthermore, we develop Monte Carlo methods based on Kullback-Leibler divergences for comparing marginal posterior density estimators. This article is a summary of the author's Ph.D. thesis and it was presented in the Savage Award session. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #16819. 	[Title] Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review [Abstract] A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but currently has yielded relatively little that is of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. After giving a brief overview of the area, we provide an expository review of thirteen convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all the methods can fail to detect the sorts of convergence failure they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence, including applying diagnostic procedures to a small number of parallel chains, monitoring autocorrelations and cross-correlations, and modifying parameterizations or sampling algorithms appropriately. We emphasize, however, that it is not possible to say with certainty that a finite sample from an MCMC algorithm is representative of an underlying stationary distribution. Mary Kathryn Cowles is Assistant Professor of Biostatistics, Harvard School of Public Health, Boston, MA 02115. Bradley P. Carlin is Associate Professor, Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455. Much of the work was done while the first author was a graduate student in the Divison of Biostatistics at the University of Minnesota and then Assistant Professor, Biostatistics Section, Department of Preventive and Societal Medicine, University of Nebraska Medical Center, Omaha, NE 68198. The work of both authors was supported in part by National Institute of Allergy and Infectious Diseases FIRST Award 1-R29-AI33466. The authors thank the developers of the diagnostics studied here for sharing their insights, experiences, and software, and Drs. Thomas Louis and Luke Tierney for helpful discussions and suggestions which greatly improved the manuscript. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #643003. 	[Title] Estimating Ratios of Normalizing Constants for Densities with Different Dimensions [Abstract] In Bayesian inference, a Bayes factor is defined as the ratio of posterior odds versus prior odds where posterior odds is simply a ratio of the normalizing constants of two posterior densities. In many practical problems, the two posteriors have different dimensions. For such cases, the current Monte Carlo methods such as the bridge sampling method (Meng and Wong 1996), the path sampling method (Gelman and Meng 1994), and the ratio importance sampling method (Chen and Shao 1994) cannot directly be applied. In this article, we extend importance sampling, bridge sampling, and ratio importance sampling to problems of different dimensions. Then we find global optimal importance sampling, bridge sampling, and ratio importance sampling in the sense of minimizing asymptotic relative mean-square errors of estimators. Implementation algorithms, which can asymptotically achieve the optimal simulation errors, are developed and two illustrative examples are also provided. Please summarise all the given information.

Paper #1131189 has the title `MARKOV CHAIN MONTE CARLO SAMPLING FOR EVALUATING MULTIDIMENSIONAL INTEGRALS WITH APPLICATION TO BAYESIAN COMPUTATION  
` and the abstract `Recently, Markov chain Monte Carlo (MCMC) sampling methods have become widely used for determining properties of a posterior distribution. Alternative to the Gibbs sampler, we elaborate on the Hit-and-Run sampler and its generalization, a black-box sampling scheme, to generate a time-reversible Markov chain from a posterior distribution. The proof of convergence and its applications to Bayesian computation with constrained parameter spaces are provided and comparisons with the other MCMC samplers are made. In addition, we propose an importance weighted marginal density estimation (IWMDE) method. An IWMDE is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w. The asymptotic properties for the IWMDE and the guidelines for choosing a weighting conditional density w are also considered. The generalized version of IWMDE for estimating marginal posterior densities when the full joint posterior density contains analytically intractable normalizing constants is developed. Furthermore, we develop Monte Carlo methods based on Kullback-Leibler divergences for comparing marginal posterior density estimators. This article is a summary of the author's Ph.D. thesis and it was presented in the Savage Award session. 
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Question: Which category should Paper #1131189 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1131189 has the title `MARKOV CHAIN MONTE CARLO SAMPLING FOR EVALUATING MULTIDIMENSIONAL INTEGRALS WITH APPLICATION TO BAYESIAN COMPUTATION  
` and the abstract `Recently, Markov chain Monte Carlo (MCMC) sampling methods have become widely used for determining properties of a posterior distribution. Alternative to the Gibbs sampler, we elaborate on the Hit-and-Run sampler and its generalization, a black-box sampling scheme, to generate a time-reversible Markov chain from a posterior distribution. The proof of convergence and its applications to Bayesian computation with constrained parameter spaces are provided and comparisons with the other MCMC samplers are made. In addition, we propose an importance weighted marginal density estimation (IWMDE) method. An IWMDE is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w. The asymptotic properties for the IWMDE and the guidelines for choosing a weighting conditional density w are also considered. The generalized version of IWMDE for estimating marginal posterior densities when the full joint posterior density contains analytically intractable normalizing constants is developed. Furthermore, we develop Monte Carlo methods based on Kullback-Leibler divergences for comparing marginal posterior density estimators. This article is a summary of the author's Ph.D. thesis and it was presented in the Savage Award session. 
`.
Question: Which category should Paper #1131189 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods