Above are papers related to the following paper: [Paper_ID] Paper #1131270. 	[Title] Blocking Gibbs Sampling for Linkage Analysis in Large Pedigrees with Many Loops [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #153063. 	[Title] Bayesian Forecasting of Multinomial Time Series through Conditionally Gaussian Dynamic Models [Abstract] Claudia Cargnoni is with the Dipartimento Statistico, Universita di Firenze, 50100 Firenze, Italy. Peter Muller is Assistant Professor, and Mike West is Professor, in the Institute of Statistics and Decision Sciences at Duke University, Durham NC 27708-0251. Research of Cargnoni was performed while visiting ISDS during 1995. Muller and West were partially supported by NSF under grant DMS-9305699. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #126793. 	[Title] Maximum Working Likelihood Inference with Markov Chain Monte Carlo [Abstract] Maximum working likelihood (MWL) inference in the presence of missing data can be quite challenging because of the intractability of the associated marginal likelihood. This problem can be further exacerbated when the number of parameters involved is large. We propose using Markov chain Monte Carlo (MCMC) to first obtain both the MWL estimator and the working Fisher information matrix and, second, using Monte Carlo quadrature to obtain the remaining components of the correct asymptotic MWL variance. Evaluation of the marginal likelihood is not needed. We demonstrate consistency and asymptotic normality when the number of independent and identically distributed data clusters is large but the likelihood may be incorrectly specified. An analysis of longitudinal ordinal data is given for an example. KEY WORDS: Convergence of posterior distributions, Maximum likelihood, Metropolis Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #38537. 	[Title] BAYESIAN STATISTICS 6, pp. 000--000  Exact sampling for Bayesian inference: towards general purpose algorithms [Abstract] There are now methods for organising a Markov chain Monte Carlo simulation so that it can be guaranteed that the state of the process at a given time is exactly drawn from the target distribution. The question of assessing convergence totally vanishes. Such methods are known as exact or perfect sampling. The approach that has received most attention uses the protocol of coupling from the past devised by Propp and Wilson (Random Structures and Algorithms,1996), in which multiple dependent paths of the chain are run from different initial states at a sequence of initial times going backwards into the past, until they satisfy the condition of coalescence by time 0. When this is achieved the state at time 0 is distributed according to the required target. This process must be implemented very carefully to assure its validity (including appropriate re-use of random number streams), and also requires one of various tricks to enable us to follow infinitely many sample paths with a finite amount of work. With the ultimate objective of Bayesian MCMC with guaranteed convergence, the purpose of this paper is to describe recent efforts to construct exact sampling methods for continuous-state Markov chains. We review existing methods based on gamma-coupling and rejection sampling (Murdoch and Green, Scandinavian Journal of Statistics, 1998), that are quite straightforward to understand, but require a closed form for the transition kernel and entail cumbersome algebraic manipulation. We then introduce two new methods based on random walk Metropolis, that offer the prospect of more automatic use, not least because the difficult, continuous, part of the transition mechanism can be coupled in a generic way, using a proposal distribution of convenience. One of the methods is based on a neat decomposition of any unimodal (multivariate) symmetric density into pieces that may be re-assembled to construct any translated copy of itself: that allows coupling of a continuum of Metropolis proposals to a finite set, at least for a compact state space. We discuss methods for economically coupling the subsequent accept/reject decisions. Our second new method deals with unbounded state spaces, using a trick due to W. S. Kendall of running a coupled dominating process in parallel with the sample paths of interest. The random subset of the state space below the dominating path is compact, allowing efficient coupling and coalescence. We look towards the possibility that application of such methods could become sufficiently convenient that they could become the basis for routine Bayesian computation in the foreseeable future. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #16843. 	[Title] Sampling from Multimodal Distributions Using Tempered Transitions [Abstract] Technical Report No. 9421, Department of Statistics, University of Toronto Abstract. I present a new Markov chain sampling method appropriate for distributions with isolated modes. Like the recently-developed method of "simulated tempering", the "tempered transition" method uses a series of distributions that interpolate between the distribution of interest and a distribution for which sampling is easier. The new method has the advantage that it does not require approximate values for the normalizing constants of these distributions, which are needed for simulated tempering, and can be tedious to estimate. Simulated tempering performs a random walk along the series of distributions used. In contrast, the tempered transitions of the new method move systematically from the desired distribution, to the easily-sampled distribution, and back to the desired distribution. This systematic movement avoids the inefficiency of a random walk, an advantage that unfortunately is cancelled by an increase in the number of interpolating distributions required. Because of this, the sampling efficiency of the tempered transition method in simple problems is similar to that of simulated tempering. On more complex distributions, however, simulated tempering and tempered transitions may perform differently. Which is better depends on the ways in which the interpolating distributions are "deceptive". Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #137868. 	[Title] On Bayesian analysis of mixtures with an unknown number of components  Summary [Abstract] New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods, that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution. The methodology is applied here to the analysis of univariate normal mixtures, using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131277. 	[Title] Bayesian Detection of Clusters and Discontinuities in Disease Maps [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #646195. 	[Title] Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses [Abstract] Technical Report No. 670 December, 1997 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 #642847. 	[Title] An Approach to Diagnosing Total Variation Convergence of MCMC Algorithms [Abstract] We introduce a convergence diagnostic procedure for MCMC which operates by estimating total variation distances for the distribution of the algorithm after certain numbers of iterations. The method has advantages over many existing methods in terms of applicability, utility, computational expense and interpretability. It can be used to assess convergence of both marginal and joint posterior densities, and we show how it can be applied to the two most commonly used MCMC samplers; the Gibbs Sampler and the Metropolis Hastings algorithm. Illustrative examples highlight the utility and interpretability of the proposed diagnostic, but also highlight some of its limitations. Please summarise all the given information.

Paper #1131270 has the title `Blocking Gibbs Sampling for Linkage Analysis in Large Pedigrees with Many Loops  
` and the abstract `nan`.
Question: Which category should Paper #1131270 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1131270 has the title `Blocking Gibbs Sampling for Linkage Analysis in Large Pedigrees with Many Loops  
` and the abstract `nan`.
Question: Which category should Paper #1131270 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