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 #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 #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 #1131274. 	[Title] Perfect Simulation in Stochastic Geometry [Abstract] Simulation plays an important role in stochastic geometry and related fields, because all but the simplest random set models tend to be intractable to analysis. Many simulation algorithms deliver (approximate) samples of such random set models, for example by simulating the equilibrium distribution of a Markov chain such as a spatial birth-and-death process. The samples usually fail to be exact because the algorithm simulates the Markov chain for a long but finite time, and thus convergence to equilibrium is only approximate. The seminal work by Propp and Wilson made an important contribution to simulation by proposing a coupling method, Coupling from the Past (CFTP), which delivers perfect, that is to say exact, simulations of Markov chains. In this paper we introduce this new idea of perfect simulation and illustrate it using two common models in stochastic geometry: the dead leaves model and a Boolean model conditioned to cover a finite set of points. 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 #646286. 	[Title] Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY [Abstract] In this article we approximate the rate of convergence of the Gibbs sampler by a normal approximation of the target distribution. Based on this approximation, we consider many implementational issues for the Gibbs sampler, e.g., updating strategy, parameterization and blocking. We give theoretical results to justify our approximation and illustrate our methods in a number of realistic examples. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #644093. 	[Title] Possible biases induced by MCMC convergence diagnostics [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #643221. 	[Title] A simulation approach to convergence rates for Markov chain Monte Carlo algorithms [Abstract] Markov chain Monte Carlo (MCMC) methods, including the Gibbs sampler and the Metropolis-Hastings algorithm, are very commonly used in Bayesian statistics for sampling from complicated, high-dimensional posterior distributions. A continuing source of uncertainty is how long such a sampler must be run in order to converge approximately to its target stationary distribution. Rosenthal (1995b) presents a method to compute rigorous theoretical upper bounds on the number of iterations required to achieve a specified degree of convergence in total variation distance by verifying drift and minorization conditions. We propose the use of auxiliary simulations to estimate the numerical values needed in Rosenthal's theorem. Our simulation method makes it possible to compute quantitative convergence bounds for models for which the requisite analytical computations would be prohibitively difficult or impossible. On the other hand, although our method appears to perform well in our example problems, it can not provide the guarantees offered by analytical proof. Acknowledgements. We thank Brad Carlin for assistance and encouragement. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131167. 	[Title] Decision Analysis by Augmented Probability Simulation [Abstract] We provide a generic Monte Carlo method to find the alternative of maximum expected utility in a decision analysis. We define an artificial distribution on the product space of alternatives and states, and show that the optimal alternative is the mode of the implied marginal distribution on the alternatives. After drawing a sample from the artificial distribution, we may use exploratory data analysis tools to approximately identify the optimal alternative. We illustrate our method for some important types of influence diagrams. (Decision Analysis, Influence Diagrams, Markov chain Monte Carlo, Simulation) 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.

Above are papers related to the following paper: [Paper_ID] Paper #643239. 	[Title] Analysis of the Gibbs sampler for a model related to James-Stein estimators [Abstract] Summary. We analyze a hierarchical Bayes model which is related to the usual empirical Bayes formulation of James-Stein estimators. We consider running a Gibbs sampler on this model. Using previous results about convergence rates of Markov chains, we provide rigorous, numerical, reasonable bounds on the running time of the Gibbs sampler, for a suitable range of prior distributions. We apply these results to baseball data from Efron and Morris (1975). For a different range of prior distributions, we prove that the Gibbs sampler will fail to converge, and use this information to prove that in this case the associated posterior distribution is non-normalizable. Acknowledgements. I am very grateful to Jun Liu for suggesting this project, and to Neal Madras for suggesting the use of the Submartingale Convergence Theorem herein. I thank Kate Cowles and Richard Tweedie for helpful conversations, and thank the referees for useful comments. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131312. 	[Title] Theoretical rates of convergence for Markov chain Monte Carlo [Abstract] We present a general method for proving rigorous, a priori bounds on the number of iterations required to achieve convergence of Markov chain Monte Carlo. We describe bounds for specific models of the Gibbs sampler, which have been obtained from the general method. We discuss possibilities for obtaining bounds more generally. 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.

Above are papers related to the following paper: [Paper_ID] Paper #642621. 	[Title] Looking at Markov Samplers through Cusum Path Plots: a simple diagnostic idea [Abstract] In this paper, we propose to monitor a Markov chain sampler using the cusum path plot of a chosen 1-dimensional summary statistic. We argue that the cusum path plot can bring out, more effectively than the sequential plot, those aspects of a Markov sampler which tell the user how quickly or slowly the sampler is moving around in its sample space, in the direction of the summary statistic. The proposal is then illustrated in four examples which represent situations where the cusum path plot works well and not well. Moreover, a rigorous analysis is given for one of the examples. We conclude that the cusum path plot is an effective tool for convergence diagnostics of a Markov sampler and for comparing different Markov samplers. 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 #1131236. 	[Title] Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration [Abstract] This paper gives precise, easy to compute bounds on the convergence time of the Gibbs sampler used in Bayesian image reconstruction. For sampling from the Gibbs distribution both with and without the presence of an external field, bounds that are N 2 in the number of pixels are obtained, with a proportionality constant that is easy to calculate. Some key words: Bayesian image restoration; Convergence; Gibbs sampler; Ising model; Markov chain Monte Carlo. 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 #644334. 	[Title] Convergence controls for MCMC algorithms, with applications to hidden Markov chains [Abstract] In complex models like hidden Markov chains, the convergence of the MCMC algorithms used to approximate the posterior distribution and the Bayes estimates of the parameters of interest must be controlled in a robust manner. We propose in this paper a series of on-line controls, which rely on classical non-parametric tests, to evaluate independence from the start-up distribution, stability of the Markov chain, and asymptotic normality. These tests lead to graphical control spreadsheets which are presented in the set-up of normal mixture hidden Markov chains to compare the full Gibbs sampler with an aggregated Gibbs sampler based on the forward-backward formulae. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #643069. 	[Title] Markov Chain Monte Carlo in Practice: A Roundtable Discussion [Abstract] Markov chain Monte Carlo (MCMC) methods make possible the use of flexible Bayesian models that would otherwise be computationally infeasible. In recent years, a great variety of such applications have been described in the literature. Applied statisticians who are new to these methods may have several questions and concerns, however: How much effort and expertise are needed to design and use a Markov chain sampler? How much confidence can one have in the answers that MCMC produces? How does the use of MCMC affect the rest of the model-building process? At the Joint Statistical Meetings in August, 1996, a panel of experienced MCMC users discussed these and other issues, as well as various "tricks of the trade". This paper is an edited recreation of that discussion. Its purpose is to offer advice and guidance to novice users of MCMC and to not-so-novice users as well. Topics include building confidence in simulation results, methods for speeding convergence, assessing standard errors, identification of models for which good MCMC algorithms exist, and the current state of software development. Please summarise all the given information.

Paper #646195 has the title `Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses  
` and the abstract `Technical Report No. 670 December, 1997 
`.
Question: Which category should Paper #646195 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #646195 has the title `Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses  
` and the abstract `Technical Report No. 670 December, 1997 
`.
Question: Which category should Paper #646195 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