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 #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 #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 #1131164. 	[Title] A Gibbs Sampling Approach to Cointegration [Abstract] This paper reviews the application of Gibbs sampling to a cointegrated VAR system. Aggregate imports and import prices for Belgium are modelled using two cointegrating relations. Gibbs sampling techniques are used to estimate from a Bayesian perspective the cointegrating relations and their weights in the VAR system. Extensive use of spectral analysis is made to get insight into convergence issues. 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 #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 #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 #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 #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 #644441. 	[Title] MCMC CONVERGENCE DIAGNOSTIC VIA THE CENTRAL LIMIT THEOREM [Abstract] Markov Chain Monte Carlo (MCMC) methods, as introduced by Gelfand and Smith (1990), provide a simulation based strategy for statistical inference. The application fields related to these methods, as well as theoretical convergence properties, have been intensively studied in the recent literature. However, many improvements are still expected to provide workable and theoretically well-grounded solutions to the problem of monitoring the convergence of actual outputs from MCMC algorithms (i.e. the convergence assessment problem). In this paper, we introduce and discuss a methodology based on the Central Limit Theorem for Markov chains to assess convergence of MCMC algorithms. Instead of searching for approximate stationarity, we primarily intend to control the precision of estimates of the invariant probability measure, or of integrals of functions with respect to this measure, through confidence regions based on normal approximation. The first proposed control method tests the normality hypothesis for normalized averages of functions of the Markov chain over independent parallel chains. This normality control provides good guarantees that the whole state space has been explored, even in multimodal situations. It can lead to automated stopping rules. A second tool connected with the normality control is based on graphical monitoring of the stabilization of the variance after n iterations near the limiting variance appearing in the CLT. Both methods require no knowledge of the sampler driving the chain. In this paper, we mainly focus on finite state Markov chains, since this setting allows us to derive consistent estimates of both the limiting variance and the variance after n iterations. Heuristic procedures based on Berry-Esseen bounds are investigated. An extension to the continuous case is also proposed. Numerical simulations illustrating the performance of these methods are given for several examples: a finite chain with multimodal invariant probability, a finite state random walk for which the theoretical rate of convergence to stationarity is known, and a continuous state chain with multimodal invariant probability issued from a Gibbs sampler. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #644448. 	[Title] Adaptive Markov Chain Monte Carlo through Regeneration  Summary [Abstract] Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution . This is done by calculating averages over the sample path of a Markov chain having as its stationary distribution. For computational efficiency, the Markov chain should be rapidly mixing. This can sometimes be achieved only by careful design of the transition kernel of the chain, on the basis of a detailed preliminary exploratory analysis of . An alternative approach might be to allow the transition kernel to adapt whenever new features of are encountered during the MCMC run. However, if such adaptation occurs infinitely often, the stationary distribution of the chain may be disturbed. We describe a framework, based on the concept of Markov chain regeneration, which allows adaptation to occur infinitely often, but which does not disturb the stationary distribution of the chain or the consistency of sample-path averages. Key Words: Adaptive method; Bayesian inference; Gibbs sampling; Markov chain Monte Carlo; 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 #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 #1131258. 	[Title] Discretization of continuous Markov chains and MCMC convergence assessment [Abstract] We show in this paper that continuous state space Markov chains can be rigorously discretized into finite Markov chains. The idea is to subsample the continuous chain at renewal times related to small sets which control the discretization. Once a finite Markov chain is derived from the MCMC output, general convergence properties on finite state spaces can be exploited for convergence assessment in several directions. Our choice is based on a divergence criterion derived from Kemeny and Snell (1960), which is first evaluated on parallel chains with a stopping time, and then implemented, more efficiently, on two parallel chains only, using Birkhoff's pointwise ergodic theorem for stopping rules. The performance of this criterion is illustrated on three standard examples. 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 #642621 has the title `Looking at Markov Samplers through Cusum Path Plots: a simple diagnostic idea  
` and the 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. 
`.
Question: Which category should Paper #642621 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #642621 has the title `Looking at Markov Samplers through Cusum Path Plots: a simple diagnostic idea  
` and the 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. 
`.
Question: Which category should Paper #642621 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