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.

Above are papers related to the following paper: [Paper_ID] Paper #1152259. 	[Title] Importance Sampling [Abstract] Technical Report No. 9805, Department of Statistics, University of Toronto Abstract. Simulated annealing | moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions | has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers. Here, it is shown how one can use the Markov chain transitions for such an annealing sequence to define an importance sampler. The Markov chain aspect allows this method to perform acceptably even for high-dimensional problems, where finding good importance sampling distributions would otherwise be very difficult, while the use of importance weights ensures that the estimates found converge to the correct values as the number of annealing runs increases. This annealed importance sampling procedure resembles the second half of the previously-studied tempered transitions, and can be seen as a generalization of a recently-proposed variant of sequential importance sampling. It is also related to thermodynamic integration methods for estimating ratios of normalizing constants. Annealed importance sampling is most attractive when isolated modes are present, or when estimates of normalizing constants are required, but it may also be more generally useful, since its independent sampling allows one to bypass some of the problems of assessing convergence and autocorrelation in Markov chain 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 #14090. 	[Title] Subregion-Adaptive Integration of Functions Having a Dominant Peak [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 #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 #1103016. 	[Title] Inference in Dynamic Error-in-Variable-Measurement Problems [Abstract] Efficient algorithms have been developed for estimating model parameters from measured data, even in the presence of gross errors. In addition to point estimates of parameters, however, assessments of uncertainty are needed. Linear approximations provide standard errors, but these can be misleading when applied to models that are substantially nonlinear. To overcome this difficulty, "profiling" methods have been developed for the case in which the regressor variables are error free. In this paper we extend profiling methods to Error-in-Variable-Measurement (EVM) models. We use Laplace's method to integrate out the incidental parameters associated with the measurement errors, and then apply profiling methods to obtain approximate confidence contours for the parameters. This approach is computationally efficient, requiring few function evaluations, and can be applied to large scale problems. It is useful when the certain measurement errors (e.g., input variables) are relatively small, but not so small that they can be ignored. 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 #1131192. 	[Title] On MCMC Sampling in Hierarchical Longitudinal Models  SUMMARY [Abstract] Markov chain Monte Carlo (MCMC) algorithms have revolutionized Bayesian practice. In their simplest form (i.e., when parameters are updated one at a time) they are, however, often slow to converge when applied to high-dimensional statistical models. A remedy for this problem is to block the parameters into groups, which are then updated simultaneously using either a Gibbs or Metropolis-Hastings step. In this paper we construct several (partially and fully blocked) MCMC algorithms for minimizing the autocorrelation in MCMC samples arising from important classes of longitudinal data models. We exploit an identity used by Chib (1995) in the context of Bayes factor computation to show how the parameters in a general linear mixed model may be updated in a single block, improving convergence and producing essentially independent draws from the posterior of the parameters of interest. We also investigate the value of blocking in non-Gaussian mixed models, as well as in a class of binary response data longitudinal models. We illustrate the approaches in detail with three real-data examples. 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 #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 #1152991. 	[Title] Importance Sampling [Abstract] Technical Report No. 9805, Department of Statistics, University of Toronto Abstract. Simulated annealing | moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions | has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers. Here, it is shown how one can use the Markov chain transitions for such an annealing sequence to define an importance sampler. The Markov chain aspect allows this method to perform acceptably even for high-dimensional problems, where finding good importance sampling distributions would otherwise be very difficult, while the use of importance weights ensures that the estimates found converge to the correct values as the number of annealing runs increases. This annealed importance sampling procedure resembles the second half of the previously-studied tempered transitions, and can be seen as a generalization of a recently-proposed variant of sequential importance sampling. It is also related to thermodynamic integration methods for estimating ratios of normalizing constants. Annealed importance sampling is most attractive when isolated modes are present, or when estimates of normalizing constants are required, but it may also be more generally useful, since its independent sampling allows one to bypass some of the problems of assessing convergence and autocorrelation in Markov chain samplers. 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.

Paper #643069 has the title `Markov Chain Monte Carlo in Practice: A Roundtable Discussion  
` and the 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. 
`.
Question: Which category should Paper #643069 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #643069 has the title `Markov Chain Monte Carlo in Practice: A Roundtable Discussion  
` and the 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. 
`.
Question: Which category should Paper #643069 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