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 #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 #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 #644494. 	[Title] Self Regenerative Markov Chain Monte Carlo  Summary [Abstract] We propose a new method of construction of Markov chains with a given stationary distribution . This method is based on construction of an auxiliary chain with some other stationary distribution and picking elements of this auxiliary chain a suitable number of times. The proposed method has many advantages over its rivals. It is easy to implement; it provides a simple analysis; it can be faster and more efficient than the currently available techniques and it can also be adapted during the course of the simulation. We make theoretical and numerical comparisons of the characteristics of the proposed algorithm with some other MCMC techniques. 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 #1131314. 	[Title] Adaptation for Self Regenerative MCMC  SUMMARY [Abstract] The self regenerative MCMC is a tool for constructing a Markov chain with a given stationary distribution by constructing an auxiliary chain with some other stationary distribution . Elements of the auxiliary chain are picked a suitable random number of times so that the resulting chain has the stationary distribution , Sahu and Zhigljavsky (1998). In this article we provide a generic adaptation scheme for the above algorithm. The adaptive scheme is to use the knowledge of the stationary distribution gathered so far and then to update during the course of the simulation. This method is easy to implement and often leads to considerable improvement. We obtain theoretical results for the adaptive scheme. Our proposed methodology is illustrated with a number of realistic examples in Bayesian computation and its performance is compared with other available MCMC techniques. In one of our applications we develop a non-linear dynamics model for modeling predator-prey relationships in the wild. 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 #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 #644470. 	[Title] Adaptive proposal distribution for random walk Metropolis algorithm [Abstract] The choice of a suitable MCMC method and further the choice of a proposal distribution is known to be crucial for the convergence of the Markov chain. However, in many cases the choice of an effective proposal distribution is difficult. As a remedy we suggest a method called Adaptive Proposal (AP). Although the stationary distribution of the AP algorithm is slightly biased, it appears to provide an efficient tool for, e.g., reasonably low dimensional problems, as typically encountered in non-linear regression problems in natural sciences. As a realistic example we include a successful application of the AP algorithm in parameter estimation for the satellite instrument 'GO-MOS'. In this paper we also present a comprehensive test procedure and systematic performance criteria for comparing Adaptive Proposal algorithm with more traditional Metropolis algorithms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #642681. 	[Title] Assessing Convergence of Markov Chain Monte Carlo Algorithms [Abstract] We motivate the use of convergence diagnostic techniques for Markov Chain Monte Carlo algorithms and review various methods proposed in the MCMC literature. A common notation is established and each method is discussed with particular emphasis on implementational issues and possible extensions. The methods are compared in terms of their interpretability and applicability and recommendations are provided for particular classes of problems. 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 #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.

Paper #1131258 has the title `Discretization of continuous Markov chains and MCMC convergence assessment  
` and the 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. 
`.
Question: Which category should Paper #1131258 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1131258 has the title `Discretization of continuous Markov chains and MCMC convergence assessment  
` and the 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. 
`.
Question: Which category should Paper #1131258 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