Above are papers related to the following paper: [Paper_ID] Paper #644427. 	[Title] Outperforming the Gibbs sampler empirical estimator for nearest neighbor random fields [Abstract] Given a Markov chain sampling scheme, does the standard empirical estimator make best use of the data? We show that this is not so and construct better estimators. We restrict attention to nearest neighbor random fields and to Gibbs samplers with deterministic sweep, but our approach applies to any sampler that uses reversible variable-at-a-time updating with deterministic sweep. The structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance. The extra computational cost is negligible. When the random field is spatially homogeneous, symmetrizations of our estimator lead to further variance reduction. The performance of the estimators is evaluated in a simulation study of the Ising model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #644577. 	[Title] Geometric Ergodicity and Hybrid Markov Chains [Abstract] Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will "inherit" the geometric ergodicity of its constituent parts. Acknowledgements. We thank Charlie Geyer for a number of very useful comments regarding spectral theory and central limit theorems. We thank Alison Gibbs, Phil Reiss, Peter Rosenthal, and Richard Tweedie for very helpful discussions. We thank the referee and the editor for many excellent suggestions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131301. 	[Title] A note on acceptance rate criteria for CLTs for Hastings-Metropolis algorithms [Abstract] This note considers positive recurrent Markov chains where the probability of remaining in the current state is arbitrarily close to 1. Specifically, conditions are given which ensure the non-existence of central limit theorems for ergodic averages of functionals of the chain. The results are motivated by applications for Metropolis-Hastings algorithms which are constructed in terms of a rejection probability, (where a rejection involves remaining at the current state). Two examples for commonly used algorithms are given, for the independence sampler and the Metropolis adjusted Langevin algorithm. The examples are rather specialised, although in both cases, the problems which arise are typical of problems commonly occurring for the particular algorithm being used. 0 I would like to thank Kerrie Mengersen Jeff Rosenthal and Richard Tweedie for useful conversations on the subject of this paper. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131334. 	[Title] APPLICATIONS OF CHEEGER'S CONSTANT TO THE CONVERGENCE RATE OF MARKOV CHAINS ON R n [Abstract] Quantitative geometric rates of convergence for reversible Markov chains are closely related to the Cheeger's constant, which is hard to calculate for general state spaces. This article describes a geometric argument to bound the Cheeger's constant for chains on bounded subsets of R n . Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #645897. 	[Title] A note on convergence rates of Gibbs sampling for nonparametric mixtures [Abstract] We consider a mixture model where the mixing distribution is random and is given a Dirichlet process prior. We describe the general structure of two Gibbs sampling algorithms that are useful for approximating Bayesian inferences in this problem. When the kernel f(x j ) of the mixture is bounded, we show that the Markov chains resulting from the Gibbs sampling are uniformly ergodic, and we provide an explicit rate bound. Unfortunately, the bound is not sharp in general; improving sensibly the bound seems however quite difficult. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131305. 	[Title] Two convergence properties of hybrid samplers [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 #1131257. 	[Title] Von Mises type statistics for single site updated local interaction random fields [Abstract] Random field models in image analysis and spatial statistics usually have local interactions. They can be simulated by Markov chains which update a single site at a time. The updating rules typically condition on only a few neighboring sites. If we want to approximate the expectation of a bounded function, can we make better use of the simulations than through the empirical estimator? We describe symmetrizations of the empirical estimator which are computationally feasible and can lead to considerable variance reduction. The method is reminiscent of the idea behind generalized von Mises statistics. To simplify the exposition, we consider mainly nearest neighbor random fields and the Gibbs sampler. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #643485. 	[Title] Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model [Abstract]  Please summarise all the given information.

Paper #644427 has the title `Outperforming the Gibbs sampler empirical estimator for nearest neighbor random fields  
` and the abstract `Given a Markov chain sampling scheme, does the standard empirical estimator make best use of the data? We show that this is not so and construct better estimators. We restrict attention to nearest neighbor random fields and to Gibbs samplers with deterministic sweep, but our approach applies to any sampler that uses reversible variable-at-a-time updating with deterministic sweep. The structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance. The extra computational cost is negligible. When the random field is spatially homogeneous, symmetrizations of our estimator lead to further variance reduction. The performance of the estimators is evaluated in a simulation study of the Ising model.
`.
Question: Which category should Paper #644427 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #644427 has the title `Outperforming the Gibbs sampler empirical estimator for nearest neighbor random fields  
` and the abstract `Given a Markov chain sampling scheme, does the standard empirical estimator make best use of the data? We show that this is not so and construct better estimators. We restrict attention to nearest neighbor random fields and to Gibbs samplers with deterministic sweep, but our approach applies to any sampler that uses reversible variable-at-a-time updating with deterministic sweep. The structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance. The extra computational cost is negligible. When the random field is spatially homogeneous, symmetrizations of our estimator lead to further variance reduction. The performance of the estimators is evaluated in a simulation study of the Ising model.
`.
Question: Which category should Paper #644427 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