Above are papers related to the following paper: [Paper_ID] Paper #126920. 	[Title] Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications [Abstract] Suppose one wishes to sample from the density (x) using Markov chain Monte Carlo (MCMC). An auxiliary variable u and its conditional distribution (ujx) can be defined, giving the joint distribution (x; u) = (x)(ujx). A MCMC scheme which samples over this joint distribution can lead to substantial gains in efficiency compared to standard approaches. The revolutionary algorithm of Swendsen and Wang (1987) is one such example. In addition to reviewing the Swendsen-Wang algorithm and its generalizations, this paper introduces a new auxiliary variable method called partial decoupling. Two applications in Bayesian image analysis are considered. The first is a binary classification problem in which partial decoupling out performs SW and single site Metropolis. The second is a PET reconstruction which uses the gray level prior of Geman and McClure (1987). A generalized Swendsen-Wang algorithm is developed for this problem, which reduces the computing time to the point that MCMC is a viable method of posterior exploration. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #126912. 	[Title] Continuous sigmoidal belief networks trained using slice sampling [Abstract] Real-valued random hidden variables can be useful for modelling latent structure that explains correlations among observed variables. I propose a simple unit that adds zero-mean Gaussian noise to its input before passing it through a sigmoidal squashing function. Such units can produce a variety of useful behaviors, ranging from deterministic to binary stochastic to continuous stochastic. I show how "slice sampling" can be used for inference and learning in top-down networks of these units and demonstrate learning on two simple problems. 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 #645571. 	[Title] A Note on the Dirichlet Process Prior in Bayesian Nonparametric Inference with Partial Exchangeability 1 [Abstract] Technical Report no. 297 Department of Statistics University of Washington 1 Sonia Petrone is Assistant Professor, Universita di Pavia, Dipartimento di Economia Politica e Metodi Quantitativi, I-27100 Pavia, Italy and Adrian E. Raftery is Professor of Statistics and Sociology, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. This research was supported by ONR grant no. N-00014-91-J-1074 and by grants from MURST, Rome. 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 #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 #126926. 	[Title] SUPPRESSING RANDOM WALKS IN MARKOV CHAIN MONTE CARLO USING ORDERED OVERRELAXATION [Abstract] Markov chain Monte Carlo methods such as Gibbs sampling and simple forms of the Metropolis algorithm typically move about the distribution being sampled via a random walk. For the complex, high-dimensional distributions commonly encountered in Bayesian inference and statistical physics, the distance moved in each iteration of these algorithms will usually be small, because it is difficult or impossible to transform the problem to eliminate dependencies between variables. The inefficiency inherent in taking such small steps is greatly exacerbated when the algorithm operates via a random walk, as in such a case moving to a point n steps away will typically take around n 2 iterations. Such random walks can sometimes be suppressed using "overrelaxed" variants of Gibbs sampling (a.k.a. the heatbath algorithm), but such methods have hitherto been largely restricted to problems where all the full conditional distributions are Gaussian. I present an overrelaxed Markov chain Monte Carlo algorithm based on order statistics that is more widely applicable. In particular, the algorithm can be applied whenever the full conditional distributions are such that their cumulative distribution functions and inverse cumulative distribution functions can be efficiently computed. The method is demonstrated on an inference problem for a simple hierarchical Bayesian model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #126927. 	[Title] Convergence properties of perturbed Markov chains [Abstract] Acknowledgements. We thank Neal Madras, Radford Neal, Peter Rosenthal, and Richard Tweedie for helpful conversations. This work was partially supported by EPSRC of the U.K., and by NSERC of Canada. 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 #103543. 	[Title] Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function [Abstract] Technical Report No. 9722, Department of Statistics, University of Toronto Abstract. One way to sample from a distribution is to sample uniformly from the region under the plot of its density function. A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal `slice' defined by the current vertical position. Variations on such `slice sampling' methods can easily be implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn. This approach is often easier to implement than Gibbs sampling, and may be more efficient than easily-constructed versions of the Metropolis algorithm. Slice sampling is therefore attractive in routine Markov chain Monte Carlo applications, and for use by software that automatically generates a Markov chain sampler from a model specification. One can also easily devise overrelaxed versions of slice sampling, which sometimes greatly improve sampling efficiency by suppressing random walk behaviour. Random walks can also be avoided in some slice sampling schemes that simultaneously update all variables. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #126909. 	[Title] Analysis of a Non-Reversible Markov Chain Sampler [Abstract] Technical Report BU-1385-M, Biometrics Unit, Cornell University Abstract We analyse the convergence to stationarity of a simple non-reversible Markov chain that serves as a model for several non-reversible Markov chain sampling methods that are used in practice. Our theoretical and numerical results show that non-reversibility can indeed lead to improvements over the diffusive behavior of simple Markov chain sampling schemes. The analysis uses both probabilistic techniques and an explicit diagonalisation. We thank David Aldous, Martin Hildebrand, Brad Mann, and Laurent Saloff-Coste for their help. Please summarise all the given information.

Paper #126920 has the title `Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications  
` and the abstract `Suppose one wishes to sample from the density (x) using Markov chain Monte Carlo (MCMC). An auxiliary variable u and its conditional distribution (ujx) can be defined, giving the joint distribution (x; u) = (x)(ujx). A MCMC scheme which samples over this joint distribution can lead to substantial gains in efficiency compared to standard approaches. The revolutionary algorithm of Swendsen and Wang (1987) is one such example. In addition to reviewing the Swendsen-Wang algorithm and its generalizations, this paper introduces a new auxiliary variable method called partial decoupling. Two applications in Bayesian image analysis are considered. The first is a binary classification problem in which partial decoupling out performs SW and single site Metropolis. The second is a PET reconstruction which uses the gray level prior of Geman and McClure (1987). A generalized Swendsen-Wang algorithm is developed for this problem, which reduces the computing time to the point that MCMC is a viable method of posterior exploration.
`.
Question: Which category should Paper #126920 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #126920 has the title `Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications  
` and the abstract `Suppose one wishes to sample from the density (x) using Markov chain Monte Carlo (MCMC). An auxiliary variable u and its conditional distribution (ujx) can be defined, giving the joint distribution (x; u) = (x)(ujx). A MCMC scheme which samples over this joint distribution can lead to substantial gains in efficiency compared to standard approaches. The revolutionary algorithm of Swendsen and Wang (1987) is one such example. In addition to reviewing the Swendsen-Wang algorithm and its generalizations, this paper introduces a new auxiliary variable method called partial decoupling. Two applications in Bayesian image analysis are considered. The first is a binary classification problem in which partial decoupling out performs SW and single site Metropolis. The second is a PET reconstruction which uses the gray level prior of Geman and McClure (1987). A generalized Swendsen-Wang algorithm is developed for this problem, which reduces the computing time to the point that MCMC is a viable method of posterior exploration.
`.
Question: Which category should Paper #126920 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