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 #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 #1131172. 	[Title] FROM METROPOLIS TO DIFFUSIONS: GIBBS STATES AND OPTIMAL SCALING [Abstract] This paper investigates the behaviour of the random walk Metropolis algorithm in high dimensional problems. Here we concentrate on the case where the components in the target density is a spatially homogeneous Gibbs distribution with finite range. The performance of the algorithm is strongly linked to the presence or absence of phase transition for the Gibbs distribution; the convergence time being approximately linear in dimension for problems where phase transition is not present. Related to this, there is an optimal way to scale the variance of the proposal distribution in order to maximise the speed of convergence of the algorithm. This turns out to involve scaling the variance of the proposal as the reciprocal of dimension (at least in the phase transition free case). Moreover the actual optimal scaling can be characterised in terms of the overall acceptance rate of the algorithm, the maximising value being 0:234, the value as predicted by studies on simpler classes of target density. The results are proved in the framework of a weak convergence result, which shows that the algorithm actually behaves like an infinite dimensional diffusion process in high dimensions. 1. Introduction and discussion of results Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #642798. 	[Title] WEAK CONVERGENCE AND OPTIMAL SCALING OF RANDOM WALK METROPOLIS ALGORITHMS [Abstract] This paper considers the problem of scaling the proposal distribution of a multidimensional random walk Metropolis algorithm, in order to maximize the efficiency of the algorithm. The main result is a weak convergence result as the dimension of a sequence of target densities, n, converges to 1. When the proposal variance is appropriately scaled according to n, the sequence of stochastic processes formed by the first component of each Markov chain, converge to the appropriate limiting Langevin diffusion process. The limiting diffusion approximation admits a straight-forward efficiency maximization problem, and the resulting asymptotically optimal policy is related to the asymptotic acceptance rate of proposed moves for the algorithm. The asymptotically optimal acceptance rate is 0.234 under quite general conditions. The main result is proved in the case where the target density has a symmetric product form. Extensions of the result are discussed. 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 #642894. 	[Title] Rates of convergence of the Hastings and Metropolis algorithms [Abstract] We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution . In the independence case (in IR k ) these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of ; in the symmetric case (in IR only) we show geometric convergence essentially occurs if and only if has geometric tails. We also evaluate recently developed computable bounds on the rates of convergence in this context: examples show that these theoretical bounds can be inherently extremely conservative, although when the chain is stochastically monotone the bounds may well be effective. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #645870. 	[Title] EXACT TRANSITION PROBABILITIES FOR THE INDEPENDENCE METROPOLIS SAMPLER [Abstract] A recent result of Jun Liu's has shown how to compute explicitly the eigen-values and eigenvectors for the Markov chain derived from a special case of the Hastings sampling algorithm, known as the indepdendence Metropolis sampler. In this note, we show how to extend the result to obtain exact n-step transition probabilities for any n. This is done first for a chain on a finite state space, and then extended to a general (discrete or continuous) state space. The paper concludes with some implications for diagnostic tests of convergence of Markov chain samplers. 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 #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 #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.

Paper #644470 has the title `Adaptive proposal distribution for random walk Metropolis algorithm  
` and the 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. 
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Question: Which category should Paper #644470 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #644470 has the title `Adaptive proposal distribution for random walk Metropolis algorithm  
` and the 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. 
`.
Question: Which category should Paper #644470 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