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 #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 #71736. 	[Title] Sequential Importance Sampling for Nonparametric Bayes Models: The Next Generation Running Title: SIS for Nonparametric Bayes [Abstract] There are two generations of Gibbs sampling methods for semi-parametric models involving the Dirichlet process. The first generation suffered from a severe drawback; namely that the locations of the clusters, or groups of parameters, could essentially become fixed, moving only rarely. Two strategies that have been proposed to create the second generation of Gibbs samplers are integration and appending a second stage to the Gibbs sampler wherein the cluster locations are moved. We show that these same strategies are easily implemented for the sequential importance sampler, and that the first strategy dramatically improves results. As in the case of Gibbs sampling, these strategies are applicable to a much wider class of models. They are shown to provide more uniform importance sampling weights and lead to additional Rao-Blackwellization of estimators. Steve MacEachern is Associate Professor, Department of Statistics, Ohio State University, Merlise Clyde is Assistant Professor, Institute of Statistics and Decision Sciences, Duke University, and Jun Liu is Assistant Professor, Department of Statistics, Stanford University. The work of the second author was supported in part by the National Science Foundation grants DMS-9305699 and DMS-9626135, and that of the last author by the National Science Foundation grants DMS-9406044, DMS-9501570, and the Terman Fellowship. Please summarise all the given information.

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 #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.

Paper #1152259 has the title `Importance Sampling  
` and the 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. 
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Question: Which category should Paper #1152259 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1152259 has the title `Importance Sampling  
` and the 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. 
`.
Question: Which category should Paper #1152259 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