Above are papers related to the following paper: [Paper_ID] Paper #645088. 	[Title] Hierarchical Spatio-Temporal Mapping of Disease Rates [Abstract] Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with socio-demographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or other adverse effects of harmful environmental exposures. Bayes and empirical Bayes methods have proven useful in smoothing crude maps of disease risk, eliminating the instability of estimates in low-population areas while maintaining geographic resolution. In this paper we extend existing hierarchical spatial models to account for temporal effects and spatio-temporal interactions. Fitting the resulting highly-parametrized models requires careful implementation of Markov chain Monte Carlo (MCMC) methods, as well as novel techniques for model evaluation and selection. We illustrate our approach using a dataset of county-specific lung cancer rates in the state of Ohio during the period 1968-1988. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #153063. 	[Title] Bayesian Forecasting of Multinomial Time Series through Conditionally Gaussian Dynamic Models [Abstract] Claudia Cargnoni is with the Dipartimento Statistico, Universita di Firenze, 50100 Firenze, Italy. Peter Muller is Assistant Professor, and Mike West is Professor, in the Institute of Statistics and Decision Sciences at Duke University, Durham NC 27708-0251. Research of Cargnoni was performed while visiting ISDS during 1995. Muller and West were partially supported by NSF under grant DMS-9305699. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #38537. 	[Title] BAYESIAN STATISTICS 6, pp. 000--000  Exact sampling for Bayesian inference: towards general purpose algorithms [Abstract] There are now methods for organising a Markov chain Monte Carlo simulation so that it can be guaranteed that the state of the process at a given time is exactly drawn from the target distribution. The question of assessing convergence totally vanishes. Such methods are known as exact or perfect sampling. The approach that has received most attention uses the protocol of coupling from the past devised by Propp and Wilson (Random Structures and Algorithms,1996), in which multiple dependent paths of the chain are run from different initial states at a sequence of initial times going backwards into the past, until they satisfy the condition of coalescence by time 0. When this is achieved the state at time 0 is distributed according to the required target. This process must be implemented very carefully to assure its validity (including appropriate re-use of random number streams), and also requires one of various tricks to enable us to follow infinitely many sample paths with a finite amount of work. With the ultimate objective of Bayesian MCMC with guaranteed convergence, the purpose of this paper is to describe recent efforts to construct exact sampling methods for continuous-state Markov chains. We review existing methods based on gamma-coupling and rejection sampling (Murdoch and Green, Scandinavian Journal of Statistics, 1998), that are quite straightforward to understand, but require a closed form for the transition kernel and entail cumbersome algebraic manipulation. We then introduce two new methods based on random walk Metropolis, that offer the prospect of more automatic use, not least because the difficult, continuous, part of the transition mechanism can be coupled in a generic way, using a proposal distribution of convenience. One of the methods is based on a neat decomposition of any unimodal (multivariate) symmetric density into pieces that may be re-assembled to construct any translated copy of itself: that allows coupling of a continuum of Metropolis proposals to a finite set, at least for a compact state space. We discuss methods for economically coupling the subsequent accept/reject decisions. Our second new method deals with unbounded state spaces, using a trick due to W. S. Kendall of running a coupled dominating process in parallel with the sample paths of interest. The random subset of the state space below the dominating path is compact, allowing efficient coupling and coalescence. We look towards the possibility that application of such methods could become sufficiently convenient that they could become the basis for routine Bayesian computation in the foreseeable future. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #137868. 	[Title] On Bayesian analysis of mixtures with an unknown number of components  Summary [Abstract] New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods, that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution. The methodology is applied here to the analysis of univariate normal mixtures, using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131277. 	[Title] Bayesian Detection of Clusters and Discontinuities in Disease Maps [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #642641. 	[Title] Bayesian Analysis of Agricultural Field Experiments [Abstract] SUMMARY The paper describes Bayesian analysis for agricultural field experiments, a topic that has received very little previous attention, despite a vast frequentist literature. Adoption of the Bayesian paradigm simplifies the interpretation of the results, especially in ranking and selection. Also, complex formulations can be analyzed with comparative ease, using Markov chain Monte Carlo methods. A key ingredient in the approach is the need for spatial representations of the unobserved fertility patterns. This is discussed in detail. Problems caused by outliers and by jumps in fertility are tackled via hierarchical-t formulations that may find use in other contexts. The paper includes three analyses of variety trials for yield and one example involving binary data; none is entirely straightforward. Some comparisons with frequentist analyses are made. The datasets are available at http://www.stat.duke.edu/~higdon/trials/data.html. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #645084. 	[Title] Modelling Risk from a Disease in Time and Space [Abstract] This paper combines existing models for longitudinal and spatial data in a hierarchical Bayesian framework, with particular emphasis on the role of time- and space-varying covariate effects. Data analysis is implemented via Markov chain Monte Carlo methods. The methodology is illustrated by a tentative re-analysis of Ohio lung cancer data 1968-88. Two approaches that adjust for unmeasured spatial covariates, particularly tobacco consumption, are described. The first includes random effects in the model to account for unobserved heterogeneity; the second adds a simple urbanization measure as a surrogate for smoking behaviour. The Ohio dataset has been of particular interest because of the suggestion that a nuclear facility in the southwest of the state may have caused increased levels of lung cancer there. However, we contend here that the data are inadequate for a proper investigation of this issue. fl Email: leo@stat.uni-muenchen.de Please summarise all the given information.

Paper #645088 has the title `Hierarchical Spatio-Temporal Mapping of Disease Rates  
` and the abstract `Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with socio-demographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or other adverse effects of harmful environmental exposures. Bayes and empirical Bayes methods have proven useful in smoothing crude maps of disease risk, eliminating the instability of estimates in low-population areas while maintaining geographic resolution. In this paper we extend existing hierarchical spatial models to account for temporal effects and spatio-temporal interactions. Fitting the resulting highly-parametrized models requires careful implementation of Markov chain Monte Carlo (MCMC) methods, as well as novel techniques for model evaluation and selection. We illustrate our approach using a dataset of county-specific lung cancer rates in the state of Ohio during the period 1968-1988. 
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Question: Which category should Paper #645088 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #645088 has the title `Hierarchical Spatio-Temporal Mapping of Disease Rates  
` and the abstract `Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with socio-demographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or other adverse effects of harmful environmental exposures. Bayes and empirical Bayes methods have proven useful in smoothing crude maps of disease risk, eliminating the instability of estimates in low-population areas while maintaining geographic resolution. In this paper we extend existing hierarchical spatial models to account for temporal effects and spatio-temporal interactions. Fitting the resulting highly-parametrized models requires careful implementation of Markov chain Monte Carlo (MCMC) methods, as well as novel techniques for model evaluation and selection. We illustrate our approach using a dataset of county-specific lung cancer rates in the state of Ohio during the period 1968-1988. 
`.
Question: Which category should Paper #645088 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