Above are papers related to the following paper: [Paper_ID] Paper #561364. 	[Title] Markov Chain Monte Carlo Model Determination for Hierarchical and Graphical Log-linear Models [Abstract] The Bayesian approach to comparing models involves calculating the posterior probability of each plausible model. For high-dimensional contingency tables, the set of plausible models is very large. We focus attention on reversible jump Markov chain Monte Carlo (Green, 1995) and develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-linear models. Even for tables of moderate size, these sets of models may be very large. The choice of suitable prior distributions for model parameters is also discussed in detail, and two examples are presented. For the first example, a 2 fi 3 fi 4 table, the model probabilities calculated using our reversible jump approach are compared with model probabilities calculated exactly or by using an alternative approximation. The second example is a 2 6 contingency table for which exact methods are infeasible, due to the large number of possible models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131267. 	[Title] Parallel Markov chain Monte Carlo sampling. [Abstract] Markov chain Monte Carlo (MCMC) samplers have proved remarkably popular as tools for Bayesian computation. However, problems can arise in their application when the density of interest is high dimensional and strongly correlated. In these circumstances the sampler may be slow to traverse the state space and mixing is poor. In this article we offer a partial solution to this problem. The state space of the Markov chain is augmented to accommodate multiple chains in parallel. Updates to individual chains are based around a genetic style crossover operator acting on `parent' states drawn from the population of chains. This process makes efficient use of gradient information implicitly encoded within the distribution of states across the population. Empirical studies support the claim that the crossover operator acting on a parallel population of chains improves mixing. This is illustrated with an example of sampling a high dimensional posterior probability density from a complex predictive model. By adopting a latent variable approach the methodology is extended to deal with variable selection and model averaging in high dimensions. This is illustrated with an example of knot selection for a spline interpolant. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #16008. 	[Title] [12] J. Whittaker. Graphical Models in Applied Mathematical Multivariate Statis- [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #105865. 	[Title] Statistical Ideas for Selecting Network Architectures [Abstract] Choosing the architecture of a neural network is one of the most important problems in making neural networks practically useful, but accounts of applications usually sweep these details under the carpet. How many hidden units are needed? Should weight decay be used, and if so how much? What type of output units should be chosen? And so on. We address these issues within the framework of statistical theory for model This paper is principally concerned with architecture selection issues for feed-forward neural networks (also known as multi-layer perceptrons). Many of the same issues arise in selecting radial basis function networks, recurrent networks and more widely. These problems occur in a much wider context within statistics, and applied statisticians have been selecting and combining models for decades. Two recent discussions are [4, 5]. References [3, 20, 21, 22] discuss neural networks from a statistical perspective. choice, which provides a number of workable approximate answers. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #642827. 	[Title] Decomposable graphical Gaussian model determination [Abstract] We propose a methodology for Bayesian model determination in decomposable graphical Gaussian models. To achieve this aim we consider a hyper inverse Wishart prior distribution on the concentration matrix for each given graph. To ensure compatibility across models, such prior distributions are obtained by marginalisation from the prior conditional on the complete graph. We explore alternative structures for the hyperparameters of the latter, and their consequences for the model. Model determination is carried out by implementing a reversible jump MCMC sampler. In particular, the dimension-changing move we propose involves adding or dropping an edge from the graph. We characterise the set of moves which preserve the decomposability of the graph, giving a fast algorithm for maintaining the junction tree representation of the graph at each sweep. As state variable, we propose to use the incomplete variance-covariance matrix, containing only the elements for which the corresponding element of the inverse is nonzero. This allows all computations to be performed locally, at the clique level, which is a clear advantage for the analysis of large and complex data-sets. Finally, the statistical and computational performance of the procedure is illustrated by means of both artificial and real multidimensional data-sets. 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 #109323. 	[Title] Estimating Bayes Factors via Posterior Simulation with the Laplace-Metropolis Estimator [Abstract] The key quantity needed for Bayesian hypothesis testing and model selection is the marginal likelihood for a model, also known as the integrated likelihood, or the marginal probability of the data. In this paper we describe a way to use posterior simulation output to estimate marginal likelihoods. We describe the basic Laplace-Metropolis estimator for models without random effects. For models with random effects the compound Laplace-Metropolis estimator is introduced. This estimator is applied to data from the World Fertility Survey and shown to give accurate results. Batching of simulation output is used to assess the uncertainty involved in using the compound Laplace-Metropolis estimator. The method allows us to test for the effects of independent variables in a random effects model, and also to test for the presence of the random effects. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #137873. 	[Title] Stacked Density Estimation [Abstract] Technical Report No. 97-36, Information and Computer Science Department, University of California, Irvine Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105698. 	[Title] Covariate Selection in Hierarchical Models of Hospital Admission Counts: A Bayes Factor Approach 1 [Abstract] TECHNICAL REPORT No. 268 Department of Statistics, GN-22 University of Washington Seattle, Washington 98195 USA 1 Susan L. Rosenkranz is Pew Health Policy Postdoctoral Fellow at the Institute for Health Policy Studies, Box 0936, University of California at San Francisco, San Francisco, CA 94143, and Adrian E. Raftery is Professor of Statistics and Sociology, Department of Statistics, GN-22, University of Washington, Seattle, WA 98195. Rosenkranz's research was supported by the National Research Service Award 5T32CA 09168-17 from the National Cancer Institute. The authors are grateful to Paula Diehr and Kevin Cain for helpful discussions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #423463. 	[Title] Model Selection for Generalized Linear Models via GLIB, with Application to Epidemiology 1 [Abstract] 1 This is the first draft of a chapter for Bayesian Biostatistics, edited by Donald A. Berry and Darlene K. Strangl. Adrian E. Raftery is Professor of Statistics and Sociology, Department of Statistics, GN-22, University of Washington, Seattle, WA 98195, USA. Sylvia Richardson is Directeur de Recherche, INSERM Unite 170, 16 avenue Paul Vaillant Couturier, 94807 Villejuif CEDEX, France. Raftery's research was supported by ONR contract no. N-00014-91-J-1074, by the Ministere de la Recherche et de l'Espace, Paris, by the Universite de Paris VI, and by INRIA, Rocquencourt, France. Raftery thanks the latter two institutions, Paul Deheuvels and Gilles Celeux for hearty hospitality during his Paris sabbatical in which part of this chapter was written. The authors are grateful to Christine Montfort for excellent research assistance and to Mariette Gerber, Michel Chavance and David Madigan for helpful discussions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #308920. 	[Title] A Graphical Characterization of Lattice Conditional Independence Models [Abstract] Lattice conditional independence (LCI) models for multivariate normal data recently have been introduced for the analysis of non-monotone missing data patterns and of nonnested dependent linear regression models ( seemingly unrelated regressions). It is shown here that the class of LCI models coincides with a subclass of the class of graphical Markov models determined by acyclic digraphs (ADGs), namely, the subclass of transitive ADG models. An explicit graph - theoretic characterization of those ADGs that are Markov equivalent to some transitive ADG is obtained. This characterization allows one to determine whether a specific ADG D is Markov equivalent to some transitive ADG, hence to some LCI model, in polynomial time, without an exhaustive search of the (exponentially large) equivalence class [D ]. These results do not require the existence or positivity of joint densities. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #79809. 	[Title] MDL and MML Similarities and Differences (Introduction to Minimum Encoding Inference Part III) [Abstract] Tech Report 207 Department of Computer Science, Monash University, Clayton, Vic. 3168, Australia Abstract: This paper continues the introduction to minimum encoding inductive inference given by Oliver and Hand. This series of papers was written with the objective of providing an introduction to this area for statisticians. We describe the message length estimates used in Wallace's Minimum Message Length (MML) inference and Rissanen's Minimum Description Length (MDL) inference. The differences in the message length estimates of the two approaches are explained. The implications of these differences for applications are discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #39890. 	[Title] A THEORY OF INFERRED CAUSATION perceive causal relationships in uncon trolled observations. 2. the task [Abstract] This paper concerns the empirical basis of causation, and addresses the following issues: We propose a minimal-model semantics of causation, and show that, contrary to common folklore, genuine causal influences can be distinguished from spurious covariations following standard norms of inductive reasoning. We also establish a sound characterization of the conditions under which such a distinction is possible. We provide an effective algorithm for inferred causation and show that, for a large class of data the algorithm can uncover the direction of causal influences as defined above. Finally, we ad dress the issue of non-temporal causation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #354004. 	[Title] Formal Rules for Selecting Prior Distributions: A Review and Annotated Bibliography [Abstract] Subjectivism has become the dominant philosophical foundation for Bayesian inference. Yet, in practice, most Bayesian analyses are performed with so-called "noninfor-mative" priors, that is, priors constructed by some formal rule. We review the plethora of techniques for constructing such priors, and discuss some of the practical and philosophical issues that arise when they are used. We give special emphasis to Jeffreys's rules and discuss the evolution of his point of view about the interpretation of priors, away from unique representation of ignorance toward the notion that they should be chosen by convention. We conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly; when sample sizes are small (relative to the number of parameters being estimated) it is dangerous to put faith in any "default" solution; but when asymptotics take over, Jeffreys's rules and their variants remain reasonable choices. We also provide an annotated bibliography. fl Robert E. Kass is Professor and Larry Wasserman is Associate Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-2717. The work of both authors was supported by NSF grant DMS-9005858 and NIH grant R01-CA54852-01. The authors thank Nick Polson for helping with a few annotations, and Jim Berger, Teddy Seidenfeld and Arnold Zellner for useful comments and discussion. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #310742. 	[Title] Bayesian Graphical Modeling for Intelligent Tutoring Systems [Abstract] Conventional Intelligent Tutoring Systems (ITS) do not acknowledge uncertainty about the student's knowledge. Yet, both the outcome of any teaching intervention and the exact state of the student's knowledge are uncertain. In recent years, researchers have made startling progress in the management of uncertainty in knowledge-based systems. Building on these developments, we describe an ITS architecture that explicitly models uncertainty. This will facilitate more accurate student modeling and provide ITS's which can learn. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5086. 	[Title] Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models [Abstract] Technical Report no. 255 Department of Statistics, University of Washington August 1993; Revised March 1994 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1106789. 	[Title] Model Selection for Consumer Loan Application Data [Abstract] Loan applications at banks are often long, requiring the applicant to provide large amounts of data. Is all of it necessary? Can we save the applicant some frustration and the bank some expense by using only a subset of the relevant variables? To answer this question, I have attempted to model the current loan approval process at a particular bank. I have used several model selection techniques for logistic regression, including stepwise regression, Occam's Window, Markov Chain Monte Carlo Model Composition (Raftery, Madigan, and Hoeting, 1993), and Bayesian Random Searching. The resulting models largely agree upon a subset of only one-third of the original variables. fl This paper was completed in partial fulfillment of the Ph.D. data analysis requirement. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #129896. 	[Title] Accounting for Model Uncertainty in Survival Analysis Improves Predictive Performance [Abstract] Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the model-building process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significance tests to select a single model, and then to make inference conditionally on the selected model. However, this ignores model uncertainty, which can be substantial. We review the standard Bayesian model averaging solution to this problem and extend it to survival analysis, introducing partial Bayes factors to do so for the Cox proportional hazards model. In two examples, taking account of model uncertainty enhances predictive performance, to an extent that could be clinically useful. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #129897. 	[Title] The out-of-bootstrap method for model averaging and selection [Abstract] We propose a bootstrap-based method for model averaging and selection that focuses on training points that are left out of individual bootstrap samples. This information can be used to estimate optimal weighting factors for combining estimates from different bootstrap samples, and also for finding the best subsets the linear model setting. These proposals provide alternatives to Bayesian approaches to model averaging and selection, requiring less computation and fewer subjective choices. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1127530. 	[Title] Bayesian inference for nondecomposable graphical Gaussian models [Abstract] In this paper we propose a method to calculate the posterior probability of a nondecomposable graphical Gaussian model. Our proposal is based on a new device to sample from Wishart distributions, conditional on the graphical constraints. As a result, our methodology allows Bayesian model selection within the whole class of graphical Gaussian models, including nondecomposable ones. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #162664. 	[Title] An Algorithm for the Construction of Bayesian Network Structures from Data [Abstract] Previous algorithms for the construction of Bayesian belief network structures from data have been either highly dependent on conditional independence (CI) tests, or have required an ordering on the nodes to be supplied by the user. We present an algorithm that integrates these two approaches - CI tests are used to generate an ordering on the nodes from the database which is then used to recover the underlying Bayesian network structure using a non CI based method. Results of preliminary evaluation of the algorithm on two networks (ALARM and LED) are presented. We also discuss some algo rithm performance issues and open problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #440815. 	[Title] Change Point and Change Curve Modeling in Stochastic Processes and Spatial Statistics [Abstract] 1 This article will appear in Volume 1, no. 4 (1994) of Journal of Applied Statistical Science. Adrian E. Raftery is Professor of Statistics and Sociology, Department of Statistics, GN-22, University of Washington, Seattle, WA 98195. This research was supported by ONR contract no. N-00014-91-J-1074, by NIH Grant no. 5R01HD26330-02, by the Ministere de la Recherche et de l'Espace, Paris, by the Universite de Paris VI, and by INRIA, Rocquencourt, France. Raftery thanks the latter two institutions, Paul Deheuvels and Gilles Celeux for hearty hospitality during his Paris sabbatical in which this article was written. This article was prepared for presentation at the Conference on Applied Change Point Analysis, University of Maryland-Baltimore, March 17-18, 1993. Parts of this article review collaborative research with others to whom I would like to express my appreciation, namely Volkan Akman, Jeff Banfield, Nhu Le, Steven Lewis, Doug Martin, Fionn Murtagh, Ross Taplin and Simon Tavare. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #15987. 	[Title] "Linear Dependencies Represented by Chain Graphs," "Graphical Modelling With MIM," Manual. "Identifying Independence in Bayesian [Abstract] 8] Dori, D. and Tarsi, M., "A Simple Algorithm to Construct a Consistent Extension of a Partially Oriented Graph," Computer Science Department, Tel-Aviv University. Also Technical Report R-185, UCLA, Cognitive Systems Laboratory, October 1992. [14] Pearl, J. and Wermuth, N., "When Can Association Graphs Admit a Causal Interpretation?," UCLA, Cognitive Systems Laboratory, Technical Report R-183-L, November 1992. [17] Verma, T.S. and Pearl, J., "Deciding Morality of Graphs is NP-complete," Technical Report R-188, UCLA, Cognitive Systems Laboratory, October 1992. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3187. 	[Title] A Reference Bayesian Test for Nested Hypotheses And its Relationship to the Schwarz Criterion [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3191. 	[Title] Model Selection and Accounting for Model Uncertainty in Linear Regression Models [Abstract] 1 Adrian E. Raftery is Professor of Statistics and Sociology, David Madigan is Assistant Professor of Statistics, and Jennifer Hoeting is a Ph.D. Candidate, all at the Department of Statistics, GN-22, University of Washington, Seattle, WA 98195. The research of Raftery and Hoeting was supported by ONR Contract N-00014-91-J-1074. Madigan's research was partially supported by NSF grant no. DMS 92111627. The authors are grateful to Danika Lew for research assistance. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3192. 	[Title] Bayesian Graphical Models for Discrete Data [Abstract] z York's research was supported by a NSF graduate fellowship. The authors are grateful to Julian Besag, David Bradshaw, Jeff Bradshaw, James Carlsen, David Draper, Ivar Heuch, Robert Kass, Augustine Kong, Steffen Lauritzen, Adrian Raftery, and James Zidek for helpful comments and discussions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #137849. 	[Title] Inference in Model-Based Cluster Analysis [Abstract] Technical Report no. 285 Department of Statistics University of Washington. March 10, 1995 Please summarise all the given information.

Paper #561364 has the title `Markov Chain Monte Carlo Model Determination for Hierarchical and Graphical Log-linear Models  
` and the abstract `The Bayesian approach to comparing models involves calculating the posterior probability of each plausible model. For high-dimensional contingency tables, the set of plausible models is very large. We focus attention on reversible jump Markov chain Monte Carlo (Green, 1995) and develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-linear models. Even for tables of moderate size, these sets of models may be very large. The choice of suitable prior distributions for model parameters is also discussed in detail, and two examples are presented. For the first example, a 2 fi 3 fi 4 table, the model probabilities calculated using our reversible jump approach are compared with model probabilities calculated exactly or by using an alternative approximation. The second example is a 2 6 contingency table for which exact methods are infeasible, due to the large number of possible models. 
`.
Question: Which category should Paper #561364 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #561364 has the title `Markov Chain Monte Carlo Model Determination for Hierarchical and Graphical Log-linear Models  
` and the abstract `The Bayesian approach to comparing models involves calculating the posterior probability of each plausible model. For high-dimensional contingency tables, the set of plausible models is very large. We focus attention on reversible jump Markov chain Monte Carlo (Green, 1995) and develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-linear models. Even for tables of moderate size, these sets of models may be very large. The choice of suitable prior distributions for model parameters is also discussed in detail, and two examples are presented. For the first example, a 2 fi 3 fi 4 table, the model probabilities calculated using our reversible jump approach are compared with model probabilities calculated exactly or by using an alternative approximation. The second example is a 2 6 contingency table for which exact methods are infeasible, due to the large number of possible models. 
`.
Question: Which category should Paper #561364 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