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 #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 #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 #1115291. 	[Title] How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis 1 [Abstract]  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 #280876. 	[Title] Principal Curve Clustering With Noise [Abstract] Technical Report 317 Department of Statistics University of Washington. 1 Derek Stanford is Graduate Research Assistant and Adrian E. Raftery is Professor of Statistics and Sociology, both at the Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322, USA. E-mail: stanford@stat.washington.edu and raftery@stat.washington.edu. Web: http://www.stat.washington.edu/raftery. This research was supported by ONR grants N00014-96-1-0192 and N00014-96-1-0330. The authors are grateful to Simon Byers, Gilles Celeux and Christian Posse for helpful discussions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5055. 	[Title] Boosting the Margin: A New Explanation for the Effectiveness of Voting Methods [Abstract] One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik's support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the bias-variance decomposition. 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 #1997. 	[Title] Cross-Validation and the Bootstrap: Estimating the Error Rate of a Prediction Rule [Abstract] A training set of data has been used to construct a rule for predicting future responses. What is the error rate of this rule? The traditional answer to this question is given by cross-validation. The cross-validation estimate of prediction error is nearly unbiased, but can be highly variable. This article discusses bootstrap estimates of prediction error, which can be thought of as smoothed versions of cross-validation. A particular bootstrap method, the 632+ rule, is shown to substantially outperform cross-validation in a catalog of 24 simulation experiments. Besides providing point estimates, we also consider estimating the variability of an error rate estimate. All of the results here are nonparametric, and apply to any possible prediction rule: however we only study classification problems with 0-1 loss in detail. Our simulations include "smooth" prediction rules like Fisher's Linear Discriminant Function, and unsmooth ones like Nearest Neighbors. 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 #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 #17242. 	[Title] Detecting Features in Spatial Point Processes with Clutter via Model-Based Clustering [Abstract] Technical Report No. 295 Department of Statistics, University of Washington October, 1995 1 Abhijit Dasgupta is a graduate student at the Department of Biostatistics, University of Washington, Box 357232, Seattle, WA 98195-7232, and his e-mail address is dasgupta@biostat.washington.edu. Adrian E. Raftery is Professor of Statistics and Sociology, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322, and his e-mail address is raftery@stat.washington.edu. This research was supported by Office of Naval Research Grant no. N-00014-91-J-1074. The authors are grateful to Peter Guttorp, Girardeau Henderson and Robert Muise for helpful discussions. 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 #154982. 	[Title] Bias, variance and prediction error for classification rules [Abstract] We study the notions of bias and variance for classification rules. Following Efron (1978) we develop a decomposition of prediction error into its natural components. Then we derive bootstrap estimates of these components and illustrate how they can be used to describe the error behaviour of a classifier in practice. In the process we also obtain a bootstrap estimate of the error of a "bagged" classifier. 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 #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 #1110000. 	[Title] FLEXIBLE PARAMETRIC MEASUREMENT ERROR MODELS [Abstract] Inferences in measurement error models can be sensitive to modeling assumptions. Specifically, if the model is incorrect then the estimates can be inconsistent. To reduce sensitivity to modeling assumptions and yet still retain the efficiency of parametric inference we propose to use flexible parametric models which can accommodate departures from standard parametric models. We use mixtures of normals for this purpose. We study two cases in detail: a linear errors-in-variables model and a change-point Berkson model. fl Raymond J. Carroll is Professor of Statistics, Nutrition and Toxicology, Department of Statistics, Texas A&M University, College Station, TX 77843-3143. Kathryn Roeder is Associate Professor, and Larry Wasser-man is Professor, Department of Statistics, Carnegie-Mellon University, Pittsburgh PA 15213-3890. Carroll's research was supported by a grant from the National Cancer Institute (CA-57030). Roeder's research was supported by NSF grant DMS-9496219. Wasserman's research was supported by NIH grant RO1-CA54852 and NSF grants DMS-9303557 and DMS-9357646. 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 #3187 has the title `A Reference Bayesian Test for Nested Hypotheses And its Relationship to the Schwarz Criterion  
` and the abstract `nan`.
Question: Which category should Paper #3187 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #3187 has the title `A Reference Bayesian Test for Nested Hypotheses And its Relationship to the Schwarz Criterion  
` and the abstract `nan`.
Question: Which category should Paper #3187 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