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 #1131300. 	[Title] Reparameterisation Issues in Mixture Modelling and their bearing on MCMC algorithms [Abstract] There is increasing need for efficient estimation of mixture distributions, especially following the explosion in the use of these as modelling tools in many applied fields. We propose in this paper a Bayesian noninformative approach for the estimation of normal mixtures which relies on a reparameterisation of the secondary components of the mixture in terms of divergence from the main component. As well as providing an intuitively appealing representation at the modelling stage, this reparameterisation has important bearing on both the prior distribution and the performance of MCMC algorithms. We compare two possible reparameterisations extending Mengersen and Robert (1996) and show that the reparameterisation which does not link the secondary components together is associated with poor convergence properties of MCMC algorithms. 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 #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 #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 #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 #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 #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 #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 #1154068. 	[Title] Bayesian MARS [Abstract] A Bayesian approach to multivariate adaptive regression spline (MARS) fitting (Friedman, 1991) is proposed. This takes the form of a probability distribution over the space of possible MARS models which is explored using reversible jump Markov chain Monte Carlo methods (Green, 1995). The generated sample of MARS models produced is shown to have good predictive power when averaged and allows easy interpretation of the relative importance of predictors to the overall fit. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #91581. 	[Title] Finding Overlapping Distributions with MML [Abstract] This paper considers an aspect of mixture modelling. Significantly overlapping distributions require more data for their parameters to be accurately estimated than well separated distributions. For example, two Gaussian distributions are considered to significantly overlap when their means are within three standard deviations of each other. If insufficient data is available, only a single component distribution will be estimated, although the data originates from two component distributions. We consider how much data is required to distinguish two component distributions from one distribution in mixture modelling using the minimum message length (MML) criterion. First, we perform experiments which show the MML criterion performs well relative to other Bayesian criteria. Second, we make two improvements to the existing MML estimates, that improve its performance with overlapping distributions. 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.

Paper #1110000 has the title `FLEXIBLE PARAMETRIC MEASUREMENT ERROR MODELS  
` and the 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. 
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Question: Which category should Paper #1110000 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1110000 has the title `FLEXIBLE PARAMETRIC MEASUREMENT ERROR MODELS  
` and the 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. 
`.
Question: Which category should Paper #1110000 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