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 #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 #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 #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 #643597. 	[Title] A Nonparametric Bayesian Approach to Modelling Nonlinear Time Series [Abstract] The Bayesian multivariate adaptive regression spline (BMARS) methodology of Denison et al. (1997) is extended to cope with nonlinear time series and financial datasets. The nonlinear time series model is closely related to the adaptive spline threshold autoregressive (ASTAR) method of Lewis and Stevens (1991) while the financial models can be thought of as Bayesian versions of both the generalised and simple autoregressive conditional het-eroscadastic (GARCH and ARCH) models. 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 #643695. 	[Title] Simulation Based Bayesian Nonparametric Regression Methods [Abstract]  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 #17363. 	[Title] Logistic Response Projection Pursuit [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3229. 	[Title] Book Review  Introduction to the Theory of Neural Computation Reviewed by: 2 [Abstract] Neural computation, also called connectionism, parallel distributed processing, neural network modeling or brain-style computation, has grown rapidly in the last decade. Despite this explosion, and ultimately because of impressive applications, there has been a dire need for a concise introduction from a theoretical perspective, analyzing the strengths and weaknesses of connectionist approaches and establishing links to other disciplines, such as statistics or control theory. The Introduction to the Theory of Neural Computation by Hertz, Krogh and Palmer (subsequently referred to as HKP) is written from the perspective of physics, the home discipline of the authors. The book fulfills its mission as an introduction for neural network novices, provided that they have some background in calculus, linear algebra, and statistics. It covers a number of models that are often viewed as disjoint. Critical analyses and fruitful comparisons between these models 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 #6910. 	[Title] Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #444191. 	[Title] Automatic Smoothing Spline Projection Pursuit  Automatic Smoothing Spline Projection Pursuit. [Abstract] kj = 1. The standard PPR algorithm of Friedman and Stuet-zle (1981) estimates the smooth functions f j using the supersmoother nonparametric scatterplot smoother. Friedman's algorithm constructs a model with M max linear combinations, then prunes back to a simpler model of size M M max , where M and M max are specified by the user. This paper discusses an alternative algorithm in which the smooth functions are estimated using smoothing splines. The direction coefficients ff j , the amount of smoothing in each direction, and the number of terms M and M max are determined to optimize a single generalized cross-validation measure. Please summarise all the given information.

Paper #1154068 has the title `Bayesian MARS  
` and the 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. 
`.
Question: Which category should Paper #1154068 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1154068 has the title `Bayesian MARS  
` and the 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. 
`.
Question: Which category should Paper #1154068 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