Above are papers related to the following paper: [Paper_ID] Paper #561809. 	[Title] Bayesian curve fitting using multivariate normal mixtures [Abstract] Problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models. Multi-dimensional density estimation using Dirichlet mixture models provides the theoretical basis for semi-parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions. These Bayesian regression functions have features similar to generalised kernel regression estimates, but the formal analysis addresses problems of multivariate smoothing parameter estimation and the assessment of uncertainties about regression functions naturally. Computations are based on multi-dimensional versions of existing Markov chain simulation analysis of univariate Dirichlet mixture models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #67584. 	[Title] Hyperparameter estimation in Dirichlet process mixture models [Abstract] In Bayesian density estimation and prediction using Dirichlet process mixtures of standard, exponential family distributions, the precision or total mass parameter of the mixing Dirichlet process is a critical hyperparame-ter that strongly influences resulting inferences about numbers of mixture components. This note shows how, with respect to a flexible class of prior distributions for this parameter, the posterior may be represented in a simple conditional form that is easily simulated. As a result, inference about this key quantity may be developed in tandem with the existing, routine Gibbs sampling algorithms for fitting such mixture models. The concept of data augmentation is important, as ever, in developing this extension of the existing algorithm. A final section notes an simple asymptotic approx imation to the posterior. 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 #1127558. 	[Title] Bayesian Models for Non-Linear Autoregressions [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #561674. 	[Title] Studies of Neurological Transmission Analysis using Hierarchical Bayesian Mixture Models [Abstract] Hierarchically structured mixture models are studied in the context of data analysis and inference on neural synaptic transmission characteristics in mammalian, and other, central nervous systems. Mixture structures arise due to uncertainties about the stochastic mechanisms governing the responses to electro-chemical stimulation of individual neuro-transmitter release sites at nerve junctions. Models attempt to capture scientific features such as the sensitivity of individual synaptic transmission sites to electro-chemical stimuli, and the extent of their electro-chemical responses when stimulated. This is done via suitably structured classes of prior distributions for parameters describing these features. Such priors may be structured to permit assessment of currently topical scientific hypotheses about fundamental neural function. Posterior analysis is implemented via stochastic simulation. Several data analyses are described to illustrate the approach, with resulting neurophysiological insights in some recently generated experimental contexts. Further developments and open questions, both neurophysiological and statistical, are noted. Research partially supported by the NSF under grants DMS-9024793, DMS-9305699 and DMS-9304250. This work represents part of a collaborative project with Dr Dennis A Turner, of Duke University Medical Center and Durham VA. Data was provided by Dr Turner and by Dr Howard V Wheal of Southampton University. A slightly revised version of this paper is published in the Journal of the American Statistical Association (vol 92, pp587-606), under the modified title Hierarchical Mixture Models in Neurological Transmission Analysis. The author is the recipient of the 1997 Mitchell Prize for "the Bayesian analysis of a substantive and concrete problem" based on the work reported in this paper. 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 #1127566. 	[Title] Hierarchical priors and mixture models, with application in regression and density estimation [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #562067. 	[Title] Computing Nonparametric Hierarchical Models [Abstract] Bayesian models involving Dirichlet process mixtures are at the heart of the modern nonparametric Bayesian movement. Much of the rapid development of these models in the last decade has been a direct result of advances in simulation-based computational methods. Some of the very early work in this area, circa 1988-1991, focused on the use of such nonparametric ideas and models in applications of otherwise standard hierarchical models. This chapter provides some historical review and perspective on these developments, with a prime focus on the use and integration of such nonparametric ideas in hierarchical models. We illustrate the ease with which the strict parametric assumptions common to most standard Bayesian hierarchical models can be relaxed to incorporate uncertainties about functional forms using Dirichlet process components, partly enabled by the approach to computation using MCMC methods. The resulting methology is illustrated with two examples taken from an unpublished 1992 report on the topic. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #561789. 	[Title] Practical Bayesian Inference Using Mixtures of Mixtures [Abstract] Discrete mixtures of normal distributions are widely used in modeling amplitude fluctuations of electrical potentials at synapses of human, and other animal nervous systems. The usual framework has independent data values y j arising as y j = j + x n 0 +j where the means j come from some discrete prior G() and the unknown x n 0 +j 's and observed x j ; j = 1; : : : ; n 0 are gaussian noise terms. A practically important development of the associated statistical methods is the issue of non-normality of the noise terms, often the norm rather than the exception in the neurological context. We have recently developed models, based on convolutions of Dirichlet process mixtures, for such problems. Explicitly, we model the noise data values x j as arising from a Dirich-let process mixture of normals, in addition to modeling the location prior G() as a Dirichlet process itself. This induces a Dirichlet mixture of mixtures of normals, whose analysis may be developed using Gibbs sampling techniques. We discuss these models and their analysis, and illustrate in the context of neurological response analysis. Please summarise all the given information.

Paper #561809 has the title `Bayesian curve fitting using multivariate normal mixtures  
` and the abstract `Problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models. Multi-dimensional density estimation using Dirichlet mixture models provides the theoretical basis for semi-parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions. These Bayesian regression functions have features similar to generalised kernel regression estimates, but the formal analysis addresses problems of multivariate smoothing parameter estimation and the assessment of uncertainties about regression functions naturally. Computations are based on multi-dimensional versions of existing Markov chain simulation analysis of univariate Dirichlet mixture models. 
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Question: Which category should Paper #561809 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #561809 has the title `Bayesian curve fitting using multivariate normal mixtures  
` and the abstract `Problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models. Multi-dimensional density estimation using Dirichlet mixture models provides the theoretical basis for semi-parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions. These Bayesian regression functions have features similar to generalised kernel regression estimates, but the formal analysis addresses problems of multivariate smoothing parameter estimation and the assessment of uncertainties about regression functions naturally. Computations are based on multi-dimensional versions of existing Markov chain simulation analysis of univariate Dirichlet mixture models. 
`.
Question: Which category should Paper #561809 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