Above are papers related to the following paper: [Paper_ID] Paper #219218. 	[Title] Monte Carlo Approach to Bayesian Regression Modeling [Abstract] In the framework of a functional response model (i.e. a regression model, or a feedforward neural network) an estimator of a nonlinear response function is constructed from a set of functional units. The parameters defining these functional units are estimated using the Bayesian approach. A sample representing the Bayesian posterior distribution is obtained by applying the Markov chain Monte Carlo procedure, namely the combination of Gibbs and Metropolis-Hastings algorithms. The method is described for histogram, B-spline and radial basis function estimators of a response function. In general, the proposed approach is suitable for finding Bayes-optimal values of parameters in a complicated parameter space. We illustrate the method on numerical examples. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1112417. 	[Title] ON MCMC METHODS IN BAYESIAN REGRESSION ANALYSIS AND MODEL SELECTION [Abstract] The objective of statistical data analysis is not only to describe the behaviour of a system, but also to propose, construct (and then to check) a model of observed processes. Bayesian methodology offers one of possible approaches to estimation of unknown components of the model (its parameters or functional components) in a framework of a chosen model type. However, in many instances the evaluation of Bayes posterior distribution (which is basal for Bayesian solutions) is difficult and practically intractable (even with the help of numerical approximations). In such cases the Bayesian analysis may be performed with the help of intensive simulation techniques called the `Markov chain Monte Carlo'. The present paper reviews the best known approaches to MCMC generation. It deals with several typical situations of data analysis and model construction where MCMC methods have been successfully applied. Special attention is devoted to the problem of selection of optimal regression model constructed from regression splines or from other functional units. Please summarise all the given information.

Paper #219218 has the title `Monte Carlo Approach to Bayesian Regression Modeling  
` and the abstract `In the framework of a functional response model (i.e. a regression model, or a feedforward neural network) an estimator of a nonlinear response function is constructed from a set of functional units. The parameters defining these functional units are estimated using the Bayesian approach. A sample representing the Bayesian posterior distribution is obtained by applying the Markov chain Monte Carlo procedure, namely the combination of Gibbs and Metropolis-Hastings algorithms. The method is described for histogram, B-spline and radial basis function estimators of a response function. In general, the proposed approach is suitable for finding Bayes-optimal values of parameters in a complicated parameter space. We illustrate the method on numerical examples. 
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Question: Which category should Paper #219218 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #219218 has the title `Monte Carlo Approach to Bayesian Regression Modeling  
` and the abstract `In the framework of a functional response model (i.e. a regression model, or a feedforward neural network) an estimator of a nonlinear response function is constructed from a set of functional units. The parameters defining these functional units are estimated using the Bayesian approach. A sample representing the Bayesian posterior distribution is obtained by applying the Markov chain Monte Carlo procedure, namely the combination of Gibbs and Metropolis-Hastings algorithms. The method is described for histogram, B-spline and radial basis function estimators of a response function. In general, the proposed approach is suitable for finding Bayes-optimal values of parameters in a complicated parameter space. We illustrate the method on numerical examples. 
`.
Question: Which category should Paper #219218 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