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An extensive and well documented package implementing Markov chain Monte Carlo methods for Bayesian inference in neural networks, Gaussian processes (regression, binary and multi-class classification), mixture models and Dirichlet Diffusion trees. The GPML toolbox implements approximate inference algorithms for Gaussian processes such as Expectation Propagation, the Laplace Approximation and Variational Bayes for a wide class of likelihood functions for both regression and classification. A collection of matlab functions for Bayesian inference with Markov chain Monte Carlo (MCMC) methods. It comes with a big algebra of covariance and mean functions allowing for flexible modeling. The purpose of this toolbox was to port some of the features in fbm to matlab for easier development for matlab users. Gaussian processes - a replacement for supervised neural networks? Implements sparse GP regression as described in Sparse Gaussian Processes using Pseudo-inputs and Flexible and efficient Gaussian process models for machine learning. Statistical Interpolation of Spatial Data: Some Theory for Kriging, Michael L. Statistics for Spatial Data (revised edition), Noel A. Cressie, Wiley, 1993 Spline Models for Observational Data, Grace Wahba, SIAM, 1990 The Bayesian Research Kitchen at The Wordsworth Hotel, Grasmere, Ambleside, Lake District, United Kingdom 05 - 07 September 2008.

Although Gaussian processes have a long history in the field of statistics, they seem to have been employed extensively only in niche areas. With the advent of kernel machines in the machine learning community, models based on Gaussian processes have become commonplace for problems of regression (kriging) and classification as well as a host of more specialized applications. Gaussian Processes for Machine Learning, Carl Edward Rasmussen and Chris Williams, the MIT Press, 2006, online version. The SPGP uses gradient-based marginal likelihood optimization to find suitable basis points and kernel hyperparameters in a single joint optimization. Bayesian Nonparametric and nonstationary regression by treed Gaussian processes with jumps to the limiting linear model (LLM). Comment: A short introduction to GPs, emphasizing the relationships to paramteric models (RBF networks, neural networks, splines).

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Special cases also implememted include Bayesian linear models, linear CART, stationary separable and isotropic Gaussian process regression.

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