## Bayesian Methods for Nonlinear Classification and RegressionNonlinear Bayesian modelling is a relatively new field, but one that has seen a recent explosion of interest. Nonlinear models offer more flexibility than those with linear assumptions, and their implementation has now become much easier due to increases in computational power. Bayesian methods allow for the incorporation of prior information, allowing the user to make coherent inference. Bayesian Methods for Nonlinear Classification and Regression is the first book to bring together, in a consistent statistical framework, the ideas of nonlinear modelling and Bayesian methods. - Focuses on the problems of classification and regression using flexible, data-driven approaches.
- Demonstrates how Bayesian ideas can be used to improve existing statistical methods.
- Includes coverage of Bayesian additive models, decision trees, nearest-neighbour, wavelets, regression splines, and neural networks.
- Emphasis is placed on sound implementation of nonlinear models.
- Discusses medical, spatial, and economic applications.
- Includes problems at the end of most of the chapters.
- Supported by a web site featuring implementation code and data sets.
The material available at the link below is 'Matlab code for implementing the examples in the book'. http://stats.ma.ic.ac.uk/~ccholmes/Book_code/book_code.html |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Bay esian Modelling | 9 |

2 | 13 |

7 | 28 |

9 | 41 |

Surface Fitting | 95 |

Classification Using Generalised Nonlinear Models | 129 |

Bayesian Tree Models | 149 |

Partition Models | 177 |

NearestNeighbour Models | 209 |

Multiple Response Models | 221 |

Appendix A Probability Distributions | 237 |

The MultinomialDirichlet Model | 243 |

265 | |

271 | |

### Common terms and phrases

acceptance probability additive model allow analysis approach approximate arm tremor assign assume auxiliary variables basis set Bayes factor Bayesian linear model Bayesian model changepoint chapter Chipman choose classification coefficients conjugate prior convergence credible intervals curve fitting data points dataset define Denison density described determine dimension draw error estimate example Figure generalised Gibbs sampler given Hence interactions iterations knot locations knot points linear model linear spline marginal likelihood Markov chain MARS model MCMC Metropolis-Hastings model parameters model space multivariate nearest-neighbour neural networks nonlinear normal distribution number of basis partition model piecewise linear plot posterior distribution posterior inference posterior mean posterior predictive posterior probability predictive distribution predictor space prior distributions prior specification problem proposed random variables regions regression function regression variance response reversible jump sampling algorithm Section simulation Smith and Kohn smoothing splitting node Statist suggested terminal nodes tree structure univariate unknown update vector wavelet zero

### Popular passages

Page 252 - Farmer, JD and Sidorowich, JJ (1987). "Predicting chaotic time series".