Bayesian methods for neural networks are of interest to researchers in statistics, engineering, and artificial intelligence. This is a very active research area in statistics and artificial intelligence.

1 Introduction.- 1.1 Bayesian and frequentist views of learning.- 1.2 Bayesian neural networks.- 1.3 Markov chain Monte Carlo methods.- 1.4 Outline of the remainder of the book.- 2 Priors for Infinite Networks.- 2.1 Priors converging to Gaussian processes.- 2.2 Priors converging to non-Gaussian stable processes.- 2.3 Priors for nets with more than one hidden layer.- 2.4 Hierarchical models.- 3 Monte Carlo Implementation.- 3.1 The hybrid Monte Carlo algorithm.- 3.2 An implementation of Bayesian neural network learning.- 3.3 A demonstration of the hybrid Monte Carlo implementation.- 3.4 Comparison of hybrid Monte Carlo with other methods.- 3.5 Variants of hybrid Monte Carlo.- 4 Evaluation of Neural Network Models.- 4.1 Network architectures, priors, and training procedures.- 4.2 Tests of the behaviour of large networks.- 4.3 Tests of Automatic Relevance Determination.- 4.4 Tests of Bayesian models on real data sets.- 5 Conclusions and Further Work.- 5.1 Priors for complex models.- 5.2 Hierarchical Models - ARD and beyond.- 5.3 Implementation using hybrid Monte Carlo.- 5.4 Evaluating performance on realistic problems.- A Details of the Implementation.- A.1 Specifications.- A.1.1 Network architecture.- A.1.2 Data models.- A.1.3 Prior distributions for parameters and hyperparameters.- A.1.4 Scaling of priors.- A.2 Conditional distributions for hyperparameters.- A.2.1 Lowest-level conditional distributions.- A.2.2 Higher-level conditional distributions.- A.3 Calculation of derivatives.- A.3.1 Derivatives of the log prior density.- A.3.2 Log likelihood derivatives with respect to unit values.- A.3.3 Log likelihood derivatives with respect to parameters.- A.4 Heuristic choice of stepsizes.- A.5 Rejection sampling from the prior.- B Obtaining the software.