Neural networks are a useful statistical tool for nonparametric
regression. In this thesis, I develop a methodology for doing
nonparametric regression within the Bayesian framework. I address the
problem of model selection and model averaging, including estimation
of normalizing constants and searching of the model space in terms of
both the optimal number of hidden nodes in the network as well as the
best subset of explanatory variables. I demonstrate how to use a
noninformative prior for a neural network, which is useful because of
the difficulty in interpreting the parameters. I also prove the
asymptotic consistency of the posterior for neural networks.
Keywords:
Nonparametric regression, Bayesian statistics,
Noninformative prior, Asymptotic consistency, Normalizing constants,
Bayesian random searching, BARS