Automatic Bayesian model averaging for linear regression and applications in Bayesian curve fitting

With the development of MCMC methods, Bayesian methods play a more and more important role in model selection and statistical prediction. However, the sensitivity of the methods to prior distributions has caused much difficul ty to users. In the context of multiple linear regression, we propose an au tomatic prior setting, in which there is no parameter to be specified by us ers. Under the prior setting, we show that sampling from the posterior dist ribution is approximately equivalent to sampling from a Boltzmann distribut ion defined on C-p values. The numerical results show that the Bayesian mod el averaging procedure resulted from the automatic prior settin provides a significant improvement in predictive performance over other two procedures proposed in the literature. The procedure is extended to the problem of Ba yesian curve fitting with regression splines. Evolutionary Monte Carlo is u sed to sample from the posterior distributions.