Abstract: In this paper the nonparametric regression model y= f(x)+ε, where f (x) is a smoothing function, is considered. The nonparametric regression f (x) is approximated by a spline function. The knot number is not fixed but given a noninformation prior, by which the uncertainty of the knot number is studied. The regression f(x) is estimated by the method of Bayesian model averaging and the posterior interval is also estimated.

Key words: reversible jumped MCMC sampling, spline regression, Bayes factor, Bayesian model averaging, reversible jumped MCMC sampling, spline regression, Bayes factor