Bayesian Analysis Of Single Index Models

We develop a fully Bayesian method to analyze the single index models, including variable selection, the index vector estimation and the link function fitting with free knot splines. The proposed method is implemented by virtue of the reversible jump Markov chain Monte Cairo technique. To obtain a faster algorithm, we not only specify the conjugate normal-inverse gamma priors for the spline coefficients and error variance to get the marginal posterior of the rest unknown quantities,more important, design a simple but more general random walk Metropolis sampler to rapidly sample from the conditional posterior distribution of the index vector.Simulated and real examples are demonstrated.