Bayes factor asymptotics for variable selection in the Gaussian process framework

We investigate Bayesian variable selection in models driven by Gaussian processes, which allows us to treat linear, nonlinear and nonparametric models, conjunction with even dependent setups, the same vein. consider Bayes factor route selection, develop a general asymptotic theory for process framework “large p, large n” settings $$p\gg n$$ , establishing almost sure exponential convergence of under appropriately mild conditions. The fixed p setup is included as special case. To illustrate, we apply our result linear regression, model squared covariance function accommodating covariates, first-order autoregressive time-varying covariates. also follow up theoretical investigations ample simulation experiments above regression contexts real, riboflavin data consisting 71 observations 4088 For implementation using factors, novel effective general-purpose transdimensional, transformation-based Markov chain Monte Carlo algorithm, has played crucial role simulated real applications.