Bayesian sieve methods: approximation rates and adaptive posterior contraction rates |
| |
Authors: | Taihe Yi Zhengming Wang Dongyun Yi |
| |
Institution: | 1. College of System Engineering, National University of Defense Technology, Changsha, People's Republic of China;2. College of Liberal Arts and Science, National University of Defense Technology, Changsha, People's Republic of China |
| |
Abstract: | In the last 20 years, a lot of achievements have been made in the study of posterior contraction rates of nonparametric Bayesian methods, and plenty of them involve sieve priors, but mainly for specific models or sieves. We provide a posterior contraction theorem for general parametric sieve priors. The theorem has weaker and simpler conditions compared with the existing results, and indicates that the sieve prior is rate adaptive. We apply the general theorem to density estimations and nonparametric regression with jumps. We also provided a reversible jump MCMC (Markov Chain Monte Carlo) algorithm for the sieve prior. |
| |
Keywords: | Sieve prior posterior contraction rate approximation rate rate adaptive change-point reversible jump MCMC |
|
|