Bayesian sieve methods: approximation rates and adaptive posterior contraction rates

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

AMS SUBJECT CLASSIFICATIONS:

• 62C10
• 62G20
• 62G05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partly supported by the National Natural Science Foundation of China [No. 61573367 and No. 61703408].