Consistent nonparametric Bayesian inference for discretely observed scalar diffusions

TL;DR

This paper develops Bayesian methods for nonparametric drift estimation in one-dimensional ergodic diffusion models using discrete low-frequency data, establishing conditions for posterior consistency.

Contribution

It provides theoretical conditions for posterior consistency in nonparametric Bayesian drift estimation and verifies these for specific priors like wavelet-based priors.

Findings

Posterior consistency is achieved under certain conditions.

Wavelet-based priors are effective for drift estimation.

Theoretical framework supports practical Bayesian inference in diffusion models.

Abstract

We study Bayes procedures for the problem of nonparametric drift estimation for one-dimensional, ergodic diffusion models from discrete-time, low-frequency data. We give conditions for posterior consistency and verify these conditions for concrete priors, including priors based on wavelet expansions.