Nonparametric Bayesian posterior contraction rates for scalar diffusions with high-frequency data

02/15/2018
by   Kweku Abraham, et al.
0

We consider inference in the scalar diffusion model dX_t=b(X_t)dt+σ(X_t)dW_t with discrete data (X_jΔ_n)_0≤ j ≤ n, n→∞, Δ_n→ 0 and periodic coefficients. For σ given, we prove a general theorem detailing conditions under which Bayesian posteriors will contract in L^2-distance around the true drift function b_0 at the frequentist minimax rate (up to logarithmic factors) over Besov smoothness classes. We exhibit natural nonparametric priors which satisfy our conditions. Our results show that the Bayesian method adapts both to an unknown sampling regime and to unknown smoothness.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/22/2022

Bayesian estimation in a multidimensional diffusion model with high frequency data

We consider nonparametric Bayesian inference in a multidimensional diffu...
research
12/22/2020

Nonparametric Bayesian inference for reversible multi-dimensional diffusions

We study nonparametric Bayesian modelling of reversible multi-dimensiona...
research
02/25/2018

Bayesian inverse problems with partial observations

We study a nonparametric Bayesian approach to linear inverse problems un...
research
08/15/2020

The art of BART: On flexibility of Bayesian forests

Considerable effort has been directed to developing asymptotically minim...
research
08/09/2023

Heavy-tailed Bayesian nonparametric adaptation

We propose a new Bayesian strategy for adaptation to smoothness in nonpa...
research
11/09/2020

A Computationally Efficient Classification Algorithm in Posterior Drift Model: Phase Transition and Minimax Adaptivity

In massive data analysis, training and testing data often come from very...
research
10/22/2017

Adaptive Bayesian nonparametric regression using kernel mixture of polynomials with application to partial linear model

We propose a kernel mixture of polynomials prior for Bayesian nonparamet...

Please sign up or login with your details

Forgot password? Click here to reset