Full adaptation to smoothness using randomly truncated series priors with Gaussian coefficients and inverse gamma scaling

Abstract

We study random series priors for estimating a functional parameter (f\in L^2[0,1]). We show that with a series prior with random truncation, Gaussian coefficients, and inverse gamma multiplicative scaling, it is possible to achieve posterior contraction at optimal rates and adaptation to arbitrary degrees of smoothness. We present general results that can be combined with existing rate of contraction results for various nonparametric estimation problems. We give concrete examples for signal estimation in white noise and drift estimation for a one-dimensional SDE.

References in corpus (5)

• Convergence rates of posterior distributions for noniid observations
• Reproducing kernel Hilbert spaces of Gaussian priors
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• Reversible jump MCMC for nonparametric drift estimation for diffusion processes
• Gaussian process methods for one-dimensional diffusions: optimal rates and adaptation

Cited by in corpus (1)

• Adaptive posterior contraction rates for empirical Bayesian drift estimation of a diffusion