On Brownian motion as a prior for nonparametric regression

Harry van Zanten

Statistics & Risk Modeling, 2009, vol. 27, issue 4, 335-356

Abstract: In this paper we consider the use of Brownian motion as a prior in a nonparametric, univariate regression setting. Using change of measure theory for continuous semimartingales we derive an explicit stochastic differential equation characterization for the posterior. In combination with stochastic calculus tools this dynamical characterization of the posterior allows us to derive new asymptotic properties of the posterior.

Keywords: nonparametric regression; Bayesian inference; Brownian motion prior; stochastic differential equations (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:27:y:2009:i:4:p:335-356:n:1

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DOI: 10.1524/stnd.2009.1034

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