On Brownian motion as a prior for nonparametric regression

J.H. Zanten, van

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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.
Original languageEnglish
Pages (from-to)335-356
JournalStatistics & Decisions
Volume27
Issue number4
DOIs
Publication statusPublished - 2009

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