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On Brownian motion as a prior for nonparametric regression
Published/Copyright:
November 19, 2010
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
Published Online: 2010-11-19
Published in Print: 2009-12
© by Oldenbourg Wissenschaftsverlag, MB Eindhoven, Germany
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Keywords for this article
nonparametric regression;
Bayesian inference;
Brownian motion prior;
stochastic differential equations
Articles in the same Issue
- A note on incomplete and boundedly complete families of discrete distributions
- Option pricing in bilateral Gamma stock models
- On LAN for parametrized continuous periodic signals in a time inhomogeneous diffusion
- On Brownian motion as a prior for nonparametric regression
- The face-lifting theorem for proportional transaction costs in multiasset models
