Smoothing with Cauchy Process Priors and Cauchy Errors

• Activity Number: 681
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Paul Speckman*+
• Companies: Univ. of Missouri-Columbia
• Keywords: nonparametric regression ; Cauchy process ; adaptive regression ; time-varying errors

Abstract

Conventional smoothing splines have a Bayesian interpretation with a Gaussian process prior and independent Gaussian errors. The usual smoothing spline is a Bayesian estimator with this setup. In this talk, we propose a Cauchy process prior with Cauchy errors. This prior allows Bayesian inference analogous to smoothing splines but for functions with discontinuities in first or second derivatives, for example. Cauchy errors can be used to model outliers. However, when the Cauchy distribution is viewed as a mixture of normals, the errors can also be regarded as a type of time-dependent error process. Thus the Cauchy process prior/Cauchy error combination can be used to model time series marked by periods of smooth change interrupted by occasional abrupt shifts in behavior and periods of high volatility. Bayesian inference is used for efficient inference.