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Normalized kernel-weighted random measures

Jim Griffin, University of Kent, United Kingdom

This talk discusses a wide class of probability measure-valued processes to be used as nonparametric priors for problems with time-varying, spatially-varying or covariate-dependent distributions. They are constructed by normalizing correlated random measures, which are stationary and have a known marginal process. Dependence is modelled using kernels (a method that has become popular in spatial modelling). The ideas extend Griffin (2007), which used an exponential kernel in time series problems, to arbitrary kernel functions. Computational issues will be discussed and the ideas will be illustrated by examples in financial time series.

Griffin, J. E. (2007): The Ornstein-Uhlenbeek Dirichlet Process and other measure valued processes for Bayesian inference, Technical Report, University of Warwick.