Xin Qi

Post date: Aug 30, 2013 6:28:23 AM

Proposed Paper:

1. Nonparametric Bayesian Models for a Spatial Covariance

Abstract:

A crucial step in the analysis of spatial data is to estimate the spatial correlation function that determines the relationship between a spatial process at two locations. The standard approach to selecting the appropriate correlation function is to use prior knowledge or exploratory analysis, such as a variogram analysis, to select the correct parametric correlation function. However, such method can be challenging and can raise issues under certain situations. In this paper, rather that selecting a particular parametric correlation function, the covariance function is treated as an unknown function to be estimated from the data. The authors propose a flexible prior for the correlation function to provide robustness to the choice of correlation function. The prior for the correlation function is specified using spectral methods and the Dirichlet process prior, which is a common prior for an unknown distribution function under nonparametric Bayesian framework.

Notes:

1. The paper I proposed is based on Zheng, Zhu and Roy's nonparametric Bayesian method (see the other paper I attched).

2. For more references on Nonparametric Bayesian inference via Dirichlet process, please see

[1] "Bayesian Estimation of the Spectral Density of a Time Series", Choudhuri, N., Ghosal, S., and Roy, A. (2004), JASA.

[2] "A Constructive Definition of Dirichlet Priors", Sethuraman, J. (1994), Statistica Sinica.