Morris, Lindsay

Spatio-temporal modelling for point referenced data

School of Mathematics and Statistics, Victoria University of Wellington

Point referenced spatial data (often referred to as geostatistical data) describes measurements that have been observed at a particular location, and finds application in climatology, ecology, environmental health, real estate marketing and many more. Gaussian processes (GPs) are the most common method for modelling spatio-temporal processes that produces point referenced data. They are ideal as they only require specification of the mean and covariance function. However, restrictive assumptions about the process are usually made, with the most constraining being the notion of stationarity. While this assumption makes inference and prediction simpler, most spatial processes have covariance structures that change over the study domain. Hence it is inappropriate to model under an assumption of stationarity.

This presentation describes the method of partitioning spatial point referenced data into smaller subdomains in order to reduce the impact of non-stationarity. Several conditional autoregressive (CAR) models are fit (in a Bayesian framework) to New Zealand particulate matter data that has been partitioned using K-means clustering. The posterior distributions of the covariance parameters are compared to those from the full data, and data partitioned based on the main island the observation is from.

This presentation is eligible for the NZSA Student Prize.