A New Multi-scale Modeling Approach for Space/time Random Field Estimation

Modern geostatistical mapping methods are being applied to various types of data to produce more realistic and flexible characterizations of a natural random process. The Bayesian Maximum Entropy (BME) is a well-known geostatistical estimation method, especially for the use of soft knowledge as well as exact measurement data. Although development in geostatistical methods helps us to solve limitations on the format of available data, real studies always present in situ problems. Spatial scale of mapping (grid) points in a mapping model is usually not considered at the spatial scale of measurement data, especially in the studies that involve health-related data. Moreover, the spatial scale of measurement data may not be uniform, but varies among different measurements. For example, in studies of epidemiology or environmental health exposure, spatial scale of available measurement data is often limited and becomes different from the interesting spatial scale that is sought for in the estimation of the unknown random fields. It may be difficult and unrealistic to obtain measurement data at the scale of interest. Most current geostatistical methods have difficulty explaining physical phenomenon of unknown random fields over a continuous mapping domain at a scale smaller than that available from measurement data. This study explores how we can define these different scales in a geostatistical mapping model, and attempts to generate a meaningful spatiotemporal map of estimates of unknown random fields at the scale of interest. The estimation process of this study is based on the BME method to allow the probabilistic type of "soft" data, which are not actually observed, but simulated at the local scale to the measurement scale. This new modelling approach has been called multiscale or local-scale mapping model. With actual mortality data collected over the 58 counties of the state of California, USA, we applied this multi-scale modelling approach, and obtained more accurate and realistic spatiotemporal maps of mortality rate estimates over California. We compared these estimates with those found by another approach that did not account for multiple scales on the same data. It was verified by actual mortality data obtained at the zip-code scale. These estimates found by the multiscale approach were considered to be more accurate than those from the other modelling approach. * Corresponding author.