Information-statistical approach for temporal-spatial data with application

A treatment for temporal-spatial data such as atmospheric temperature using an information-statistical approach is proposed. Conditioning on specific spatial nature of the data, the temporal aspect of the data is first modeled parametrically as Gaussian, and Schwarz information criterion is then applied to detect multiple mean change points—thus the Gaussian statistical models—to account for changes of the population mean over time. To examine the spatial characteristics of the data, successive mean change points are qualified by finite categorical values. The distribution of the finite categorical values is then used to estimate a non-parametric probability model through a non-linear SVD-based optimization approach; where the optimization criterion is Shannon expected entropy. This optimal probability model accounts for the spatial characteristics of the data and is then used to derive spatial association patterns subject to chi-square statistic hypothesis test. The proposed approach is applied to examine the weather data set obtained from NOAA. Selected temperature data are studied. These data cover different geographical localities in the United States, with some spanning over 200 years. Preliminary results are reported.