Spatial statistics What is spatial statistics?  Refers to a very broad collection of methods and techniques of visualization, exploration and analysis applied to data with spatial stucture.  Spatiotemporal-when time is involved Why is it useful?  A lot of data contain geographic information  Interest in studying response patterns over a particular region  Ignoring the spatial structure -> spurious results A few examples.  Meteorology –weather patterns over a country/region  Environmental Science –pollutant concentrations over an area  Epidemiology –disease monitoring 1

Properties of computer experiments Computer experiments refer to those experiments that are performed in computers using physical models and finite element analysis. Deterministic outputs (no random error)  No replicates required  Interpolation Large number of variables Time-consuming, expensive 2

Computer experiments modeling Universal kriging Ordinary kriging 3

Estimation 4

Kriging example 5

ordinary kriging predictor:. 23 6