PubH 8472 Spatial Biostatistics- Spring 2009

This course is about spatial data, spatial statistical models, and spatial inference on unknown parameters or unobserved spatial data. Let s be a generic data location in d-dimensional Euclidean space and suppose that the potential datum Z( s ) at spatial location s is a random quantity. Now, let s range over index set D so as to generate a spatial stochastic process. This model is general enough to cover three important cases:

  1. Geostatistical Models. D is a fixed subset of d-dimensional Euclidean space that contains a d-dimensional rectangle of positive volume; Z( s ) is a random vector at location s .

  2. Spatial Lattice Models. D is a fixed collection of countably many points (spatially regular or irregular) of d-dimensional Euclidean space; Z( s ) is a random vector at location s .

  3. Spatial Point Processes. D is a point process in d-dimensional Euclidean space; Z( s ) is a random vector at location s . [Here both index set D and measurement Z(.) are a source of randomness in the spatial statistical model.]

Each of these cases will be covered in this class with emphasis on statistical modeling and application using available software. A number of spatial data sets from the environmental and health sciences will be used to illustrate the statistical methods.