Spatial Analysis Using Big Data

4.7. Hierarchical Bayesian model

4.7.1. Data model, process model, and parameter model

Modeling uncertainty in data (y), process (z), and parameters (θ) is crucially important. Models identify spatial and temporal processes hidden behind noisy data. Given this background, the following factorization of [y,z,θ]   =   [y|z, θ][z|θ][θ] is becoming popular because of its flexibility in modeling uncertainty in each element (Berliner, 1996; Cressie and Wikle, 2011):

Data model : [ y | z , θ ] ,

(4.6.1)

Process model : [ z | θ ] ,

(4.6.2)

Parameter model : [ θ ] .

(4.6.3)

Extension of the ...