Tags :: Spatial Statistics

The classic problem being given observations \[ Z(s_1), Z(s_2), \dots, Z(s_n) \rightarrow \] predict \(Z(s_0)\)

As related to spatial point processes, we instead observe over a continous space. Why do we need a model for covariance? - We simply can’t estimate the covariance of each point.

Optimal spatial prediction

• Just optimal interporlation
• Many people will just use kriging.

the idea is to find the optimal weights for combining observed data to predict new locations. There are several types of kriging depndending on goal and type of data.

We assume a mean zero process. tilde is used to denote a random process with some mean function, but to start we remove the mean and add it back in later \[ Z(x) = \tilde{Z}(s) - \mu{s} \]

Simple kriging

How do we choose best \(\lambda_i(s_o)\)? We minimize mpse which will result in matrices of covariances, weights, and variances.