rcage (version 1.2)

MIpriorInv: Inverse of the MI Prior Distribution

Description

Calculates the inverse of the MI prior distribution, which is motivated by specifying the covariance so that it is "close" to the covariance from an Intrinsic Conditional Auto-Regressive model on the domain of the finest resolution. See reference for details.

Usage

MIpriorInv(psi, dB, ..., dMax = NULL)

Arguments

psi

A matrix object. The estimated OC basis {nB x r}, where nB is the number of areal units in the finest resolution spatial object (dB)

dB

A SpatialPolygons or SpatialPoints object. The finest resolution {nB}

...

Ignored.

dMax

Numeric maximum distance between points to be considered adjacent. Ignored if dB is SpatialPolygons. If dB is SpatialPoints and dMax is not specified, it is taken to be the 0.1 quantile of the distances.

Value

The inverse of the MI prior as an rxr matrix.

Details

For clarity -- function returns $$K^{-1} = R_{B}^{-1} A^{+}{Q_B'(I-A)Q_{B}} R_{B}^{-1},$$ where \(A^{+}\) is the first order adjacency matrix and \(Q_B, R_B\) is the QR decomposition of the basis matrix.

References

Bradley, J. R., Wikle, C. K., and Holan, S. H. (2017). Regionalization of Multiscale Spatial Processes using a Criterion for Spatial Aggregation Error. Journal of the Royal Statistical Society - Series B, 79, 815--832. <doi:10.1111/rssb.12179>

Examples

# NOT RUN {
data(countyExample)

nc <- county[county@data[,"STATE"] == 37, ]
psi <- matrix(data = rbinom(n = 1000, size = 1, prob = 0.5), 
              nrow = 100L, ncol = 10L)
MIpriorInv(psi = psi, dB = nc)

# }