as.carCM: Convert weights vector to parameters of 'dcar_proper'...

In nimble: MCMC, Particle Filtering, and Programmable Hierarchical Modeling

Convert weights vector to parameters of dcar_proper distributio

Description

Convert weights vector to C and M parameters of dcar_proper distribution

Usage

as.carCM(adj, weights, num)

Arguments

adj	vector of indices of the adjacent locations (neighbors) of each spatial location. This is a sparse representation of the full adjacency matrix.
weights	vector of symmetric unnormalized weights associated with each pair of adjacent locations, of the same length as adj. This is a sparse representation of the full (unnormalized) weight matrix.
num	vector giving the number of neighbors of each spatial location, with length equal to the total number of locations.

Details

Given a symmetric matrix of unnormalized weights, this function will calculate corresponding values for the C and M arguments suitable for use in the dcar_proper distribution. This function can be used to transition between usage of dcar_normal and dcar_proper, since dcar_normal uses the adj, weights, and num arguments, while dcar_proper requires adj, num, and also the C and M as returned by this function.

Here, C is a sparse vector representation of the row-normalized adjacency matrix, and M is a vector containing the conditional variance for each region. The resulting values of C and M are guaranteed to satisfy the symmetry constraint imposed on C and M, that M^{-1} C is symmetric, where M is a diagonal matrix and C is the row-normalized adjacency matrix.

Value

A named list with elements C and M. These may be used as the C and M arguments to the dcar_proper distribution.

Author(s)

Daniel Turek

See Also

CAR-Normal, CAR-Proper

nimble documentation built on Sept. 11, 2024, 7:10 p.m.