Inverse of G by the Vecchia recursion

Inverse of G by the Vecchia recursion

Usage

vecchia_inverse(m = NULL, k = 100, lambda = 0.01, g = NULL)

Arguments

m

matrix of 0/1/2 genotypes (animals in rows); NA imputed by the mean, and an animal with a call rate below 0.90 refused, as in model(). Rows should come ancestors first: conditioning on the past is what the recursion means

k

neighbors per animal, chosen as the k strongest |g_ij| among the PREVIOUS rows (deterministic ties by index). k >= n - 1 reproduces the exact inverse

lambda

shrinkage on the diagonal of G, as in apy_inverse()

g

optionally, a ready relationship matrix (then m is ignored): the recursion applies to any symmetric positive-definite matrix, the pedigree A included, with the parents as neighbors it reproduces Henderson's A^-1 exactly

Value

list with i, j, x, n (triplets of the lower triangle of the approximate G^-1), the diagnostic mendeliano (the conditional residual d_i of each animal; tiny = collinear with its neighborhood) and the parameters used

References

Vecchia, A.V. (1988). Estimation and model identification for continuous spatial processes. Journal of the Royal Statistical Society B 50:297-312.

Schafer, F., Katzfuss, M. & Owhadi, H. (2021). SIAM Journal on Scientific Computing 43:A2019-A2046.