LL2_kappa: Compute part of appa log-likelihood

View source: R/EM_templateICA.R

LL2_kappaR Documentation

Compute part of appa log-likelihood

Description

Compute part of log-likelihood involving kappa (or kappa_q) for numerical optimization

Usage

LL2_kappa(
  kappa,
  Amat,
  Fmat,
  Gmat,
  GFinvG,
  OplusW,
  u,
  v,
  C1 = 1/(4 * pi),
  Q = NULL
)

Arguments

kappa

Value of kappa for which to compute log-likelihood

Amat

Mesh projection matrix

Fmat

Matrix used in computation of SPDE precision

Gmat

Matrix used in computation of SPDE precision

GFinvG

Matrix used in computation of SPDE precision

OplusW

Sparse matrix containing estimated values of RHS of trace in part 2 of log-likelihood. In common smoothness model, represents the sum over q=1,...,Q.

u

Vector needed for part 3 of log-likelihood

v

Vector needed for part 3 of log-likelihood

C1

For the unit variance case, \tau^2 = C1/\kappa^2, where C1 = 1/(4\pi) when \alpha=2, \nu=1, d=2

Q

Equal to the number of ICs for the common smoothness model, or NULL for the IC-specific smoothness model

Details

This is the function to be maximized in order to determine the MLE for \kappa or the \kappa_q's in the M-step of the EM algorithm in spatial template ICA. In the model where \kappa_q can be different for each IC q, the optimization function factorizes over the \kappa_q's. This function computes the value of the part of the optimization function pertaining to one of the \kappa_q's.

Value

Value of log-likelihood at logkappa


templateICAr documentation built on June 22, 2024, 11:45 a.m.