LL2_kappa: Compute part of appa log-likelihood

In templateICAr: Estimate Brain Networks and Connectivity with ICA and Empirical Priors

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.