Profile log-likelihood of one single-cell bulk sample in ILR coordinates
Source:R/02_02_single_cell_decovart_estimate_ratios.R
profile_loglik_single_cell_ilr.Rd\(\ell^{\ast}(\boldsymbol{\rho})
=\ell(\boldsymbol{\psi}(\boldsymbol{\rho}),\hat c,\hat\phi)\), with the
scales recomputed in closed form at every composition
(see single_cell_nuisance_scales()). By the envelope theorem its score
is the score of loglik_single_cell() at those scales, mapped by
\(\mathbf{J}_{\psi}^{\top}\). Its Hessian is the Schur complement of
the observed Hessian in \((\boldsymbol{p},c,\phi)\), mapped by the
second-order chain rule.
The profile objective returns -Inf where a closed-form scale is not
positive, so the trust-region driver rejects that trial point.
Usage
profile_loglik_single_cell_ilr(z, y, mean_signature_matrix, Sigma, V = NULL)
gradient_profile_loglik_single_cell_ilr(
z,
y,
mean_signature_matrix,
Sigma,
V = NULL
)
hessian_profile_loglik_single_cell_ilr(
z,
y,
mean_signature_matrix,
Sigma,
V = NULL
)Arguments
- z
ILR coordinate of length \(J-1\).
- y
Bulk vector of length \(G\).
- mean_signature_matrix
Reference mean, \(G\times J\).
- Sigma
Cell-level covariances, \(G\times G\times J\).
- V
Optional ILR basis. See
isometric_logistic().