Observed Hessian of the single-cell log-likelihood in ILR coordinates

Second-order chain rule through jacobian_isometric_logistic() and hessian_isometric_logistic(), as for hessian_loglik_constrained().

Usage

hessian_loglik_single_cell_ilr(
  z,
  y,
  mean_signature_matrix,
  Sigma,
  mean_scale,
  variance_scale,
  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, \(G\times G\times J\).

mean_scale

Positive plug-in \(c=an\).

variance_scale

Positive plug-in \(\phi=a^2 n\).

V

Optional ILR basis. See isometric_logistic().

Value

Symmetric numeric \((J-1)\times(J-1)\) matrix.