mu_d_gamma_tilde: Calculate derivative of mu_ij with respect to an entry of...

In statdivlab/tinyvamp: Modeling complex measurement error in microbiome experiments

Calculate derivative of mu_ij with respect to an entry of gamma_tilde

Description

Calculate derivative of mu_ij with respect to an entry of gamma_tilde

Usage

mu_d_gamma_tilde(
  i,
  j,
  k_tilde,
  gammas,
  B,
  X,
  Z,
  P,
  X_tilde,
  Z_tilde,
  Z_tilde_gamma_cols,
  alpha_tilde = NULL,
  Z_tilde_list = NULL,
  P_tilde,
  gamma_tilde
)

Arguments

i	The sample index (must be in 1, ..., n)
j	The taxon index (must be in 1, ..., J)
k_tilde	The element of gamma_tilde with respect to which to take derivative
gammas	Numeric vector of read intensities
B	Detection efficiency matrix
X	The efficiency design matrix (n x p)
Z	The sample design matrix (n x K)
P	The sample relative abundance matrix (K x J)
X_tilde	The spurious read efficiency design (K_tilde x p)
Z_tilde	The spurious read design (n x K_tilde)
Z_tilde_gamma_cols	Numeric vector containing indexes of columns of Z_tilde to scale by exp(gamma); NULL if no columns to be scaled
P_tilde	The spurious source relative abundance matrix (K_tilde x J)
gamma_tilde	Spurious read intensity parameter

Value

A derivative d mu_ij / d gamma_tilde_k_tilde

statdivlab/tinyvamp documentation built on July 28, 2023, 11:21 p.m.