Yf_BC_conditionals: Conditional for Yf

In andrewzm/atminv: Reproducible package for Section 4.1 of "Spatio-temporal bivariate statistical models for atmospheric trace-gas inversion"

Description

Returns the conditional distribution and its derivative of the flux field given the flux field parameters and the mole-fraction observations

Usage

Yf_BC_conditionals(Z, Zinv, C_m, Qobs, B, X, Q_zeta, S_f_trans, lambda = 0,
  lambda_fix = NA, Pericchi = TRUE, ind = 1:nrow(S_f_trans))

Arguments

Z	matrix of mole fraction observations (of size m x 1)
C_m	observation incidence matrix (of size m x n_m)
Qobs	observation precision matrix (of size m x m)
B	source-receptor relationship matrix (of size n_m x n_f)
X	covariates matrix (of size n_f x p)
Q_zeta	precision matrix of discrepancy field (of size n_m x n_m). Should be sparse
S_f_trans	covariance matrix of flux field in transformed (Gaussian) space (of size n_f x n_f)
lambda	Box-Cox transformation parameter
ind	vector of indices on which to consider the flux (some unidentifiable grid cells may be omitted)

Examples

n_f <- 20
n_m <- m_obs <- 100
cond_fns <- Yf_BC_conditionals(Z = 200 + matrix(rnorm(n_m,sd=100),n_m,1),
                               C_m = .symDiagonal(n_m),
                               Qobs = Diagonal(n_m),
                               B = matrix(rnorm(n_m*n_f),n_m,n_f),
                               X = matrix(rep(1,n_f)),
                               Q_zeta = n_m*Diagonal(n_m),
                               S_f_trans = Diagonal(n_f),
                               lambda = 0.1
                             )
Yf <- matrix(rpois(n_f,20),n_f,1)                              
cond_fns$logf(Yf)
cond_fns$gr_logf(Yf)

andrewzm/atminv documentation built on May 10, 2019, 11:14 a.m.