log_f_theta_m: Conditional for mole-fraction field discrepancy parameters

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 of the mole-fraction field discrepancy parameters given the mole-fraction observations and the flux field

Usage

log_f_theta_m(theta, Yf, s, t, C_m, Qobs, Z, B, Q_zeta_fn)

Arguments

theta	mole-fraction field parameters – see details
s	observation spatial locations
t	observation temporal indices
C_m	observation incidence matrix (of size m x n_m)
Qobs	observation precision matrix (of size m x m)
Z	matrix of mole fraction observations (of size m x 1)
B	source-receptor relationship matrix (of size n_m x n_f)
Q_zeta_fn	function which returns the inverse of the mole-fraction discrepancy correlation matrix. This function should be of the form Q_zeta_fn(s,t,d_t,d_s) where s,t are as above, d_t is the temporal length scale parameter and d_s is the spatial length scale parameter

Details

To be completed

Examples

n_m <- m_obs <- 100
n_f <- 20
Yf <- matrix(rpois(n_f,20),n_f,1)    
log_f_theta_m( theta = c(4,0.8,1),
               Yf=Yf,
               s = 1:10,
               t = 1:10,
               C_m = .symDiagonal(n_m),
               Qobs = Diagonal(n_m),
               Z = 200 + matrix(rnorm(n_m,sd=100),n_m,1),
               B = matrix(rnorm(n_m*n_f),n_m,n_f),
               Q_zeta_fn = function(s,t,d_t,d_s) Diagonal(length(t) * length(s)))

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