computeW: Obtain quantities associated with W

Description Usage Arguments Value Author(s) Examples

View source: R/computeW.R

Description

This function computes quantities associated with the covariance matrix W, and these quantities are used to evaluate the likelihood function for the proposed statistical model.

Usage

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computeW(y, x, B, neighborhood_matrix, gamma_prior)

Arguments

y

an n by N matrix of ensembles of measured climate variable (e.g., temperature) increases

x

a list of m elements, each of which is model-output climate variable (e.g., temperature) increases under a specific forcing scenario

B

an n by r basis function matrix

neighborhood_matrix

an n by n matrix

gamma_prior

a vector of possible discrete values for the prior distribution of gamma

Value

a list of 7 elements

Author(s)

Pulong Ma <[email protected]>

Examples

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#################### simulate data ########################
set.seed(1234)
n <- 30 # number of spatial grid cells on the globe
N <- 10 # number of ensemble members
m <- 3 # number of forcing scenarios
Lj <- c(5, 3, 7) # number of runs for each scenario
L0 <- 8 # number of control runs without any external forcing scenario
trend <- 30
DAdata <- simDAdata(n, N, m, Lj, L0, trend)
# ensembles of the measured variable
y <- DAdata[[1]]
# model outputs for the measured variable under different forcing scenarios
x <- DAdata[[2]]
# model outputs for the measured variable without any external forcing scenario
x0 <- DAdata[[3]]
#################### end of simulation ####################



###########################################################
### preprocessing 
# center the data
y <- y - mean(y)
for(j in 1:m){
  x[[j]] <- x[[j]]-mean(x[[j]])
}
# construct basis function matrix B with principal components
r <- 3
empiricalcovmat <- cov(t(x0))

# compute first r eigenvalues and eigenvectors
temp <- RSpectra::eigs_sym(empiricalcovmat, r, which="LM")
B <- temp$vectors
K_hat <- temp$values


lambda_mean <- log(K_hat)
lambda_var <- var(lambda_mean)/3^2


### pre-computation for W

# possible values for the discrete prior of gamma
gamma_prior <- c(0.5,0.99,1,1.01,2,5)
ng <- length(gamma_prior)

# neighborhood matrix (replace by real one)
neighborhood_matrix <- Matrix::sparseMatrix(1:n, 1:n, x=rep(1,n))
## Not run: 
outW <- computeW(y,x,B,neighborhood_matrix,gamma_prior)

## End(Not run)

mapn/DAbayes documentation built on May 21, 2017, 5:47 p.m.