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INLA spatial parameters test
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library(INLA) | |
m = 50 | |
points = matrix(runif(m*2), m, 2) | |
mesh = inla.mesh.2d(loc=points,cutoff=0.05,offset=c(0.1, 0.4),max.edge=c(0.05, 0.5) ) | |
bnd = inla.nonconvex.hull(points, convex=0.12) | |
mesh = inla.mesh.2d(boundary=bnd,cutoff=0.05,offset = c(1, 0.5),max.edge=c(0.1, 0.5) ) | |
A = inla.spde.make.A(mesh, loc=points) | |
sigma0 = 1 ## Field std.dev. for theta=0 | |
size = min(c(diff(range(mesh$loc[,1])), diff(range(mesh$loc[,2])))) | |
range0 = size/5 ## A fifth of the approximate domain width. | |
kappa0 = sqrt(8)/range0 | |
tau0 = 1/(sqrt(4*pi)*kappa0*sigma0) | |
spde = inla.spde2.matern(mesh, | |
B.tau=cbind(log(tau0), -1, +1), | |
B.kappa=cbind(log(kappa0), 0, -1), | |
theta.prior.mean=c(0,0), | |
theta.prior.prec=c(0.1, 1) ) | |
mesh.index = inla.spde.make.index(name="field", n.spde=spde$n.spde) | |
sigma.true = 3 * sigma0 | |
range.true = range0 | |
theta.true = log(c(sigma.true/sigma0, range.true/range0)) | |
Q = inla.spde.precision(spde, theta=theta.true) | |
x = inla.qsample(n=1, Q) | |
y = as.vector(A %*% x) | |
stack = inla.stack(data=list(y=y), A=list(A), effects=list(mesh.index)) | |
result = inla(y ~ -1 + f(field, model=spde), family="gaussian", | |
data=inla.stack.data(stack, spde=spde), | |
control.predictor=list(A=inla.stack.A(stack)), | |
control.family=list(initial=0, fixed=TRUE)) | |
summary(result) | |
spde2.result = inla.spde2.result(result, "field", spde) | |
plot(spde2.result$marginals.range.nominal[[1]]) # Nominal range posterior density | |
abline(v=range.true) | |
plot(spde2.result$marginals.variance.nominal[[1]]) # Nomial variance posterior density | |
abline(v=sigma.true^2) | |
# Convert thetas to variance and range | |
c(sigma.est = exp(spde2.result$summary.theta$mean[1]) * sigma0, sqrt(exp(spde2.result$summary.log.variance.nominal$mean))) | |
c(range.est = exp(spde2.result$summary.theta$mean[2]) * range0, exp(spde2.result$summary.log.range.nominal$mean)) |
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