CRPScirc function

The Continuous Ranked Probability Score for Circular Variables.

CRPScirc function computes the The Continuous Ranked Probability Score for Circular Variables

CRPScirc(obs, sim, bycol = FALSE)

Arguments

• obs,: a vector of the values of the process at the test locations
• sim,: a matrix with nrow the test locations and ncol the number of posterior samples from the posterior distributions
• bycol,: logical. It is TRUE if the columns of sim represent the observations and the rows the posterior samples, the default value is FALSE

Returns

a list of 2 elements

• CRPSvec: a vector of CRPS, one element for each test point
• CRPS: the overall mean

Examples

#' library(CircSpaceTime)
## auxiliary function
rmnorm<-function(n = 1, mean = rep(0, d), varcov){
  d <- if (is.matrix(varcov))
    ncol(varcov)
  else 1
  z <- matrix(rnorm(n * d), n, d) %*% chol(varcov)
  y <- t(mean + t(z))
  return(y)
}

####
# Simulation with exponential spatial covariance function
####
set.seed(1)
n <- 20
coords <- cbind(runif(n,0,100), runif(n,0,100))
Dist <- as.matrix(dist(coords))

rho     <- 0.05
sigma2  <- 0.3
alpha   <- c(0.5)
SIGMA   <- sigma2*exp(-rho*Dist)

Y <- rmnorm(1,rep(alpha,times=n), SIGMA)
theta <- c()
for(i in 1:n) {
  theta[i] <- Y[i]%%(2*pi)
}
rose_diag(theta)

#validation set
val <- sample(1:n,round(n*0.1))

set.seed(12345)
mod <- WrapSp(
  x       = theta[-val],
  coords    = coords[-val,],
  start   = list("alpha"      = c(.36,0.38),
                 "rho"     = c(0.041,0.052),
                 "sigma2"    = c(0.24,0.32),
                 "k"       = rep(0,(n - length(val)))),
  priors   = list("rho"      = c(0.04,0.08), #few observations require to be more informative
                  "sigma2"    = c(2,1),
                  "alpha" =  c(0,10)
  ),
  sd_prop   = list( "sigma2" = 0.1,  "rho" = 0.1),
  iter    = 1000,
  BurninThin    = c(burnin = 500, thin = 5),
  accept_ratio = 0.234,
  adapt_param = c(start = 40000, end = 45000, exp = 0.5),
  corr_fun = "exponential",
  kappa_matern = .5,
  parallel = FALSE,
  #With doParallel, bigger iter (normally around 1e6) and n_cores>=2 it is a lot faster
  n_chains = 2 ,
  n_cores = 1
)
check <- ConvCheck(mod)
check$Rhat ## close to 1 means convergence has been reached
## graphical check
par(mfrow = c(3,1))
coda::traceplot(check$mcmc)
par(mfrow = c(1,1))
##### We move to the spatial interpolation

Krig <- WrapKrigSp(
  WrapSp_out = mod,
  coords_obs =  coords[-val,],
  coords_nobs =  coords[val,],
  x_obs = theta[-val]
)

#### check the quality of the prediction using APE and CRPS
ApeCheck <- APEcirc(theta[val],Krig$Prev_out)
CrpsCheck <- CRPScirc(theta[val],Krig$Prev_out)

References

Grimit, Eric P., Tilmann Gneiting, Veronica J. Berrocal, Nicholas Alexander Johnson. "The Continuous Ranked Probability Score for Circular Variables and its Application to Mesoscale Forecast Ensemble Verification", Q.J.R. Meteorol. Soc. 132 (2005), 2925-2942.

See Also

ProjKrigSp and WrapKrigSp for posterior spatial interpolation, and ProjKrigSpTi and WrapKrigSpTi for posterior spatio-temporal interpolation

Other model performance indices: APEcirc