# get permutation tests etc for the Full/lv run. To this end we run the oos script number 3 again, since in the original run SD_hat was not computed
# with SMAs. The first script ran for a long time and then ran into an error. It si corrected now and we don't run everything again but try
# kicking off where we started.
rm(list = ls())
time_s3oos = proc.time()
setwd("~/NR/SFE")
options(max.print = 1e3)
library(PostProcessing)
library(data.table)
name_abbr = "Full/lv"
save_dir = paste0("~/PostClimDataNoBackup/SFE/Derived/", name_abbr,"/")
load(file = paste0(save_dir,"setup.RData"))
# add this now, for the future
comment = 'This is the full globe, lv stands for long validation (years 2001-2016).'
###### getting sample variances of ensemble ######
DT[,var_bar := (SST_hat - SST_bar)^2]
###### getting mean scores for different ways of variance estimation ######
load(paste0(save_dir,"scores.bc.sd.sma.RData"))
load(paste0(save_dir,"scores.bc.sd.ema.RData"))
# get means over all months for sma
msc_sd_sma = sc_sd_sma[,lapply(.SD,mean),by = year][,month := NULL]
# get minimum for each row
row_min = NULL
min_l = NULL
for(i in 1:msc_sd_sma[,.N])
{
row = msc_sd_sma[,-1,with = FALSE][i,]
row_min = c(row_min,min(row))
min_l = c(min_l,which.min(row))
}
msc_sd_sma[,min_crps := row_min][,min_l := min_l]
# get means over all months for ema
msc_sd_ema = sc_sd_ema[,lapply(.SD,mean),by = year][,month := NULL]
# get minimum for each row
row_min = NULL
min_a = NULL
for(i in 1:msc_sd_sma[,.N])
{
row = msc_sd_ema[,-1,with = FALSE][i,]
row_min = c(row_min,min(row))
min_a = c(min_a,par_vec[which.min(row)])
}
msc_sd_ema[,min_crps := row_min][,min_a := min_a]
###### finding optimal way of variance estimation for each year in the validation period ######
# exponential moving averages are preferred, as the parameter estimation for them typically is more stable ######
opt_par_sd = data.table(year = validation_years,method = NA_character_,par = NA_real_)
opt_par_sd = data.table(year = validation_years)
opt_par_sd[,crps_sma := msc_sd_sma[,min_crps]]
opt_par_sd[,par_sma := msc_sd_sma[,min_l]]
opt_par_sd[,crps_ema := msc_sd_ema[,min_crps]]
opt_par_sd[,par_ema := msc_sd_ema[,min_a]]
# exponential moving averages are more stable, so we give them a slight edge:
opt_par_sd[, par := par_sma * (crps_sma < 0.95 * crps_ema) + par_ema * (crps_sma >= 0.95 * crps_ema)]
opt_par_sd[crps_sma < 0.95 * crps_ema, method :='sma' ]
opt_par_sd[crps_sma > 0.95 * crps_ema, method :='ema' ]
###############################################################
##### variance correction year by year, validation period #####
# sma
for(y in validation_years)
{
print(y)
temp = sd_est_2(dt = DT,
method = 'sma',
par_1 = opt_par_sd[year == y,par_sma])[year == y,]
DT[year == y,SD_hat_sma := temp[,SD_hat]]
}
rm(temp)
# ema
for(y in validation_years)
{
print(y)
temp = sd_est_2(dt = DT,
method = 'ema',
par_1 = opt_par_sd[year == y,par_ema])[year == y,]
DT[year == y,SD_hat_ema := temp[,SD_hat]]
}
rm(temp)
# For the training years, the variance correction considers also the future (contained in the training period),
# and uses the parameter estimated for the first validation year:
#sma
opt_sma_par_tr_sd = opt_par_sd[year == min(year),par_sma]
DT_sma_tr_sd = sd_est_2(dt = DT[year %in% training_years],
method = 'sma', par_1 = opt_sma_par_tr_sd,
twosided = TRUE)
DT[year %in% training_years, SD_hat_sma := DT_sma_tr_sd[,.(SD_hat)]]
rm(DT_sma_tr_sd,opt_sma_par_tr_sd)
#ema
opt_ema_par_tr_sd = opt_par_sd[year == min(year),par_ema]
DT_ema_tr_sd = sd_est_2(dt = DT[year %in% training_years],
method = 'ema',par_1 = opt_ema_par_tr_sd,
twosided = TRUE)
DT[year %in% training_years, SD_hat_ema := DT_ema_tr_sd[,SD_hat]]
rm(DT_ema_tr_sd,opt_ema_par_tr_sd)
######################################################
### pick optimal performance method for each year: ###
ema_years = opt_par_sd[method == 'ema',year]
if(min(validation_years) %in% ema_years) ema_years = c(training_years,ema_years)
DT[year %in% ema_years, SD_hat := SD_hat_ema]
DT[!(year %in% ema_years), SD_hat := SD_hat_sma]
#### time, update script counter, save ####
script_counter = 3
save.image(file = paste0(save_dir,'setup.RData'))
##############################################
### correct colnames ###
DT[,Bias_Est_EMA := Bias_Est]
DT[,SST_hat_EMA := SST_hat]
######################################################################################
### permutation tests and bootstrap confidence intervals for al model combinations ###
######################################################################################
models = c('lr_m','lr_loc','lr_both','sma','ema')
scores = c('MSE','CRPS')
perm_test_dt = as.data.table(expand.grid(model1 = models,model2 = models,score = scores))
################
N=5000 # number of permutations for permutation test and resamples for bootstrap
q_probs = c(0.025,0.975) # probabilities for bootstrap quantiles of the score differences
# MSE:
for(mod1 in models)
{
print(mod1)
dat1 = MSE_linear_models[,get(mod1)]
for(mod2 in models)
{
dat2 = MSE_linear_models[,get(mod2)]
p_val = permutation_test_difference(dat1,dat2,N)$p_val
perm_test_dt[model1 == mod1 & model2 == mod2 & score == 'MSE',p_value := p_val]
bt = bootstrap_difference(dat1,dat2,N = N,q_prob = q_probs)
perm_test_dt[model1 == mod1 & model2 == mod2 & score == 'MSE',paste0('bt_q',q_probs[1]) := bt$q[1]]
perm_test_dt[model1 == mod1 & model2 == mod2 & score == 'MSE',paste0('bt_q',q_probs[2]) := bt$q[2]]
}
}
# CRPS (for variance estimation)
for(mod1 in models)
{
print(mod1)
dat1 = CRPS_comparison[,get(mod1)]
for(mod2 in models)
{
dat2 = CRPS_comparison[,get(mod2)]
p_val = permutation_test_difference(dat1,dat2,N)$p_val
perm_test_dt[model1 == mod1 & model2 == mod2 & score == 'CRPS',p_value := p_val]
bt = bootstrap_difference(dat1,dat2,N = N,q_prob = q_probs)
perm_test_dt[model1 == mod1 & model2 == mod2 & score == 'CRPS',paste0('bt_q',q_probs[1]) := bt$q[1]]
perm_test_dt[model1 == mod1 & model2 == mod2 & score == 'CRPS',paste0('bt_q',q_probs[2]) := bt$q[2]]
}
}
###############33
save(perm_test_dt,file = paste0(save_dir,'perm_test_univ_mod.RData'))
save.image(file = paste0(save_dir,"setup.RData"))
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