scripts/various/get.bootstrap.cis.univariate.R

In ClaudioHeinrich/pp.sst: postprocessing sea surface temperature forecasts

# 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

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).'


# start timer:

time_s2oos = proc.time()


###### run bias analysis for simple moving averages ######

past_0 = 5 # How many years before validation period do we consider for the MSEs:
# For prediction in year y, the parameters are chosen to minimize the MSE over the years y_0 - past_0, ... ,y - 1,
# where y_0 is the first year of the validation period.


num_years = max(validation_years) - DT[,min(year)]

win_length = 1 : (num_years-1)

MSE_by_par = function(k)
{
  temp = bias_correct(dt = DT, 
                      method = "sma", 
                      par_1 = k)
  return(temp[year %between% c(min(validation_years - past_0),max(validation_years)),SST_hat])
}


BC = parallel::mclapply(X = win_length, FUN = MSE_by_par,mc.cores = mc_cores)

# restrict to validation years + the past_0 years before 

Bias_est_dt = DT[year %between% c(min(validation_years - past_0),max(validation_years)),
                 .(year,month,Lon,Lat,SST_bar)]

for(k in win_length)
{print(k)
  Bias_est_dt[,paste0('l',k):= BC[[k]]]
  Bias_est_dt[,paste0('err',k):= (SST_bar - eval(parse(text = paste0('l',k))))^2]
}

#get MSE by year and month, for each year based on all previous years contained in Bias_est_dt

sc_sma = NULL

for(y in validation_years)
{print(y)
  mean_sc_bm = function(m)
  {
    temp = data.table(year = y ,month = m,Bias_est_dt[year < y & month == m,
                                                      lapply(X = .SD,FUN = mean,na.rm = TRUE),
                                                      .SDcols = paste0('err',win_length)])
    return(temp)     
  }
  
  MSE_y = rbindlist(parallel::mclapply(X = months,FUN = mean_sc_bm,mc.cores = mc_cores))
  sc_sma = rbindlist(list(sc_sma,MSE_y))
}


save(sc_sma, file = paste0(save_dir,"scores.bc.sma.RData"))


###### run bias analysis for exponential moving averages ######

par_vec = seq(0.05,0.4,length.out = 24) 

MSE_by_par = function(a)
{
  temp = bias_correct(dt = DT, 
                      method = "ema", 
                      par_1 = a)
  return(temp[year %between% c(min(validation_years - past_0),max(validation_years)),SST_hat])
}


BC = parallel::mclapply(X = par_vec, FUN = MSE_by_par,mc.cores = mc_cores)

# restrict to validation years + the past_0 years before 

Bias_est_dt = DT[year %between% c(min(validation_years - past_0),max(validation_years)),
                 .(year,month,Lon,Lat,SST_bar)]

for(a in par_vec)
{ind = which(par_vec == a )
print(ind)
ra = round(a,4)
Bias_est_dt[,paste0('a',ra):= BC[[ind]]]
Bias_est_dt[,paste0('err',ra):= (SST_bar - eval(parse(text = paste0('a',ra))))^2]
}

#get MSE by year and month, for each year based on all previous years contained in Bias_est_dt

sc_ema = NULL

for(y in validation_years)
{print(y)
  mean_sc_bm = function(m)
  {
    temp = data.table(year = y ,month = m,Bias_est_dt[year < y & month == m,
                                                      lapply(X = .SD,FUN = mean,na.rm = TRUE),
                                                      .SDcols = paste0('err',round(par_vec,4))])
    return(temp)     
  }
  
  MSE_y = rbindlist(parallel::mclapply(X = months,FUN = mean_sc_bm,mc.cores = mc_cores))
  sc_ema = rbindlist(list(sc_ema,MSE_y))
}


save(sc_ema, file = paste0(save_dir,"scores.bc.ema.RData"))


###### getting mean scores for different ways of bias correction ######

load(paste0(save_dir,"scores.bc.sma.RData"))
load(paste0(save_dir,"scores.bc.ema.RData"))

# get means over all months for sma

msc_sma = sc_sma[,lapply(.SD,mean),by = year][,month := NULL]

# get minimum for each row

row_min = NULL
min_l = NULL

for(i in 1:msc_sma[,.N])
{
  row = msc_sma[,-1,with = FALSE][i,]
  row_min = c(row_min,min(row))
  min_l = c(min_l,which.min(row))
}

msc_sma[,min_MSE := row_min][,min_l := min_l]


# get means over all months for ema

msc_ema = sc_ema[,lapply(.SD,mean),by = year][,month := NULL]

# get minimum for each row

row_min = NULL
min_a = NULL

for(i in 1:msc_sma[,.N])
{
  row = msc_ema[,-1,with = FALSE][i,]
  row_min = c(row_min,min(row))
  min_a = c(min_a,par_vec[which.min(row)])
}

msc_ema[,min_MSE := row_min][,min_a := min_a]


###### finding optimal way of bias correction for each year in the validation period ######

# exponential moving averages are preferred, as the parameter estimation for them typically is more stable ######

opt_par = data.table(year = validation_years)

opt_par[,mse_sma := msc_sma[,min_MSE]]
opt_par[,par_sma := msc_sma[,min_l]]

opt_par[,mse_ema := msc_ema[,min_MSE]]
opt_par[,par_ema := msc_ema[,min_a]]

# exponential moving averages are more stable, so we give them a slight edge:
opt_par[, par := par_sma * (mse_sma < 0.95 * mse_ema) + par_ema * (mse_sma >= 0.95 * mse_ema)]


opt_par[mse_sma < 0.95 * mse_ema, method :='sma' ]
opt_par[mse_sma > 0.95 * mse_ema, method :='ema' ]

#################################################################
######## bias correction year by year, validation period ########

# sma

for(y in validation_years)
{
  print(y) 
  temp_sma = bias_correct(dt = DT,
                          method = 'sma',
                          par_1 = opt_par[year == y,par_sma])[year == y,]
  DT[year == y,Bias_Est_SMA := temp_sma[,Bias_est]][year == y ,SST_hat_sma := temp_sma[,SST_hat]]
}
rm(temp_sma)

#ema

for(y in validation_years)
{
  print(y) 
  temp_ema = bias_correct(dt = DT,
                          method = 'ema',
                          par_1 = opt_par[year == y,par_ema])[year == y,]
  DT[year == y,Bias_Est_EMA := temp_ema[,Bias_est]][year == y ,SST_hat_ema := temp_ema[,SST_hat]]
}
rm(temp_ema)


# For the training years, the bias 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 = opt_par[year == min(year),par_sma]

DT_sma_tr = bias_correct(dt = DT[year %in% training_years],
                         method = 'sma',par_1 = opt_sma_par_tr,
                         twosided = TRUE)

DT[year %in% training_years, c('Bias_Est_SMA','SST_hat_sma') := DT_sma_tr[,.(Bias_est,SST_hat)]]

rm(DT_sma_tr,opt_sma_par_tr)

#ema

opt_ema_par_tr = opt_par[year == min(year),par_ema]

DT_ema_tr = bias_correct(dt = DT[year %in% training_years],
                         method = 'ema',par_1 = opt_ema_par_tr,
                         twosided = TRUE)

DT[year %in% training_years, c('Bias_Est_EMA','SST_hat_ema') := DT_ema_tr[,.(Bias_est,SST_hat)]]

rm(DT_ema_tr,opt_ema_par_tr)

######################################################
### pick optimal performance method for each year: ###

ema_years = opt_par[method == 'ema',year]

if(min(validation_years) %in% ema_years) ema_years = c(training_years,ema_years)

DT[year %in% ema_years, Bias_Est := Bias_Est_EMA]
DT[year %in% ema_years, SST_hat := SST_hat_ema]

DT[!(year %in% ema_years), Bias_Est := Bias_Est_SMA]
DT[!(year %in% ema_years), SST_hat := SST_hat_sma]




#### time, update script counter, save ####

time_s2oos = proc.time() - time_s2oos

script_counter = 2

save.image(file = paste0(save_dir,"setup.RData"))


#############################################################################
#############################################################################

###### getting sample variances of ensemble  ######

DT[,var_bar := (SST_hat - SST_bar)^2]


#####################################################################
###### running variance estimation with simple moving averages ######


past_0 = 5  # How many years before validation period do we consider for the CRPS:
# For prediction in year y, the parameters are chosen to minimize the MSE over the years y_0 - past_0, ... ,y - 1,
# where y_0 is the first year of the validation period.

num_years = max(validation_years) - DT[,min(year)]

# get SDs for a range of parameters and all relevant years

SD_by_par = function(k)
{
  sd_hat = sd_est_2(DT,method = 'sma',par_1 = k)
  return(sd_hat[year %between% c(min(validation_years - past_0),max(validation_years)),SD_hat])
}

win_length = 1 : (num_years-1)

SDs = parallel::mclapply(X = win_length, FUN = SD_by_par,mc.cores = mc_cores)


# restrict to validation years + the past_0 years before 

SD_dt = DT[year %between% c(min(validation_years - past_0),max(validation_years)),
           .(year,month,Lon,Lat,SST_bar,SST_hat)]

for(k in win_length)
{print(k)
  SD_dt[,paste0('l',k):= SDs[[k]]]
  SD_dt[,paste0('crps',k):= crps_na_rm(y = SST_bar,mean = SST_hat,sd = eval(parse(text = paste0('l',k))))]
}




#get mean CRPS by month, for each year averaged over all previous years contained in SD_dt

sc_sd_sma = NULL

for(y in validation_years)
{print(y)
  mean_sc_sd_bm = function(m)
  {
    temp = data.table(year = y ,month = m,SD_dt[year < y & month == m,
                                                lapply(X = .SD,FUN = mean,na.rm = TRUE),
                                                .SDcols = paste0('crps',win_length)])
    return(temp)     
  }
  
  CRPS_y = rbindlist(parallel::mclapply(X = months,FUN = mean_sc_sd_bm,mc.cores = mc_cores))
  sc_sd_sma = rbindlist(list(sc_sd_sma,CRPS_y))
}


save(sc_sd_sma, file = paste0(save_dir,"scores.bc.sd.sma.RData"))


####################################################################
###### run variance estimation by exponential moving averages ######

par_vec = seq(0.05, 0.4, length.out = 24) 

SD_by_par = function(a)
{
  sd_hat = sd_est_2(dt = DT,
                    method = "ema", 
                    par_1 = a)
  return(sd_hat[year %between% c(min(validation_years - past_0),max(validation_years)),SD_hat])
}


SDs = parallel::mclapply(X = par_vec, FUN = SD_by_par,mc.cores = mc_cores)

# restrict to validation years + the past_0 years before 

SD_dt = DT[year %between% c(min(validation_years - past_0),max(validation_years)),
           .(year,month,Lon,Lat,SST_bar,SST_hat)]


for(a in par_vec)
{ind = which(par_vec == a )
print(ind)
ra = round(a,4)
SD_dt[,paste0('a',ra):= SDs[[ind]]]
SD_dt[,paste0('crps',ra):= crps_na_rm(y = SST_bar,mean = SST_hat,sd = eval(parse(text = paste0('a',ra))))]
}

#get mean crps by month, averaged over all previous years contained in SD_dt

sc_sd_ema = NULL

for(y in validation_years)
{print(y)
  mean_sc_sd_bm = function(m)
  {
    temp = data.table(year = y ,month = m,SD_dt[year < y & month == m,
                                                lapply(X = .SD,FUN = mean,na.rm = TRUE),
                                                .SDcols = paste0('crps',round(par_vec,4))])
    return(temp)     
  }
  
  CRPS_y = rbindlist(parallel::mclapply(X = months,FUN = mean_sc_sd_bm,mc.cores = mc_cores))
  sc_sd_ema = rbindlist(list(sc_sd_ema,CRPS_y))
}


save(sc_sd_ema, file = paste0(save_dir,"scores.bc.sd.ema.RData"))



###### 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[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 ####

time_s3oos = proc.time() - time_s3oos

script_counter = 3

save.image()()


##############################################

### 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"))