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Simulation_singlestep.R
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Simulation_singlestep = function(x, scenario.settings,
name_file_performance,
sigma2_xi,
b0, b1, sigma2_e,
sigma2iid_Poisson,
gamma0_Poisson){
scenario_n = x #number of the scenario (useful for exporting the output)
#--- Set some parameters according to the scenario
sample.by = scenario.settings[x,"sample.by"] #how to sample monitoring stations
prop.points.for.area = scenario.settings[x,"prop.points.for.area"] #proportion of monitoring stats for each area to be sampled
range.scale = scenario.settings[x,"range.scale"]
res_pred_grid = scenario.settings[x,"res_pred_grid"]
fixed_E = scenario.settings[x,"E"]
RR = scenario.settings[x,"RR"]
gamma1_Poisson = log(RR)
gamma0_Poisson = scenario.settings[x,"gamma0"]
#--- Simulate the covariate values at the regular grid points
set.seed(123)
z_sim_grid = rnorm(highres_simulation_reggrid^2)
#values of the fixed parameter for the PRIOR exposure method
if(scenario_n %% 2 > 0) { #odd scenario with RR=1.05
b <- seq(-0.2, 0.2, by = 0.01 ) # 0.001 --> 401 values.005
} else { #even scenario with RR=1.25
b <- seq(-0.5, 0.5, by = 0.01) #0.001 --> 401 values with 0.0025 #0.001 with 1001 values
}
# ------------------------------------------------------------
# ---------- FOR LOOP OVER simulation (1,...,n_simulations)
# ------------------------------------------------------------
posterior_b0_PI_FF = c()
posterior_b1_PI_FF = c()
posterior_sigma2e_PI_FF = c()
posterior_sigma2xi_PI_FF = c()
posterior_range_PI_FF = c()
cor_pred_obs_area_method1 = cor_pred_obs_area_method2 = c()
cor_pred_obs_predgrid_method1 = cor_pred_obs_predgrid_method2 = c()
posterior_gamma0_PI_method1 = posterior_gamma0_PI_method2 = c()
posterior_gamma0_FF_method1 = posterior_gamma0_FF_method2 = c()
posterior_gamma0_PE_method1 = posterior_gamma0_PE_method2 = c()
posterior_gamma1_PI_method1 = posterior_gamma1_PI_method2 = c()
posterior_gamma1_FF_method1 = posterior_gamma1_FF_method2 = c()
posterior_gamma1_PE_method1 = posterior_gamma1_PE_method2 = c()
posterior_sigma2iid_PI_method1 = posterior_sigma2iid_PI_method2 = c()
posterior_sigma2iid_FF_method1 = posterior_sigma2iid_FF_method2 = c()
posterior_sigma2iid_PE_method1 = posterior_sigma2iid_PE_method2 = c()
n.skip = 0
which.skip = c()
which.skip.withnames = c()
for(sim_i in 1:n_simulations){
############################################################
# Simulate the data
############################################################
simulated.data = Data_simulation(scenario_n,
sample.by,
prop.points.for.area,
res_pred_grid,
range.scale, sigma2_xi, b0, b1, sigma2_e,
z_sim_grid,
gamma1_Poisson, gamma0_Poisson,
sigma2iid_Poisson, fixed_E)
load(paste0(getwd(),
"/Data","/weights_grid_areas_intersection_res_pred_grid_",res_pred_grid,".Rdata"))
load(paste0(getwd(),
"/Data","/weights_points_areas_inside_closest_",res_pred_grid,".Rdata"))
#--- Extract elements from the list
shapefile_sim_complete = simulated.data$shapefile_sim_complete
n_areas = nrow(shapefile_sim_complete@data)
cat(paste("@@@@@@@@@@ Scenario n.", scenario_n, "-------------------> Simulation n.", sim_i, "of", n_simulations,"\n"))
cat(paste("N. monitoring stats = ", simulated.data$n.monitoringstats,"\n"))
monitoringstations.data = simulated.data$monitoringstations.data
monitoringstations.coords = simulated.data$monitoringstations.coords
#NB: monitoring stats coordinates do not change across iteratios (given a scenario)
sim_grid_inside_df = simulated.data$sim_grid_inside_df
sim_grid_inside_df_pred = simulated.data$sim_grid_inside_df_pred
shapefile_sim_centroids = gCentroid(shapefile_sim_complete, byid = T)
##### Uncomment these lines if you want to change the station locations for each iterations
#file.remove(paste0(getwd(),
# "/Simulations/Data",
# "/monitoringstationsdata_scenario",scenario_n,".Rdata"))
pred_grid = simulated.data$pred_grid
z_pred_grid = simulated.data$sim_grid_inside_df_pred$z
max_dist = simulated.data$max_dist
r = max_dist * range.scale #spatial range
kappa_xi = sqrt(8) / r
if(sim_i==1){
posterior_lincombs_method1 = vector("list",length=n_simulations)
posterior_lincombs_method2 = vector("list",length=n_simulations)
simulated_data_shapefile = vector("list",length=n_simulations)
}
############################################################
# Inla mesh + spatial process definition
############################################################
domain = rbind(c(min(shapefile_sim_centroids$x),min(shapefile_sim_centroids$y)),
c(max(shapefile_sim_centroids$x),min(shapefile_sim_centroids$y)),
c(min(shapefile_sim_centroids$x),max(shapefile_sim_centroids$y)),
c(max(shapefile_sim_centroids$x),max(shapefile_sim_centroids$y)))
mesh_sim = inla.mesh.2d(#loc = pred_grid,
loc.domain=domain,
max.edge = c(0.15,0.5),
cutoff = c(0.05,2), offset = c(0.2,0.3))
# pdf(paste0(getwd(),"/Figures/scenario_n",scenario_n,"/mesh.pdf"))
# plot(mesh_sim,las=1)
# points(domain,col=2,pch=19,cex=2)
# plot(shapefile_sim_complete,axes=T,add=T,border=4,lwd=2)
# dev.off()
spde <- inla.spde2.matern(mesh=mesh_sim, alpha=2)
spde$n.spde
s_index <- inla.spde.make.index(name="spatial.field", n.spde=spde$n.spde)
##############################################################
# ------ DEFINE THE inla.stack OBJECTS
##############################################################
A_est <- inla.spde.make.A(mesh=mesh_sim,
loc=as.matrix(monitoringstations.coords))
stack_est <- inla.stack(data=list(x=monitoringstations.data$exposure_with_meas_err),
A=list(A_est,1),
effects=list(c(s_index, list(intercept=1)),
list(z=monitoringstations.data$z)),
tag="est")
A_pred <- inla.spde.make.A(mesh=mesh_sim,
loc=pred_grid@coords)
stack_pred <- inla.stack(data=list(x=NA),
A=list(A_pred,1),
effects=list(c(s_index,list(intercept=1)),
list(z=z_pred_grid)),
tag="pred")
stack <- inla.stack(stack_est, stack_pred)
##############################################################
# Define the linear combinations in the INLA style for method 1: intersections
##############################################################
#dim_lp <- nrow(inla.stack.A(stack)) + ncol(inla.stack.A(stack))
dim_lp = nrow(monitoringstations.coords) + nrow(pred_grid@coords)
index_pred <- inla.stack.index(stack,"pred")$data #NB! numbers start from nrow(monitoringstations.coords)+1
#each row is an area, each column is a component of the linear combination
lincombs.weights_method1 = matrix(0, nrow = n_areas, ncol = length(pred_grid))
lc_all_method1 = c()
for(i in seq(1, length(unique(weights_grid_areas_intersection$AREAKEY)))) { #this corresponds to n_area
#cat("------------- Area n.",i,"----", "\n" )
pixel_area = weights_grid_areas_intersection[which(weights_grid_areas_intersection$AREAKEY==unique(weights_grid_areas_intersection$AREAKEY)[i]),]
#Extract from the SP_ID string only the number related to the pixel (remove g and other numbers at the end)
pixel_area$index = as.numeric(substring(gsub( " .*$", "", pixel_area$pixel ),2))
pixel_area = pixel_area[order(pixel_area$index),]
#Fill in the matrix with the weights (sum by row = 1)
lincombs.weights_method1[i,(index_pred[pixel_area$index] - nrow(monitoringstations.coords))] = pixel_area$weights
lc_vec <- rep(NA,times=dim_lp)
lc_vec[index_pred][pixel_area$index] <- pixel_area$weights
lc_predictor <- inla.make.lincomb(APredictor = lc_vec)
names(lc_predictor) <- paste0("lc_area_ID=",pixel_area$AREAKEY[1])
assign(paste0("lc_area_ID=",pixel_area$AREAKEY[1]), lc_predictor)
lc_all_method1 = c(lc_all_method1, get(paste0("lc_area_ID=",pixel_area$AREAKEY[1])))
}
#Check that the sum by row is 1
if( sum(apply(lincombs.weights_method1,1,sum)) != n_areas) print ("!!!!!!!! Errror in creating the lincomb weight matrix!!!!!!!")
#how many lincombs for each area
n_lc_all_method1 = unlist(lapply(lc_all_method1,
function(x) length(x[[1]]$APredictor$weight)))
##############################################################
# Define the linear combinations in the INLA style for method 2: points inside/closest
##############################################################
#each row is an area, each column is a component of the linear combination
lincombs.weights_method2 = matrix(0, nrow = n_areas, ncol = length(pred_grid))
lc_all_method2 = c()
for(i in seq(1, length(unique(weights_points_areas_inside_closest$AREAKEY)))) { #this corresponds to n_area
#cat("------------- Area n.",i,"----", "\n" )
pixel_area = weights_points_areas_inside_closest[which(weights_points_areas_inside_closest$AREAKEY==unique(weights_points_areas_inside_closest$AREAKEY)[i]),]
#Fill in the matrix with the weights (sum by row = 1)
pixel_area$index = pixel_area$pixel
lincombs.weights_method2[i,(index_pred[pixel_area$index] - nrow(monitoringstations.coords))] = pixel_area$weights
lc_vec <- rep(NA,times=dim_lp)
lc_vec[index_pred][pixel_area$index] <- pixel_area$weights
lc_predictor <- inla.make.lincomb(APredictor = lc_vec)
names(lc_predictor) <- paste0("lc_area_ID=",pixel_area$AREAKEY[1])
assign(paste0("lc_area_ID=",pixel_area$AREAKEY[1]), lc_predictor)
lc_all_method2 = c(lc_all_method2, get(paste0("lc_area_ID=",pixel_area$AREAKEY[1])))
}
#Check that the sum by row is 1
if( sum(apply(lincombs.weights_method2,1,sum)) != n_areas) print ("!!!!!!!! Errror in creating the lincomb weight matrix!!!!!!!")
#How many lincombs for each area
n_lc_all_method2 = unlist(lapply(lc_all_method2,function(x) length(x[[1]]$APredictor$weight)))
##############################################################
# FIRST STAGE: run SPDE with linear combinations
##############################################################
formula <- x ~ -1 + intercept + z + f(spatial.field, model=spde)
#The two runs differ in the lincomb specification
start.exposure = Sys.time()
output_withlincomb_method1 = inla(formula,
data=inla.stack.data(stack, spde=spde),
family="gaussian",
#control.family = list(hyper=list(prec=list(prior = "logtnormal",
# param = c(sqrt(sigma2_e),100)))), #prior on the sd
control.compute=list(config=TRUE),
control.predictor=list(A=inla.stack.A(stack), compute=TRUE),
lincomb = lc_all_method1, verbose=F)
stop.exposure = Sys.time()
output_withlincomb_method2 = inla(formula,
data=inla.stack.data(stack, spde=spde),
family="gaussian",
#control.family = list(hyper=list(prec=list(prior = "logtnormal",
# param = c(sqrt(sigma2_e),100)))), #prior on the sd
control.compute=list(config=TRUE),
control.predictor=list(A=inla.stack.A(stack), compute=TRUE),
lincomb = lc_all_method2, verbose=F)
output_withlincomb = output_withlincomb_method1 #parameter posterior distributions do not change with method1/method2
#--- Sample n_random_fromposterior values from the parameter posterior distributions (for the exposure model)
#--- and save the results
posterior_b0_PI_FF = c(posterior_b0_PI_FF,
inla.rmarginal(n_random_fromposterior, output_withlincomb$marginals.fixed$intercept))
posterior_b1_PI_FF = c(posterior_b1_PI_FF,
inla.rmarginal(n_random_fromposterior, output_withlincomb$marginals.fixed$z))
meas_err_var = try(inla.tmarginal(function(x) 1/x,
output_withlincomb$marginals.hyper[[1]]))
if (class(meas_err_var) == "try-error") next
posterior_sigma2e_PI_FF = c(posterior_sigma2e_PI_FF,
inla.rmarginal(n_random_fromposterior, meas_err_var))
output.field <- inla.spde2.result(inla=output_withlincomb, name="spatial.field",
spde=spde, do.transf=TRUE)
posterior_range_PI_FF = c(posterior_range_PI_FF,
inla.rmarginal(n_random_fromposterior, output.field$marginals.range.nominal[[1]]))
posterior_sigma2xi_PI_FF = c(posterior_sigma2xi_PI_FF,
inla.rmarginal(n_random_fromposterior, output.field$marginals.variance.nominal[[1]]))
#--- Summaries from the posterior distributions of the lincombs:
lincomb_marginals_method1 = output_withlincomb_method1$marginals.lincomb.derived
lincomb_marginals_method2 = output_withlincomb_method2$marginals.lincomb.derived
# # check the prediction at the grid level
cor_pred_obs_predgrid_method1[sim_i] = cor(sim_grid_inside_df_pred$exposure,
output_withlincomb_method1$summary.linear.predictor$`0.5quant`[index_pred])
cor_pred_obs_predgrid_method2[sim_i] = cor(sim_grid_inside_df_pred$exposure,
output_withlincomb_method2$summary.linear.predictor$`0.5quant`[index_pred])
# # The linear predictor is the same with method1/method2
# plot(output_withlincomb_method1$summary.linear.predictor$`0.5quant`[index_pred],
# output_withlincomb_method2$summary.linear.predictor$`0.5quant`[index_pred])
# This is just a check for the prediction (done only for the last simulation)
if(sim_i==n_simulations){
check_df = simulated.data$sim_grid_inside_df_pred
check_df$exposure_est = output_withlincomb_method2$summary.linear.predictor[index_pred, "mean"]
true_area_exposure = aggregate(exposure ~ AREAKEY,
data=check_df,
FUN=mean)
est_area_exposure = aggregate(exposure_est ~ AREAKEY,
data=check_df,
FUN=mean)
shapefile_sim_check = merge(shapefile_sim_complete,
true_area_exposure,
by = "AREAKEY",
all.x = T)
shapefile_sim_check = merge(shapefile_sim_check,
est_area_exposure,
by = "AREAKEY",
all.x = T)
pdf(paste0(getwd(), "/Figures/Exposurebias_area_scenario",scenario_n,".pdf"),width=5, height=6)
p = spplot(shapefile_sim_check,c("true_area_exposure","exposure","exposure_est"))
print(p)
#true_area_exposure is different from exposure because the first is computed
#on the big number of points used for exposure simulation while the latter
#is compute using the prediciton grid proints
dev.off()
pdf(paste0(getwd(), "/Figures/Exposurebias_predgrid_scenario",scenario_n,".pdf"),width=5, height=6)
mean_pred_true = matrix(simulated.data$sim_grid_inside_df_pred$exposure, res_pred_grid, res_pred_grid, byrow=T)
mean_pred_grid = matrix(output_withlincomb_method2$summary.linear.predictor[index_pred, "mean"], res_pred_grid, res_pred_grid, byrow=T)
#image.plot(mean_pred_true)
#image.plot(mean_pred_grid)
mypalette = colorRampPalette(brewer.pal(11,"RdBu"))(100)
diff_predgrid = mean_pred_grid - mean_pred_true
image.plot(simulated.data$pred_grid_x1,simulated.data$pred_grid_x2,diff_predgrid,
col= mypalette, main=paste ("Scenario=",scenario_n,"Iteration=",sim_i))
plot(shapefile_sim_complete,add=T,lwd=2)
dev.off()
}
##############################################################
# AREA EXPOSURE ESTIMATION METHOD 1: LINCOMBS with intersections
# Extract EXPOSURE relevant results for PLUG-IN PI (posterior median)
##############################################################
#--- Median + Create data frame with the posterior median + Add to the shapefile
posterior_median_method1 = unlist(lapply(lincomb_marginals_method1, function(x) inla.qmarginal(0.5, x)))
posterior_median_method1 = data.frame("AREAKEY"=substring(names(posterior_median_method1),
nchar(names(posterior_median_method1[1]))-5,max(nchar(names(posterior_median_method1)))),
posterior_median_method1)
shapefile_sim_complete = merge(shapefile_sim_complete,
posterior_median_method1,by="AREAKEY",all.x=T)
#spplot(shapefile_sim_complete,c("true_area_exposure","posterior_median_method1"))
#plot(shapefile_sim_complete@data$true_area_exposure,shapefile_sim_complete@data$posterior_median_method1)
cor_pred_obs_area_method1[sim_i] = cor(shapefile_sim_complete@data$true_area_exposure,
shapefile_sim_complete@data$posterior_median_method1)
##############################################################
# AREA EXPOSURE ESTIMATION METHOD 2: AREA AVERAGE (with points inside/nearest point)
##############################################################
#--- Median + Create data frame with the posterior median + Add to the shapefile
posterior_median_method2 = unlist(lapply(lincomb_marginals_method2, function(x) inla.qmarginal(0.5, x)))
posterior_median_method2 = data.frame("AREAKEY"=substring(names(posterior_median_method2),
nchar(names(posterior_median_method2[1]))-5,max(nchar(names(posterior_median_method2)))),
posterior_median_method2)
shapefile_sim_complete = merge(shapefile_sim_complete,
posterior_median_method2,by="AREAKEY",all.x=T)
#spplot(shapefile_sim_complete,c("true_area_exposure","posterior_median_method1", "posterior_median_method2"))
#plot(shapefile_sim_complete@data$true_area_exposure,shapefile_sim_complete@data$posterior_median_method1)
#points(shapefile_sim_complete@data$true_area_exposure,shapefile_sim_complete@data$posterior_median_method2,col=2)
cor_pred_obs_area_method2[sim_i] = cor(shapefile_sim_complete@data$true_area_exposure,shapefile_sim_complete@data$posterior_median_method2)
###############################################################
## Simulate from EXPOSURE posterior distribution at the area level: method1
###############################################################
# Sample n_random_fromPPD samples from the joint posterior and compute manually the lincombs
# (These samples will be used for computing performance indexes)
list_samples_joint_posterior_method1 = list()
list_samples_joint_posterior_method2 = list()
for(jj in 1:n_random_fromPPD){
sample_joint_posterior_method1 = inla.posterior.sample(1,output_withlincomb_method1)
sample_joint_posterior_method2 = inla.posterior.sample(1,output_withlincomb_method2)
# Extract the part about the predictions (at the regular grid resolution)
sample_joint_posterior_grid_method1 = sample_joint_posterior_method1[[1]]$latent[1:dim_lp][index_pred]
sample_joint_posterior_grid_method2 = sample_joint_posterior_method2[[1]]$latent[1:dim_lp][index_pred]
#length(sample_joint_posterior_grid_method1) #this has the same resolution of the regular grid!
# Compute the area prediction for method1
sample_joint_posterior_area_method1 = c()
for(j in 1:n_areas){
index_area = lc_all_method1[[j]][[1]]$APredictor$idx - nrow(monitoringstations.coords)
#NB: indexes start from nrow(monitoringstations.coords)+1
#that's the reason why we have - nrow(monitoringstations.coords)
weight_area = lc_all_method1[[j]][[1]]$APredictor$weight
sample_joint_posterior_area_method1[j] = sum(sample_joint_posterior_grid_method1[index_area] * weight_area) #posterior area exposure mean
}
list_samples_joint_posterior_method1[[jj]] = data.frame(sample_joint_post_exposure_method1 = sample_joint_posterior_area_method1,
"AREAKEY"=unique(weights_grid_areas_intersection$AREAKEY))
sample_joint_posterior_area_method2 = c()
for(j in 1:n_areas){
index_area = lc_all_method2[[j]][[1]]$APredictor$idx - nrow(monitoringstations.coords)
#NB: indexes start from nrow(monitoringstations.coords)+1
#that's the reason why we have - nrow(monitoringstations.coords)
weight_area = lc_all_method2[[j]][[1]]$APredictor$weight
sample_joint_posterior_area_method2[j] = sum(sample_joint_posterior_grid_method2[index_area] * weight_area)
}
list_samples_joint_posterior_method2[[jj]] = data.frame(sample_joint_post_exposure_method2 = sample_joint_posterior_area_method2,
"AREAKEY"=unique(weights_points_areas_inside_closest$AREAKEY))
}
#Save the same simulated values in another format for computing at the end the performance indexes
temp_method1 = as.data.frame(lapply(list_samples_joint_posterior_method1,
function(x) x$sample_joint_post_exposure))
colnames(temp_method1) = paste("Sim",seq(1,n_random_fromPPD))
temp_method1 = as.matrix(temp_method1)
posterior_lincombs_method1[[sim_i]] = temp_method1 #matrix n_areas * n_random_fromPPD
#Save the same simulated values in another format for computing at the end the performance indexes
temp_method2 = as.data.frame(lapply(list_samples_joint_posterior_method2, function(x) x$sample_joint_post_exposure))
colnames(temp_method2) = paste("Sim",seq(1,n_random_fromPPD))
temp_method2 = as.matrix(temp_method2)
posterior_lincombs_method2[[sim_i]] = temp_method2 #matrix n_areas * n_random_fromPPD
##############################################################################################################################
## SECOND STAGE POISSON MODEL with PI approach (method1 and method2)
##############################################################################################################################
#--- Prepare the data
data_Poisson = shapefile_sim_complete@data
data_Poisson$id = seq(1:n_areas)
#--- Method1
formula.Poisson.PI.method1 = y_Poisson ~ 1 + posterior_median_method1 + f(id,model="iid")
start.Poisson.PI.method1 = Sys.time()
output.Poisson.PI.method1 = inla(formula.Poisson.PI.method1,family="poisson",
data=data_Poisson,
offset=log(expected))
posterior_gamma0_PI_method1 = c(posterior_gamma0_PI_method1,
inla.rmarginal(n_random_fromposterior, output.Poisson.PI.method1$marginals.fixed$`(Intercept)`))
posterior_gamma1_PI_method1 = c(posterior_gamma1_PI_method1,
inla.rmarginal(n_random_fromposterior, output.Poisson.PI.method1$marginals.fixed$posterior_median_method1))
sigma2iid_marg_post_PI_method1 = inla.tmarginal(function(x) 1/x,
output.Poisson.PI.method1$marginals.hyperpar$`Precision for id`)
posterior_sigma2iid_PI_method1 = c(posterior_sigma2iid_PI_method1,
inla.rmarginal(n_random_fromposterior, sigma2iid_marg_post_PI_method1))
stop.Poisson.PI.method1 = Sys.time()
#--- Method2
formula.Poisson.PI.method2 = y_Poisson ~ 1 + posterior_median_method2 + f(id,model="iid")
start.Poisson.PI.method2 = Sys.time()
output.Poisson.PI.method2 = inla(formula.Poisson.PI.method2,family="poisson",
data=data_Poisson,
offset=log(expected))
posterior_gamma0_PI_method2 = c(posterior_gamma0_PI_method2,
inla.rmarginal(n_random_fromposterior, output.Poisson.PI.method2$marginals.fixed$`(Intercept)`))
posterior_gamma1_PI_method2 = c(posterior_gamma1_PI_method2,
inla.rmarginal(n_random_fromposterior, output.Poisson.PI.method2$marginals.fixed$posterior_median_method2))
sigma2iid_marg_post_PI_method2 = inla.tmarginal(function(x) 1/x,
output.Poisson.PI.method2$marginals.hyperpar$`Precision for id`)
posterior_sigma2iid_PI_method2 = c(posterior_sigma2iid_PI_method1,
inla.rmarginal(n_random_fromposterior, sigma2iid_marg_post_PI_method2))
stop.Poisson.PI.method2 = Sys.time()
##############################################################
# SECOND STAGE: Poisson model with FF approach (method1 and method2)
##############################################################
#--- Method1
formula.Poisson.FF.method1 = y_Poisson ~ 1 + sample_joint_post_exposure_method1 + f(id,model="iid")
start.Poisson.FF.meethod1 = Sys.time()
for(j_FF in 1:n_random_fromPPD){
output.Poisson.FF.method1 <- inla(formula.Poisson.FF.method1,family="poisson",
data=data.frame(data_Poisson,
list_samples_joint_posterior_method1[[j_FF]]),
offset=log(expected))
posterior_gamma0_FF_method1 = c(posterior_gamma0_FF_method1,
inla.rmarginal(n_random_fromposterior, output.Poisson.FF.method1$marginals.fixed$`(Intercept)`))
posterior_gamma1_FF_method1 = c(posterior_gamma1_FF_method1,
inla.rmarginal(n_random_fromposterior, output.Poisson.FF.method1$marginals.fixed$sample_joint_post_exposure_method1))
sigma2iid_marg_post_FF.method1 = inla.tmarginal(function(x) 1/x,
output.Poisson.FF.method1$marginals.hyperpar$`Precision for id`)
posterior_sigma2iid_FF_method1 = c(posterior_sigma2iid_FF_method1,
inla.rmarginal(n_random_fromposterior, sigma2iid_marg_post_FF.method1))
}
stop.Poisson.FF.method1 = Sys.time()
#--- Method2
formula.Poisson.FF.method2 = y_Poisson ~ 1 + sample_joint_post_exposure_method2 + f(id,model="iid")
start.Poisson.FF.meethod2 = Sys.time()
for(j_FF in 1:n_random_fromPPD){
output.Poisson.FF.method2 <- inla(formula.Poisson.FF.method2,family="poisson",
data=data.frame(data_Poisson,
list_samples_joint_posterior_method2[[j_FF]]),
offset=log(expected))
posterior_gamma0_FF_method2 = c(posterior_gamma0_FF_method2,
inla.rmarginal(n_random_fromposterior, output.Poisson.FF.method2$marginals.fixed$`(Intercept)`))
posterior_gamma1_FF_method2 = c(posterior_gamma1_FF_method2,
inla.rmarginal(n_random_fromposterior, output.Poisson.FF.method2$marginals.fixed$sample_joint_post_exposure_method2))
sigma2iid_marg_post_FF.method2 = inla.tmarginal(function(x) 1/x,
output.Poisson.FF.method2$marginals.hyperpar$`Precision for id`)
posterior_sigma2iid_FF_method2 = c(posterior_sigma2iid_FF_method2,
inla.rmarginal(n_random_fromposterior, sigma2iid_marg_post_FF.method2))
}
stop.Poisson.FF.method2 = Sys.time()
##############################################################
# SECOND STAGE: Poisson model with PE approach
##############################################################
#--- Define prior mean and precision for exposure for each area (taken from the lincombs marginal posterior distributions)
all_post_mean_method1 = unlist(lapply(lincomb_marginals_method1, function(x) inla.zmarginal(x,silent=T)$mean))
all_post_sd_method1 = unlist(lapply(lincomb_marginals_method1, function(x) inla.zmarginal(x,silent=T)$sd))
all_post_mean_method2 = unlist(lapply(lincomb_marginals_method2, function(x) inla.zmarginal(x,silent=T)$mean))
all_post_sd_method2 = unlist(lapply(lincomb_marginals_method2, function(x) inla.zmarginal(x,silent=T)$sd))
#data_Poisson$meanexp = apply(cbind(all_post_mean_method1,all_post_mean_method2), 1 ,mean)
data_Poisson$meanexp_method1 = all_post_mean_method1
data_Poisson$meanexp_method2 = all_post_mean_method2
#data_Poisson$precexp = apply(cbind(1/(all_post_sd_method1^2), 1/(all_post_sd_method2^2)), 1 ,mean)
data_Poisson$precexp_method1 = 1/(all_post_sd_method1^2)
data_Poisson$precexp_method2 = 1/(all_post_sd_method2^2)
# Another id for purely iid random effect
data_Poisson$id2 <- data_Poisson$id
# NB: the values of b are set at the beginning of the file (see around line 22)
#--- Method1
#--- Run INLA in parallel (the number of models is given by length(b))
start.Poisson.PE.method1 = Sys.time()
PE_results_method1 = mclapply(b, function(X){fit.inla.method1(d=data_Poisson, X)})
mliks_method1 <- unlist(lapply(PE_results_method1, function(X){X$mlik[1,1]}))
bma.w.method1 <- exp(mliks_method1 - max(mliks_method1) + dnorm(b, mean = 0, sd = sqrt(1/.001), log = TRUE))
#Index to remove models with a very low weight
bma.idx.method1 <- which(bma.w.method1 > 1e-10)
#--- Extract results for gamma1
gamma1_PE_method1 <- inla.smarginal(cbind(b, bma.w.method1))
#--- Re-scale BMA weights
bma.w.method1 <- bma.w.method1 /sum(bma.w.method1)
#--- Re-scale marginal to REALLY integrate 1
h.method1 <- gamma1_PE_method1$x[2] - gamma1_PE_method1$x[1]
w.method1 <- sum(h.method1 * gamma1_PE_method1$y)
gamma1_PE_method1$y <- gamma1_PE_method1$y / w.method1
#Plot
#plot(gamma1_PE_method1, type = "l")
#abline(v=log(RR))
#--- Simulate from the posterior of gamma1
posterior_gamma1_PE_method1 = c(posterior_gamma1_PE_method1,
inla.rmarginal(n_random_fromposterior, gamma1_PE_method1))
#--- Extract results for intercept
gamma0_marg_post_PE_method1_list = lapply(PE_results_method1,
function(Y){inla.tmarginal(identity, Y$marginals.fixed$`(Intercept)`)})
gamma0_PE_method1 <- try(INLABMA:::fitmargBMA(gamma0_marg_post_PE_method1_list[bma.idx.method1], bma.w.method1[bma.idx.method1]))
if(class(gamma0_PE_method1)=="data.frame"){
posterior_gamma0_PE_method1 = c(posterior_gamma0_PE_method1,
inla.rmarginal(n_random_fromposterior, gamma0_PE_method1))
} else { #error in integrate
n.skip = n.skip + 1
which.skip.withnames = c(which.skip.withnames,paste0("gamma0_",sim_i))
which.skip.withnames = c(which.skip.withnames,sim_i)
#Remove for FF, PI, PE and the other parameters the simulated values of this iteration that we are skipping
posterior_gamma0_FF_method1 = posterior_gamma0_FF_method1[- ((length(posterior_gamma0_FF_method1)-n_random_fromposterior+1):length(posterior_gamma0_FF_method1))]
posterior_gamma1_FF_method1 = posterior_gamma1_FF_method1[- ((length(posterior_gamma1_FF_method1)-n_random_fromposterior+1):length(posterior_gamma1_FF_method1))]
posterior_sigma2iid_FF_method1 = posterior_sigma2iid_FF_method1[- ((length(posterior_sigma2iid_FF_method1)-n_random_fromposterior+1):length(posterior_sigma2iid_FF_method1))]
posterior_gamma0_PI_method1 = posterior_gamma0_PI_method1[- ((length(posterior_gamma0_PI_method1)-n_random_fromposterior+1):length(posterior_gamma0_PI_method1))]
posterior_gamma1_PI_method1 = posterior_gamma1_PI_method1[- ((length(posterior_gamma1_PI_method1)-n_random_fromposterior+1):length(posterior_gamma1_PI_method1))]
posterior_sigma2iid_PI_method1 = posterior_sigma2iid_PI_method1[- ((length(posterior_sigma2iid_PI_method1)-n_random_fromposterior+1):length(posterior_sigma2iid_PI_method1))]
posterior_gamma1_PE_method1 = posterior_gamma1_PE_method1[- ((length(posterior_gamma1_PE_method1)-n_random_fromposterior+1):length(posterior_gamma1_PE_method1))]
next
}
#--- Extract results for sigma2iid
sigma2iid_marg_post_PE_method1_list = lapply(PE_results_method1,
function(Y){inla.tmarginal(function(x) 1/x, Y$marginals.hyperpar$`Precision for id2`)})
sigma2iid_PE_method1 = try(INLABMA:::fitmargBMA(sigma2iid_marg_post_PE_method1_list[bma.idx.method1], bma.w.method1[bma.idx.method1]))
if(class(sigma2iid_PE_method1)=="data.frame"){
posterior_sigma2iid_PE_method1 = c(posterior_sigma2iid_PE_method1,
inla.rmarginal(n_random_fromposterior, sigma2iid_PE_method1))
} else { #error in integrate
n.skip = n.skip + 1
which.skip.withnames = c(which.skip.withnames,paste0("sigma2iid_",sim_i))
which.skip = c(which.skip,sim_i)
#Remove for FF, PI, PE and the other parameters the simulated values of this iteration that we are skipping
posterior_gamma0_FF_method1 = posterior_gamma0_FF_method1[- ((length(posterior_gamma0_FF_method1)-n_random_fromposterior+1):length(posterior_gamma0_FF_method1))]
posterior_gamma1_FF_method1 = posterior_gamma1_FF_method1[- ((length(posterior_gamma1_FF_method1)-n_random_fromposterior+1):length(posterior_gamma1_FF_method1))]
posterior_sigma2iid_FF_method1 = posterior_sigma2iid_FF_method1[- ((length(posterior_sigma2iid_FF_method1)-n_random_fromposterior+1):length(posterior_sigma2iid_FF_method1))]
posterior_gamma0_PI_method1 = posterior_gamma0_PI_method1[- ((length(posterior_gamma0_PI_method1)-n_random_fromposterior+1):length(posterior_gamma0_PI_method1))]
posterior_gamma1_PI_method1 = posterior_gamma1_PI_method1[- ((length(posterior_gamma1_PI_method1)-n_random_fromposterior+1):length(posterior_gamma1_PI_method1))]
posterior_sigma2iid_PI_method1 = posterior_sigma2iid_PI_method1[- ((length(posterior_sigma2iid_PI_method1)-n_random_fromposterior+1):length(posterior_sigma2iid_PI_method1))]
posterior_gamma0_PE_method1 = posterior_gamma0_PE_method1[- ((length(posterior_gamma0_PE_method1)-n_random_fromposterior+1):length(posterior_gamma0_PE_method1))]
posterior_gamma1_PE_method1 = posterior_gamma1_PE_method1[- ((length(posterior_gamma1_PE_method1)-n_random_fromposterior+1):length(posterior_gamma1_PE_method1))]
next
}
stop.Poisson.PE.method1 = Sys.time()
#--- Method2
#--- Run INLA in parallel (the number of models is given by length(b))
start.Poisson.PE.method2 = Sys.time()
PE_results_method2 = mclapply(b, function(X){fit.inla.method2(d=data_Poisson, X)})
mliks_method2 <- unlist(lapply(PE_results_method2, function(X){X$mlik[1,1]}))
bma.w.method2 <- exp(mliks_method2 - max(mliks_method2) + dnorm(b, mean = 0, sd = sqrt(1/.001), log = TRUE))
#Index to remove models with a very low weight
bma.idx.method2 <- which(bma.w.method2 > 1e-10)
#--- Extract results for gamma1
gamma1_PE_method2 <- inla.smarginal(cbind(b, bma.w.method2))
#--- Re-scale BMA weights
bma.w.method2 <- bma.w.method2 /sum(bma.w.method2)
#--- Re-scale marginal to REALLY integrate 1
h.method2 <- gamma1_PE_method2$x[2] - gamma1_PE_method2$x[1]
w.method2 <- sum(h.method2 * gamma1_PE_method2$y)
gamma1_PE_method2$y <- gamma1_PE_method2$y / w.method2
#Plot
#plot(gamma1_PE_method2, type = "l")
#abline(v=log(RR))
#--- Simulate from the posterior of gamma1
posterior_gamma1_PE_method2 = c(posterior_gamma1_PE_method2,
inla.rmarginal(n_random_fromposterior, gamma1_PE_method2))
#--- Extract results for intercept
gamma0_marg_post_PE_method2_list = lapply(PE_results_method2,
function(Y){inla.tmarginal(identity, Y$marginals.fixed$`(Intercept)`)})
gamma0_PE_method2 <- try(INLABMA:::fitmargBMA(gamma0_marg_post_PE_method2_list[bma.idx.method2], bma.w.method2[bma.idx.method2]))
if(class(gamma0_PE_method2)=="data.frame"){
posterior_gamma0_PE_method2 = c(posterior_gamma0_PE_method2,
inla.rmarginal(n_random_fromposterior, gamma0_PE_method2))
} else { #error in integrate
n.skip = n.skip + 1
which.skip.withnames = c(which.skip.withnames,paste0("gamma0_",sim_i))
which.skip.withnames = c(which.skip.withnames,sim_i)
#Remove for FF, PI, PE and the other parameters the simulated values of this iteration that we are skipping
posterior_gamma0_FF_method2 = posterior_gamma0_FF_method2[- ((length(posterior_gamma0_FF_method2)-n_random_fromposterior+1):length(posterior_gamma0_FF_method2))]
posterior_gamma1_FF_method2 = posterior_gamma1_FF_method2[- ((length(posterior_gamma1_FF_method2)-n_random_fromposterior+1):length(posterior_gamma1_FF_method2))]
posterior_sigma2iid_FF_method2 = posterior_sigma2iid_FF_method2[- ((length(posterior_sigma2iid_FF_method2)-n_random_fromposterior+1):length(posterior_sigma2iid_FF_method2))]
posterior_gamma0_PI_method2 = posterior_gamma0_PI_method2[- ((length(posterior_gamma0_PI_method2)-n_random_fromposterior+1):length(posterior_gamma0_PI_method2))]
posterior_gamma1_PI_method2 = posterior_gamma1_PI_method2[- ((length(posterior_gamma1_PI_method2)-n_random_fromposterior+1):length(posterior_gamma1_PI_method2))]
posterior_sigma2iid_PI_method2 = posterior_sigma2iid_PI_method2[- ((length(posterior_sigma2iid_PI_method2)-n_random_fromposterior+1):length(posterior_sigma2iid_PI_method2))]
posterior_gamma1_PE_method2 = posterior_gamma1_PE_method2[- ((length(posterior_gamma1_PE_method2)-n_random_fromposterior+1):length(posterior_gamma1_PE_method2))]
next
}
#--- Extract results for sigma2iid
sigma2iid_marg_post_PE_method2_list = lapply(PE_results_method2,
function(Y){inla.tmarginal(function(x) 1/x, Y$marginals.hyperpar$`Precision for id2`)})
sigma2iid_PE_method2 = try(INLABMA:::fitmargBMA(sigma2iid_marg_post_PE_method2_list[bma.idx.method2], bma.w.method2[bma.idx.method2]))
if(class(sigma2iid_PE_method2)=="data.frame"){
posterior_sigma2iid_PE_method2 = c(posterior_sigma2iid_PE_method2,
inla.rmarginal(n_random_fromposterior, sigma2iid_PE_method2))
} else { #error in integrate
n.skip = n.skip + 1
which.skip.withnames = c(which.skip.withnames,paste0("sigma2iid_",sim_i))
which.skip = c(which.skip,sim_i)
#Remove for FF, PI, PE and the other parameters the simulated values of this iteration that we are skipping
posterior_gamma0_FF_method2 = posterior_gamma0_FF_method2[- ((length(posterior_gamma0_FF_method2)-n_random_fromposterior+1):length(posterior_gamma0_FF_method2))]
posterior_gamma1_FF_method2 = posterior_gamma1_FF_method2[- ((length(posterior_gamma1_FF_method2)-n_random_fromposterior+1):length(posterior_gamma1_FF_method2))]
posterior_sigma2iid_FF_method2 = posterior_sigma2iid_FF_method2[- ((length(posterior_sigma2iid_FF_method2)-n_random_fromposterior+1):length(posterior_sigma2iid_FF_method2))]
posterior_gamma0_PI_method2 = posterior_gamma0_PI_method2[- ((length(posterior_gamma0_PI_method2)-n_random_fromposterior+1):length(posterior_gamma0_PI_method2))]
posterior_gamma1_PI_method2 = posterior_gamma1_PI_method2[- ((length(posterior_gamma1_PI_method2)-n_random_fromposterior+1):length(posterior_gamma1_PI_method2))]
posterior_sigma2iid_PI_method2 = posterior_sigma2iid_PI_method2[- ((length(posterior_sigma2iid_PI_method2)-n_random_fromposterior+1):length(posterior_sigma2iid_PI_method2))]
posterior_gamma0_PE_method2 = posterior_gamma0_PE_method2[- ((length(posterior_gamma0_PE_method2)-n_random_fromposterior+1):length(posterior_gamma0_PE_method2))]
posterior_gamma1_PE_method2 = posterior_gamma1_PE_method2[- ((length(posterior_gamma1_PE_method2)-n_random_fromposterior+1):length(posterior_gamma1_PE_method2))]
next
}
stop.Poisson.PE.method2 = Sys.time()
###############################################################
## Some final savings
###############################################################
#--- Save the shapefile data
simulated_data_shapefile[[sim_i]] = shapefile_sim_complete@data
#--- Save a file containing information about each area (how many lincombs and monitoring stats)
n_lc_all = data.frame(n_lc_all_method1,n_lc_all_method2)
#n_lc_all$AREAKEY = substring(rownames(n_lc_all),
# nchar(rownames(n_lc_all[1]))-5,max(nchar(rownames(n_lc_all))))
n_lc_all$AREAKEY = sub('.*=', '', rownames(n_lc_all)) #extract everything after the =
#--- Add the number of monitoring stations
nstats = data.frame(table(monitoringstations.data$AREAKEY),
AREAKEY=names(table(monitoringstations.data$AREAKEY)))
nstats = nstats[,-1]
colnames(nstats)= c("n_monit_stats","AREAKEY")
info_area = merge(n_lc_all,nstats, all.x=T)
#--- Add the number of points used for simulating the area true level
nsimpoints = data.frame(table(sim_grid_inside_df$AREAKEY),
AREAKEY=names(table(sim_grid_inside_df$AREAKEY)))
nsimpoints = nsimpoints[,-1]
colnames(nsimpoints)= c("n_sim_points","AREAKEY")
info_area2 = merge(info_area,nsimpoints)
write.table(info_area2,
paste0(getwd(),"/Output/info_area_scenario_",scenario_n,".csv"),
sep=";",append=F,row.names = F)
} #close for(sim_i in 1:n_simulations)
##############################################################
# Save all the posteriors
##############################################################
correlations = data.frame(rbind(cor_pred_obs_predgrid_method1,
cor_pred_obs_predgrid_method2,
cor_pred_obs_area_method1,
cor_pred_obs_area_method2))
colnames(correlations) = paste0("sim",seq(1,n_simulations))
correlations$scenario = rep(scenario_n,4)
if(!file.exists(paste0(getwd(),"/Output/correlations_",scenario_n,".csv"))) {
write.table(correlations,
paste0(getwd(),"/Output/correlations_",scenario_n,".csv"),
sep=";",append=F,row.names = T)
} else {
write.table(correlations,
paste0(getwd(),"/Output/correlations_",scenario_n,".csv"),
sep=";",append=T,row.names = T,col.names = F)
}
time.exposure = stop.exposure - start.exposure
time.Poisson.PI.method1 = stop.Poisson.PI.method1 - start.Poisson.PI.method1
time.Poisson.PI.method2 = stop.Poisson.PI.method2 - start.Poisson.PI.method2
time.Poisson.FF.method1 = stop.Poisson.FF.method1 - start.Poisson.FF.meethod1
time.Poisson.FF.method2 = stop.Poisson.FF.method2 - start.Poisson.FF.meethod2
time.Poisson.PE.method1 = stop.Poisson.PE.method1 - start.Poisson.PE.method1
time.Poisson.PE.method2 = stop.Poisson.PE.method2 - start.Poisson.PE.method2
save(posterior_gamma0_PI_method1, posterior_gamma0_PI_method2,
posterior_gamma0_PE_method1, posterior_gamma0_PE_method2,
posterior_gamma0_FF_method1, posterior_gamma0_FF_method2,
posterior_gamma1_PI_method1, posterior_gamma1_PI_method2,
posterior_gamma1_PE_method1, posterior_gamma1_PE_method2,
posterior_gamma1_FF_method1, posterior_gamma1_FF_method2,
posterior_sigma2iid_PI_method1,posterior_sigma2iid_PI_method2,
posterior_sigma2iid_PE_method1, posterior_sigma2iid_PE_method2,
posterior_sigma2iid_FF_method1,posterior_sigma2iid_FF_method2,
simulated_data_shapefile,
#cor_pred_obs_predgrid_method1,cor_pred_obs_predgrid_method2,
#cor_pred_obs_area_method1,cor_pred_obs_area_method2,
posterior_lincombs_method1,
posterior_lincombs_method2,
sim_grid_inside_df,
sim_grid_inside_df_pred,
time.exposure,
time.Poisson.PI.method2, time.Poisson.PI.method1,
time.Poisson.FF.method1, time.Poisson.FF.method2,
time.Poisson.PE.method1, time.Poisson.PE.method2,
file=paste0(getwd(),"/Output/","AllposteriorsANDsimulatedData_scenarioN",scenario_n,".RData"))
##############################################################
# Compute bias, RMSE and coverage for the exposure model parameters
##############################################################
#--- Parameter bias + rmse + coverage
b0_perf_indexes_PI_FF = unlist(my_bias_RMSE_coverage(posterior_b0_PI_FF, n_simulations, rep(b0,n_simulations)))
b1_perf_indexes_PI_FF = unlist(my_bias_RMSE_coverage(posterior_b1_PI_FF, n_simulations, rep(b1,n_simulations)))
sigma2e_perf_indexes_PI_FF = unlist(my_bias_RMSE_coverage(posterior_sigma2e_PI_FF, n_simulations, rep(sigma2_e,n_simulations)))
sigma2xi_perf_indexes_PI_FF = unlist(my_bias_RMSE_coverage(posterior_sigma2xi_PI_FF, n_simulations, rep(sigma2_xi,n_simulations)))
range_perf_indexes_PI_FF = unlist(my_bias_RMSE_coverage(posterior_range_PI_FF, n_simulations, rep(r,n_simulations)))
#--- Export exposure model parameter performance
output_exposurepar_performance = rbind(
c(b0_perf_indexes_PI_FF,
b1_perf_indexes_PI_FF,
sigma2e_perf_indexes_PI_FF,
sigma2xi_perf_indexes_PI_FF,
range_perf_indexes_PI_FF)
)
output_exposurepar_performance = data.frame(method=c(paste0("PI-FF",scenario_n)),output_exposurepar_performance)
colnames(output_exposurepar_performance)[-1] = do.call(paste0,
expand.grid(c("bias","rmse","coverage%"),c("b0","b1","sigma2e","sigma2xi","range")))
if(!file.exists(paste0(getwd(),"/Output/Exposure_",name_file_performance))) {
write.table(output_exposurepar_performance,
paste0(getwd(),"/Output/Exposure_",name_file_performance),
sep=";",row.names = F)
} else {
write.table(output_exposurepar_performance,
paste0(getwd(),"/Output/Exposure_",name_file_performance),
sep=";",row.names = F,append=T,col.names = F)
}
##############################################################
# Plot posterior distributions EXPOSURE model parameters
##############################################################
pdf(paste0(getwd(),"/Figures/","Posteriors__exposure_scenarioN",scenario_n,".pdf"))
par(mfrow=c(3,2))
density_b0_PI_FF = density(posterior_b0_PI_FF)
plot(density_b0_PI_FF,main="",ylab = expression(b[0]))
abline(v=b0,lty=4,col=2,lwd=2)
abline(v=median(posterior_b0_PI_FF))
boxplot(matrix(posterior_b0_PI_FF,ncol=n_simulations))
abline(h=b0,lty=4,col=2,lwd=2)
density_b1_PI_FF = density(posterior_b1_PI_FF)
plot(density_b1_PI_FF,main="",ylab = expression(b[1]))
abline(v=b1,lty=4,col=2,lwd=2)
abline(v=median(posterior_b1_PI_FF))
boxplot(matrix(posterior_b1_PI_FF,ncol=n_simulations))
abline(h=b1,lty=4,col=2,lwd=2)
density_sigma2e_PI_FF = density(posterior_sigma2e_PI_FF)
plot(density_sigma2e_PI_FF,main="",ylab = expression(sigma[e]^2))
abline(v=sigma2_e,lty=4,col=2,lwd=2)
abline(v=median(posterior_sigma2e_PI_FF))
boxplot(matrix(posterior_sigma2e_PI_FF,ncol=n_simulations))
abline(h=sigma2_e,lty=4,col=2,lwd=2)
density_sigma2xi_PI_FF = density(posterior_sigma2xi_PI_FF)
plot(density_sigma2xi_PI_FF,main="",ylab = expression(sigma[omega]^2))
abline(v=sigma2_xi,lty=4,col=2,lwd=2)
abline(v=median(posterior_sigma2xi_PI_FF))
boxplot(matrix(posterior_sigma2xi_PI_FF,ncol=n_simulations))
abline(h=sigma2_xi,lty=4,col=2,lwd=2)
density_range_PI_FF = density(posterior_range_PI_FF)
plot(density_range_PI_FF,main="",ylab = "range")
abline(v=r,lty=4,col=2,lwd=2)
abline(v=median(posterior_range_PI_FF))
boxplot(matrix(posterior_range_PI_FF,ncol=n_simulations))
abline(h=r,lty=4,col=2,lwd=2)
dev.off()
##############################################################
# Compute bias+mse+coverage for exposure area prediction
##############################################################
#comparing methods using the posterior exposure distribution for each area
list_simulatedvalues_method1 = posterior_lincombs_method1
list_simulatedvalues_method2 = posterior_lincombs_method2
bias_method1 = bias_method2 = matrix(NA,nrow=n_simulations,ncol=n_areas)
rmse_method1 = rmse_method2 = matrix(NA,nrow=n_simulations,ncol=n_areas)
cov_method1 = cov_method2 = matrix(NA,nrow=n_simulations,ncol=n_areas)
for(i in 1:n_simulations){
temp_bias_method1 = temp_bias_method2 = c()
temp_cov_method1 = temp_cov_method2 = c()
temp_rmse_method1 = temp_rmse_method2 = c()
matrix_simulatedvalues_method1 = list_simulatedvalues_method1[[i]]
matrix_simulatedvalues_method2 = list_simulatedvalues_method2[[i]]
#For each area compute the relative bias and the coverage (nb: the true values change)
for(A in 1:n_areas){
#temp_bias[A] = mean((matrix_simulatedvalues[A,] - true_exposure[A]) / true_exposure[A])
temp_bias_method1[A] = mean(matrix_simulatedvalues_method1[A,] - simulated_data_shapefile[[i]]$true_area_exposure[A])
temp_bias_method2[A] = mean(matrix_simulatedvalues_method2[A,] - simulated_data_shapefile[[i]]$true_area_exposure[A])
temp_rmse_method1[A] = sqrt(mean((matrix_simulatedvalues_method1[A,] - simulated_data_shapefile[[i]]$true_area_exposure[A])^2))
temp_rmse_method2[A] = sqrt(mean((matrix_simulatedvalues_method2[A,] - simulated_data_shapefile[[i]]$true_area_exposure[A])^2))
q0025_method1 = quantile(matrix_simulatedvalues_method1[A,],0.025)
q0975_method1 = quantile(matrix_simulatedvalues_method1[A,],0.975)
temp_cov_method1[A] = (q0025_method1 < simulated_data_shapefile[[i]]$true_area_exposure[A]) & (simulated_data_shapefile[[i]]$true_area_exposure[A] < q0975_method1)
q0025_method2 = quantile(matrix_simulatedvalues_method2[A,],0.025)
q0975_method2 = quantile(matrix_simulatedvalues_method2[A,],0.975)
temp_cov_method2[A] = (q0025_method2 < simulated_data_shapefile[[i]]$true_area_exposure[A]) & (simulated_data_shapefile[[i]]$true_area_exposure[A] < q0975_method2)
}
bias_method1[i,] = temp_bias_method1
bias_method2[i,] = temp_bias_method2
cov_method1[i,] = temp_cov_method1
cov_method2[i,] = temp_cov_method2
rmse_method1[i,] = temp_rmse_method1
rmse_method2[i,] = temp_rmse_method2
}
mean_bias_method1 = apply(bias_method1,2,mean) #mean over simulations
mean_bias_method2 = apply(bias_method2,2,mean) #mean over simulations
mean_coverage_method1 = apply(cov_method1,2,sum) / n_simulations * 100
mean_coverage_method2 = apply(cov_method2,2,sum) / n_simulations * 100
mean_rmse_method1 = apply(rmse_method1,2,mean)
mean_rmse_method2 = apply(rmse_method2,2,mean)
mean_overiteration_summarystats = data.frame(rbind(mean_bias_method1,mean_bias_method2,
mean_rmse_method1,mean_rmse_method2,
mean_coverage_method1,mean_coverage_method2))
mean_overiteration_summarystats$scenario = rep(scenario_n,6)
mean_overiteration_summarystats$method = c("mean_bias_method1","mean_bias_method2",
"mean_rmse_method1","mean_rmse_method2",
"mean_coverage_method1","mean_coverage_method2")
if(!file.exists(paste0(getwd(),"/Output/Comparingexposure_meanoveriterations_",name_file_performance))) {
write.table(mean_overiteration_summarystats,
paste0(getwd(),"/Output/Comparingexposure_meanoveriterations_",name_file_performance),
sep=";",row.names = F)
} else {
write.table(mean_overiteration_summarystats,
paste0(getwd(),"/Output/Comparingexposure_meanoveriterations_",name_file_performance),
sep=";",row.names = F,append=T,col.names = F)
}
##############################################################
# PLOT bias+mse+coverage for exposure area prediction
##############################################################
#--- Plot the mean bias
area_bias = data.frame(bias_method1 = mean_bias_method1,bias_method2 = mean_bias_method2)
area_bias$AREAKEY = shapefile_sim_complete@data$AREAKEY
shapefile_sim_complete = merge(shapefile_sim_complete, area_bias, by="AREAKEY")
pdf(paste0(getwd(),"/Figures/","Area_bias_scenarioN",scenario_n,".pdf"))
mypalette = colorRampPalette(brewer.pal(11,"RdBu"))(100)
coordinates(monitoringstations.coords) = c("x1","x2")
proj4string(monitoringstations.coords) = proj4string(shapefile_sim_complete)
p=spplot(shapefile_sim_complete, c("bias_method1","bias_method2"),
#names.attr = c("PI-FF"),
#sp.layout = c('sp.points', monitoringstations.coords, col='magenta', pch=16),
col.regions=mypalette, cut=16)
#sp.layout = c('sp.points', pred_grid, col='magenta', pch=16))
print(p)
dev.off()