scripts/robust_regression/power_plant/PP4.R
In rchan26/hierarchicalFusion: Divide-and-Conquer Monte Carlo Fusion
library(DCFusion)
library(HMCBRR)
library(readxl)
##### Initialise example #####
seed <- 2022
set.seed(seed)
nsamples_MCF <- 100000
nsamples_GBF <- 50000
nsamples_DCGBF <- 10000
warmup <- 10000
time_choice <- 1
nu <- 5
sigma <- 1
prior_means <- rep(0, 5)
prior_variances <- rep(10, 5)
ESS_threshold <- 0.5
CESS_0_threshold <- 0.5
CESS_j_threshold <- 0.05
diffusion_estimator <- 'NB'
n_cores <- parallel::detectCores()
##### Loading in Data #####
# Features consist of hourly average ambient variables
# - Temperature (T) in the range 1.81°C and 37.11°C,
# - Ambient Pressure (AP) in the range 992.89-1033.30 millibar,
# - Relative Humidity (RH) in the range 25.56% to 100.16%
# - Exhaust Vacuum (V) in the range 25.36-81.56 cm Hg
# - Net hourly electrical energy output (EP) 420.26-495.76 MW
load_pp_data <- function(file, standardise_variables = TRUE) {
original_data <- as.data.frame(readxl::read_xlsx(file))
colnames(original_data) <- c('T', 'V', 'AP', 'RH', 'EP')
if (standardise_variables) {
X <- subset(original_data, select = -c(EP))
variable_means <- rep(NA, ncol(X))
variable_sds <- rep(NA, ncol(X))
for (col in 1:ncol(X)) {
variable_means[col] <- mean(X[,col])
variable_sds[col] <- sd(X[,col])
X[,col] <- (X[,col]-variable_means[col])/variable_sds[col]
}
design_mat <- as.matrix(cbind(rep(1, nrow(X)), X))
colnames(design_mat)[1] <- 'intercept'
return(list('data' = cbind('EP' = original_data$EP, X),
'y' = original_data$EP,
'X' = design_mat,
'variable_means' = variable_means,
'variable_sds' = variable_sds))
} else {
X <- subset(original_data, select = -c(EP))
design_mat <- as.matrix(cbind(rep(1, nrow(X)), X))
colnames(design_mat)[1] <- 'intercept'
return(list('data' = original_data,
'y' = original_data$EP,
'X' = design_mat))
}
}
power_plant <- load_pp_data('scripts/robust_regression/power_plant/power_plant.xlsx')
##### Sampling from full posterior #####
full_posterior <- hmc_sample_BRR(noise_error = 'student_t',
y = power_plant$y,
X = power_plant$X,
C = 1,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
iterations = nsamples_MCF + warmup,
warmup = warmup,
chains = 1,
seed = seed,
output = T)
##### Sampling from sub-posterior C=4 #####
data_split_4 <- split_data(power_plant$data,
y_col_index = 1,
X_col_index = 2:5,
C = 4,
as_dataframe = F)
sub_posteriors_4 <- hmc_base_sampler_BRR(noise_error = 'student_t',
nsamples = nsamples_MCF,
data_split = data_split_4,
C = 4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
warmup = warmup,
seed = seed,
output = T)
# compare_samples_bivariate(sub_posteriors_4, colours = c('red', 'blue', 'green', 'orange'), c(-4,4))
##### Applying other methodologies #####
print('Applying other methodologies')
consensus_mat_4 <- consensus_scott(S = 4, samples_to_combine = sub_posteriors_4, indep = F)
consensus_sca_4 <- consensus_scott(S = 4, samples_to_combine = sub_posteriors_4, indep = T)
neiswanger_true_4 <- neiswanger(S = 4,
samples_to_combine = sub_posteriors_4,
anneal = TRUE)
neiswanger_false_4 <- neiswanger(S = 4,
samples_to_combine = sub_posteriors_4,
anneal = FALSE)
weierstrass_importance_4 <- weierstrass(Samples = sub_posteriors_4,
method = 'importance')
weierstrass_rejection_4 <- weierstrass(Samples = sub_posteriors_4,
method = 'reject')
# ##### Poisson (Hypercube Centre) #####
# print('Poisson Fusion (hypercube centre)')
# Poisson_hc_4 <- bal_binary_fusion_SMC_BRR(N_schedule = rep(nsamples_MCF, 2),
# m_schedule = rep(2, 2),
# time_schedule = rep(time_choice, 2),
# base_samples = sub_posteriors_4,
# L = 3,
# dim = 5,
# data_split = data_split_4,
# nu = nu,
# sigma = sigma,
# prior_means = prior_means,
# prior_variances = prior_variances,
# C = 4,
# precondition = TRUE,
# resampling_method = 'resid',
# ESS_threshold = ESS_threshold,
# cv_location = 'hypercube_centre',
# diffusion_estimator = 'Poisson',
# seed = seed,
# n_cores = n_cores)
# Poisson_hc_4$particles <- resample_particle_y_samples(particle_set = Poisson_hc_4$particles[[1]],
# multivariate = TRUE,
# resampling_method = 'resid',
# seed = seed)
# Poisson_hc_4$proposed_samples <- Poisson_hc_4$proposed_samples[[1]]
# print(integrated_abs_distance(full_posterior, Poisson_hc_4$particles$y_samples))
##### NB (Hypercube Centre) #####
print('NB Fusion (hypercube centre)')
NB_hc_4 <- bal_binary_fusion_SMC_BRR(N_schedule = rep(nsamples_MCF, 2),
m_schedule = rep(2, 2),
time_schedule = rep(time_choice, 2),
base_samples = sub_posteriors_4,
L = 3,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
cv_location = 'hypercube_centre',
diffusion_estimator = 'NB',
seed = seed,
n_cores = n_cores)
NB_hc_4$particles <- resample_particle_y_samples(particle_set = NB_hc_4$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
NB_hc_4$proposed_samples <- NB_hc_4$proposed_samples[[1]]
print(integrated_abs_distance(full_posterior, NB_hc_4$particles$y_samples))
##### Generalised Bayesian Fusion #####
##### all at once #####
GBF_4 <- list('reg' = bal_binary_GBF_BRR(N_schedule = nsamples_GBF,
m_schedule = 4,
time_mesh = NULL,
base_samples = sub_posteriors_4,
L = 2,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
adaptive_mesh = FALSE,
mesh_parameters = list('condition' = 'SH',
'CESS_0_threshold' = CESS_0_threshold,
'CESS_j_threshold' = CESS_j_threshold,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed),
'adaptive' = bal_binary_GBF_BRR(N_schedule = nsamples_GBF,
m_schedule = 4,
time_mesh = NULL,
base_samples = sub_posteriors_4,
L = 2,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
adaptive_mesh = TRUE,
mesh_parameters = list('condition' = 'SH',
'CESS_0_threshold' = CESS_0_threshold,
'CESS_j_threshold' = CESS_j_threshold,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed))
# regular mesh
GBF_4$reg$particles <- resample_particle_y_samples(particle_set = GBF_4$reg$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
print(integrated_abs_distance(full_posterior, GBF_4$reg$particles$y_samples))
compare_samples_bivariate(posteriors = list(full_posterior,
GBF_4$reg$proposed_samples[[1]],
GBF_4$reg$particles$y_samples),
colours = c('black', 'green', 'red'),
common_limit = c(-4, 4))
# adaptive mesh
GBF_4$adaptive$particles <- resample_particle_y_samples(particle_set = GBF_4$adaptive$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
print(integrated_abs_distance(full_posterior, GBF_4$adaptive$particles$y_samples))
compare_samples_bivariate(posteriors = list(full_posterior,
GBF_4$adaptive$proposed_samples[[1]],
GBF_4$adaptive$particles$y_samples),
colours = c('black', 'green', 'red'),
common_limit = c(-4, 4))
##### bal binary combining two sub-posteriors at a time #####
balanced_C4 <- list('reg' = bal_binary_GBF_BRR(N_schedule = rep(nsamples_DCGBF, 2),
m_schedule = rep(2, 2),
time_mesh = NULL,
base_samples = sub_posteriors_4,
L = 3,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
adaptive_mesh = FALSE,
mesh_parameters = list('condition' = 'SH',
'CESS_0_threshold' = CESS_0_threshold,
'CESS_j_threshold' = CESS_j_threshold,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed),
'adaptive' = bal_binary_GBF_BRR(N_schedule = rep(nsamples_DCGBF, 2),
m_schedule = rep(2, 2),
time_mesh = NULL,
base_samples = sub_posteriors_4,
L = 3,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
adaptive_mesh = TRUE,
mesh_parameters = list('condition' = 'SH',
'CESS_0_threshold' = CESS_0_threshold,
'CESS_j_threshold' = CESS_j_threshold,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed))
# regular mesh
balanced_C4$reg$particles <- resample_particle_y_samples(particle_set = balanced_C4$reg$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
balanced_C4$reg$proposed_samples <- balanced_C4$reg$proposed_samples[[1]]
print(integrated_abs_distance(full_posterior, balanced_C4$reg$particles$y_samples))
# adaptive mesh
balanced_C4$adaptive$particles <- resample_particle_y_samples(particle_set = balanced_C4$adaptive$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
balanced_C4$adaptive$proposed_samples <- balanced_C4$adaptive$proposed_samples[[1]]
print(integrated_abs_distance(full_posterior, balanced_C4$adaptive$particles$y_samples))
##### IAD #####
integrated_abs_distance(full_posterior, GBF_4$reg$particles$y_samples)
integrated_abs_distance(full_posterior, GBF_4$adaptive$particles$y_samples)
integrated_abs_distance(full_posterior, balanced_C4$reg$particles$y_samples)
integrated_abs_distance(full_posterior, balanced_C4$adaptive$particles$y_samples)
# integrated_abs_distance(full_posterior, Poisson_hc_4$particles$y_samples)
integrated_abs_distance(full_posterior, NB_hc_4$particles$y_samples)
integrated_abs_distance(full_posterior, consensus_mat_4$samples)
integrated_abs_distance(full_posterior, consensus_sca_4$samples)
integrated_abs_distance(full_posterior, neiswanger_true_4$samples)
integrated_abs_distance(full_posterior, neiswanger_false_4$samples)
integrated_abs_distance(full_posterior, weierstrass_importance_4$samples)
integrated_abs_distance(full_posterior, weierstrass_rejection_4$samples)
save.image('PP4.RData')
rchan26/hierarchicalFusion documentation built on Sept. 11, 2022, 10:30 p.m.
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library(DCFusion)
library(HMCBRR)
library(readxl)
##### Initialise example #####
seed <- 2022
set.seed(seed)
nsamples_MCF <- 100000
nsamples_GBF <- 50000
nsamples_DCGBF <- 10000
warmup <- 10000
time_choice <- 1
nu <- 5
sigma <- 1
prior_means <- rep(0, 5)
prior_variances <- rep(10, 5)
ESS_threshold <- 0.5
CESS_0_threshold <- 0.5
CESS_j_threshold <- 0.05
diffusion_estimator <- 'NB'
n_cores <- parallel::detectCores()
##### Loading in Data #####
# Features consist of hourly average ambient variables
# - Temperature (T) in the range 1.81°C and 37.11°C,
# - Ambient Pressure (AP) in the range 992.89-1033.30 millibar,
# - Relative Humidity (RH) in the range 25.56% to 100.16%
# - Exhaust Vacuum (V) in the range 25.36-81.56 cm Hg
# - Net hourly electrical energy output (EP) 420.26-495.76 MW
load_pp_data <- function(file, standardise_variables = TRUE) {
original_data <- as.data.frame(readxl::read_xlsx(file))
colnames(original_data) <- c('T', 'V', 'AP', 'RH', 'EP')
if (standardise_variables) {
X <- subset(original_data, select = -c(EP))
variable_means <- rep(NA, ncol(X))
variable_sds <- rep(NA, ncol(X))
for (col in 1:ncol(X)) {
variable_means[col] <- mean(X[,col])
variable_sds[col] <- sd(X[,col])
X[,col] <- (X[,col]-variable_means[col])/variable_sds[col]
}
design_mat <- as.matrix(cbind(rep(1, nrow(X)), X))
colnames(design_mat)[1] <- 'intercept'
return(list('data' = cbind('EP' = original_data$EP, X),
'y' = original_data$EP,
'X' = design_mat,
'variable_means' = variable_means,
'variable_sds' = variable_sds))
} else {
X <- subset(original_data, select = -c(EP))
design_mat <- as.matrix(cbind(rep(1, nrow(X)), X))
colnames(design_mat)[1] <- 'intercept'
return(list('data' = original_data,
'y' = original_data$EP,
'X' = design_mat))
}
}
power_plant <- load_pp_data('scripts/robust_regression/power_plant/power_plant.xlsx')
##### Sampling from full posterior #####
full_posterior <- hmc_sample_BRR(noise_error = 'student_t',
y = power_plant$y,
X = power_plant$X,
C = 1,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
iterations = nsamples_MCF + warmup,
warmup = warmup,
chains = 1,
seed = seed,
output = T)
##### Sampling from sub-posterior C=4 #####
data_split_4 <- split_data(power_plant$data,
y_col_index = 1,
X_col_index = 2:5,
C = 4,
as_dataframe = F)
sub_posteriors_4 <- hmc_base_sampler_BRR(noise_error = 'student_t',
nsamples = nsamples_MCF,
data_split = data_split_4,
C = 4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
warmup = warmup,
seed = seed,
output = T)
# compare_samples_bivariate(sub_posteriors_4, colours = c('red', 'blue', 'green', 'orange'), c(-4,4))
##### Applying other methodologies #####
print('Applying other methodologies')
consensus_mat_4 <- consensus_scott(S = 4, samples_to_combine = sub_posteriors_4, indep = F)
consensus_sca_4 <- consensus_scott(S = 4, samples_to_combine = sub_posteriors_4, indep = T)
neiswanger_true_4 <- neiswanger(S = 4,
samples_to_combine = sub_posteriors_4,
anneal = TRUE)
neiswanger_false_4 <- neiswanger(S = 4,
samples_to_combine = sub_posteriors_4,
anneal = FALSE)
weierstrass_importance_4 <- weierstrass(Samples = sub_posteriors_4,
method = 'importance')
weierstrass_rejection_4 <- weierstrass(Samples = sub_posteriors_4,
method = 'reject')
# ##### Poisson (Hypercube Centre) #####
# print('Poisson Fusion (hypercube centre)')
# Poisson_hc_4 <- bal_binary_fusion_SMC_BRR(N_schedule = rep(nsamples_MCF, 2),
# m_schedule = rep(2, 2),
# time_schedule = rep(time_choice, 2),
# base_samples = sub_posteriors_4,
# L = 3,
# dim = 5,
# data_split = data_split_4,
# nu = nu,
# sigma = sigma,
# prior_means = prior_means,
# prior_variances = prior_variances,
# C = 4,
# precondition = TRUE,
# resampling_method = 'resid',
# ESS_threshold = ESS_threshold,
# cv_location = 'hypercube_centre',
# diffusion_estimator = 'Poisson',
# seed = seed,
# n_cores = n_cores)
# Poisson_hc_4$particles <- resample_particle_y_samples(particle_set = Poisson_hc_4$particles[[1]],
# multivariate = TRUE,
# resampling_method = 'resid',
# seed = seed)
# Poisson_hc_4$proposed_samples <- Poisson_hc_4$proposed_samples[[1]]
# print(integrated_abs_distance(full_posterior, Poisson_hc_4$particles$y_samples))
##### NB (Hypercube Centre) #####
print('NB Fusion (hypercube centre)')
NB_hc_4 <- bal_binary_fusion_SMC_BRR(N_schedule = rep(nsamples_MCF, 2),
m_schedule = rep(2, 2),
time_schedule = rep(time_choice, 2),
base_samples = sub_posteriors_4,
L = 3,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
cv_location = 'hypercube_centre',
diffusion_estimator = 'NB',
seed = seed,
n_cores = n_cores)
NB_hc_4$particles <- resample_particle_y_samples(particle_set = NB_hc_4$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
NB_hc_4$proposed_samples <- NB_hc_4$proposed_samples[[1]]
print(integrated_abs_distance(full_posterior, NB_hc_4$particles$y_samples))
##### Generalised Bayesian Fusion #####
##### all at once #####
GBF_4 <- list('reg' = bal_binary_GBF_BRR(N_schedule = nsamples_GBF,
m_schedule = 4,
time_mesh = NULL,
base_samples = sub_posteriors_4,
L = 2,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
adaptive_mesh = FALSE,
mesh_parameters = list('condition' = 'SH',
'CESS_0_threshold' = CESS_0_threshold,
'CESS_j_threshold' = CESS_j_threshold,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed),
'adaptive' = bal_binary_GBF_BRR(N_schedule = nsamples_GBF,
m_schedule = 4,
time_mesh = NULL,
base_samples = sub_posteriors_4,
L = 2,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
adaptive_mesh = TRUE,
mesh_parameters = list('condition' = 'SH',
'CESS_0_threshold' = CESS_0_threshold,
'CESS_j_threshold' = CESS_j_threshold,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed))
# regular mesh
GBF_4$reg$particles <- resample_particle_y_samples(particle_set = GBF_4$reg$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
print(integrated_abs_distance(full_posterior, GBF_4$reg$particles$y_samples))
compare_samples_bivariate(posteriors = list(full_posterior,
GBF_4$reg$proposed_samples[[1]],
GBF_4$reg$particles$y_samples),
colours = c('black', 'green', 'red'),
common_limit = c(-4, 4))
# adaptive mesh
GBF_4$adaptive$particles <- resample_particle_y_samples(particle_set = GBF_4$adaptive$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
print(integrated_abs_distance(full_posterior, GBF_4$adaptive$particles$y_samples))
compare_samples_bivariate(posteriors = list(full_posterior,
GBF_4$adaptive$proposed_samples[[1]],
GBF_4$adaptive$particles$y_samples),
colours = c('black', 'green', 'red'),
common_limit = c(-4, 4))
##### bal binary combining two sub-posteriors at a time #####
balanced_C4 <- list('reg' = bal_binary_GBF_BRR(N_schedule = rep(nsamples_DCGBF, 2),
m_schedule = rep(2, 2),
time_mesh = NULL,
base_samples = sub_posteriors_4,
L = 3,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
adaptive_mesh = FALSE,
mesh_parameters = list('condition' = 'SH',
'CESS_0_threshold' = CESS_0_threshold,
'CESS_j_threshold' = CESS_j_threshold,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed),
'adaptive' = bal_binary_GBF_BRR(N_schedule = rep(nsamples_DCGBF, 2),
m_schedule = rep(2, 2),
time_mesh = NULL,
base_samples = sub_posteriors_4,
L = 3,
dim = 5,
data_split = data_split_4,
nu = nu,
sigma = sigma,
prior_means = prior_means,
prior_variances = prior_variances,
C = 4,
precondition = TRUE,
resampling_method = 'resid',
ESS_threshold = ESS_threshold,
adaptive_mesh = TRUE,
mesh_parameters = list('condition' = 'SH',
'CESS_0_threshold' = CESS_0_threshold,
'CESS_j_threshold' = CESS_j_threshold,
'vanilla' = FALSE),
diffusion_estimator = diffusion_estimator,
seed = seed))
# regular mesh
balanced_C4$reg$particles <- resample_particle_y_samples(particle_set = balanced_C4$reg$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
balanced_C4$reg$proposed_samples <- balanced_C4$reg$proposed_samples[[1]]
print(integrated_abs_distance(full_posterior, balanced_C4$reg$particles$y_samples))
# adaptive mesh
balanced_C4$adaptive$particles <- resample_particle_y_samples(particle_set = balanced_C4$adaptive$particles[[1]],
multivariate = TRUE,
resampling_method = 'resid',
seed = seed)
balanced_C4$adaptive$proposed_samples <- balanced_C4$adaptive$proposed_samples[[1]]
print(integrated_abs_distance(full_posterior, balanced_C4$adaptive$particles$y_samples))
##### IAD #####
integrated_abs_distance(full_posterior, GBF_4$reg$particles$y_samples)
integrated_abs_distance(full_posterior, GBF_4$adaptive$particles$y_samples)
integrated_abs_distance(full_posterior, balanced_C4$reg$particles$y_samples)
integrated_abs_distance(full_posterior, balanced_C4$adaptive$particles$y_samples)
# integrated_abs_distance(full_posterior, Poisson_hc_4$particles$y_samples)
integrated_abs_distance(full_posterior, NB_hc_4$particles$y_samples)
integrated_abs_distance(full_posterior, consensus_mat_4$samples)
integrated_abs_distance(full_posterior, consensus_sca_4$samples)
integrated_abs_distance(full_posterior, neiswanger_true_4$samples)
integrated_abs_distance(full_posterior, neiswanger_false_4$samples)
integrated_abs_distance(full_posterior, weierstrass_importance_4$samples)
integrated_abs_distance(full_posterior, weierstrass_rejection_4$samples)
save.image('PP4.RData')
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