library(tidyverse)

source("assets/01_common.R")

set.seed(2002)
# Experts
N <- 2
# Observations
T <- 2^5
# Size of probability grid
P <- 999
prob_grid <- 1:P / (P + 1)

# Realized observations
y <- rnorm(T)

# Deviation of the experts
dev <- c(-1, 3)
experts_sd <- c(1, sqrt(4))

# Expert predictions
experts <- array(dim = c(P, N))

seq(-5, 10, length.out = P) -> x_grid

experts[, 1] <- qnorm(prob_grid, mean = dev[1], sd = experts_sd[1])
experts[, 2] <- qnorm(prob_grid, mean = dev[2], sd = experts_sd[2])

experts <- rbind(c(rep(min(experts), N)), experts)
experts <- rbind(experts, c(rep(max(experts), N)))
prob_grid <- c(0, prob_grid, 1)

naive <- 1

df <- data.frame(
  x = rep(prob_grid, each = N),
  y = c(t(experts)),
  expert = rep(1:N, (P + 2)),
  naive = rep(naive, (P + 2) * N)
)

naive <- seq(0, 1, length.out = 11)

dfs <- list()

df_old <- df

for (i in seq_along(naive)) {
  df_old$naive <- naive[i]

  df_new <- data.frame(
    x = prob_grid,
    y = (experts[, 1] * (naive[i] * (0.5) + (1 - naive[i]) * (1 - prob_grid)) + (naive[i] * 0.5 + (1 - naive[i]) * (prob_grid)) * experts[, 2]),
    expert = 3,
    naive = rep(naive[i], (P + 2))
  )

  dfs[[i + 1]] <- bind_rows(df_old, df_new)
}

dfs <- reduce(dfs, bind_rows)

colnames(dfs) <- c("y", "x", "b", "mu")

dfs %>%
  ggplot(aes(x = x, y = y, color = factor(b))) +
  geom_line() +
  labs(
    title = "Expert Predictions",
    x = "Probability Grid",
    y = "Predicted Value"
  ) +
  theme_minimal() +
  scale_color_brewer(palette = "Set1") +
  theme(legend.position = "top") +
  facet_wrap(. ~ mu, ncol = 3)

write_csv(dfs, "assets/crps_learning/weights_plot/cdf_data.csv")