高校数学の質問スレ（医者・東大卒専用） Part438

高校数学の質問スレ（医者・東大卒専用） Part438 (979ﾚｽ)
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793: １３２人目の素数さん [sage] 2025/04/18(金) 12:53:56.52 ID:XpMQ9r6R

# Required package
library(HDInterval)

# Function to estimate alpha and beta of a Beta distribution
# from given HPI [L, U] and mean m
estimate_beta_params_from_HPI <- function(L, U, m, conf = 0.95, verbose = TRUE) {
# Initial guesses for alpha and beta
alpha0 <- m * 10
beta0 <- (1 - m) * 10

# Objective function: minimize error between estimated HPI/mean and given values
objective_fn <- function(par) {
a <- par[1]
b <- par[2]
if (a <= 0 || b <= 0) return(Inf)
hpi <- hdi(qbeta, shape1 = a, shape2 = b, credMass = conf)
est_mean <- a / (a + b)
hpi_error <- (hpi[1] - L)^2 + (hpi[2] - U)^2
mean_error <- (est_mean - m)^2
return(hpi_error + mean_error * 10)  # Penalize deviation in mean
}

# Optimization
res <- optim(c(alpha0, beta0), objective_fn, method = "L-BFGS-B",
lower = c(0.001, 0.001))

alpha_hat <- res$par[1]
beta_hat <- res$par[2]

# Validate result
estimated_mean <- alpha_hat / (alpha_hat + beta_hat)
estimated_hpi <- hdi(qbeta, shape1 = alpha_hat, shape2 = beta_hat, credMass = conf)

if (verbose) {
cat("---- Result ----\n")
cat(sprintf("Estimated alpha: %.4f\n", alpha_hat))
cat(sprintf("Estimated beta : %.4f\n", beta_hat))
cat(sprintf("→ Mean         : %.4f (target: %.4f)\n", estimated_mean, m))
cat(sprintf("→ %.0f%% HPI     : [%.4f, %.4f] (target: [%.4f, %.4f])\n",
conf * 100, estimated_hpi[1], estimated_hpi[2], L, U))
}

return(list(alpha = alpha_hat,
beta = beta_hat,
mean = estimated_mean,
hpi = estimated_hpi))
}

# --- Example usage ---

# Suppose we are given:
# - Mean = 0.6
# - 95% HPI = [0.45, 0.75]
result <- estimate_beta_params_from_HPI(L = 0.45, U = 0.75, m = 0.6)

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