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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823: １３２人目の素数さん [sage] 2025/05/02(金) 11:02:18.75 ID:+8QO9mMm

set.seed(123)
library(fmsb)

alpha <- 0.05
N <- 1000

# Simulation function
sim <- function() {
# Random group sizes
n1 <- sample(250:350, 1)     # Low-dose
n2 <- sample(250:350, 1)     # High-dose
n3 <- N - n1 - n2            # Placebo
if (n3 < 100) return(NULL)   # Skip too-small placebo

# Success rates from uniform distribution
p1 <- runif(1)
p2 <- runif(1)
p3 <- runif(1)

# Binomial draws
x1 <- rbinom(1, n1, p1)
x2 <- rbinom(1, n2, p2)
x3 <- rbinom(1, n3, p3)

# 3-group matrix
m3 <- rbind(success = c(x1, x2, x3),
failure = c(n1 - x1, n2 - x2, n3 - x3))
colnames(m3) <- c("Low", "High", "Placebo")

# Add 4th group = combined (low + high)
x4 <- x1 + x2
n4 <- n1 + n2
m4 <- cbind(m3, Combined = c(x4, n4 - x4))

# Perform pairwise Fisher's exact tests across 4 groups
pw <- suppressWarnings(pairwise.fisher.test(m4[1,], colSums(m4), p.adj="bonf")$p.value)
pw_vals <- as.vector(pw)
pw_vals <- pw_vals[!is.na(pw_vals)]
names_all <- names(pw_vals)

# Identify significant pairs
sig_idx <- which(pw_vals < alpha)
sig_names <- names(pw_vals)[sig_idx]

# Check if only Combined vs Placebo is significant
is_valid <- length(sig_idx) == 1 &&
any(grepl("Placebo-Combined|Combined-Placebo", sig_names))

if (is_valid) {
return(list(m = m4, probs = c(p1, p2, p3), sizes = c(n1, n2, n3), pvals = pw))
} else {
return(NULL)
}
}

# Run until condition met
res <- NULL
while (is.null(res)) {
res <- sim()
}

# Output results
print(res$m)
cat("Success probabilities (Low, High, Placebo):", round(res$probs, 3), "\n")
cat("Sample sizes (Low, High, Placebo):", res$sizes, "\n")
cat("Pairwise Bonferroni-adjusted p-values:\n")
print(res$pvals)

http://rio2016.5ch.net/test/read.cgi/math/1723152147/823

845: １３２人目の素数さん [sage] 2025/05/24(土) 08:37:05.75 ID:VetM3rz7

library(rjags)

# Fit a Bayesian logistic regression model using JAGS and return predictions and posterior summaries
fit_bayesian_logistic_jags <- function(data, formula, newdata,
n.chains = 3, n.iter = 5000, n.burnin = 1000) {
# Extract response variable name from the formula
response_var <- all.vars(formula)[1]
y <- data[[response_var]]

# Convert factor response to binary numeric (0/1)
if (is.factor(y)) y <- as.numeric(y) - 1
y <- as.numeric(y)

# Construct design matrices for training and new data
X <- model.matrix(formula, data)
new_X <- model.matrix(delete.response(terms(formula)), newdata)

# Prepare data list for JAGS
jags_data <- list(
y = y,
X = X,
n = nrow(X),
p = ncol(X),
new_X = new_X,
scale_beta = rep(2.5, ncol(X))  # Prior scale for each coefficient
)

# Define the JAGS model
model_string <- "
model {
for (j in 1:p) {
beta[j] ~ dt(0, 1 / pow(scale_beta[j], 2), 1)
}

for (i in 1:n) {
logit_p[i] <- inprod(X[i,], beta[])
y[i] ~ dbern(1 / (1 + exp(-logit_p[i])))
}

new_logit <- inprod(new_X[1,], beta[])
new_p <- 1 / (1 + exp(-new_logit))
}
"

# Initialize and run the JAGS model
model <- jags.model(textConnection(model_string), data = jags_data,
n.chains = n.chains, quiet = TRUE)
update(model, n.burnin)

# Draw posterior samples
samples <- coda.samples(model, c("beta", "new_p"), n.iter - n.burnin)
mat <- as.matrix(samples)

# Return results
list(
model = samples,
predicted_prob = mean(mat[, "new_p"]),
summary = summary(samples)
)
}

http://rio2016.5ch.net/test/read.cgi/math/1723152147/845

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