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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843: １３２人目の素数さん [sage] 2025/05/24(土) 08:17:52.86 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)
)
}

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