test_that("normal01 recovers a location through standardized residuals", {
  set.seed(102); truth <- -0.55; y <- rnorm(120, truth, 1)
  model <- 'param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) - mu(1) ~ normal01();
}'
  d <- hobbs_test_draws(model, list(y = y)); expect_posterior_near(d, "mu[1]", truth, 0.25)
})

test_that("normal01 gives the correct normal posterior", {
  set.seed(102)
  truth <- -0.55
  sigma <- 1
  prior_sd <- 3
  n <- 120
  y <- rnorm(n, truth, sigma)

  model <- 'param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) - mu(1) ~ normal01();
}'

  d <- hobbs_test_draws(model, list(y = y))

  posterior_var <- 1 / (1 / prior_sd^2 + n / sigma^2)
  posterior_mean <- posterior_var * sum(y) / sigma^2
  posterior_sd <- sqrt(posterior_var)

  expect_equal(mean(d$`mu[1]`), posterior_mean, tolerance = 0.025)
  expect_lt(abs(sd(d$`mu[1]`) - posterior_sd), 0.015)
})

test_that("normal01 matches Stan and JAGS", {
  skip_if_reference_samplers_missing()
  set.seed(102)
  truth <- -0.55
  y <- rnorm(120, truth, 1)
  n <- length(y)

  hobbs_model <- 'param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) - mu(1) ~ normal01();
}'

  stan_model <- '
data {
  int<lower=1> n;
  vector[n] y;
}
parameters {
  vector[1] mu;
}
model {
  mu[1] ~ normal(0, 3);
  y ~ normal(mu[1], 1);
}'

  jags_model <- '
model {
  mu[1] ~ dnorm(0, 0.1111111111111111)
  for (i in 1:n) { y[i] ~ dnorm(mu[1], 1) }
}'

  data <- list(n = n, y = y)
  d_hobbs <- hobbs_test_draws(hobbs_model, list(y = y))
  d_stan <- stan_test_draws(stan_model, data, "mu")
  d_jags <- jags_test_draws(jags_model, data, "mu")

  expect_posterior_matches_reference(d_hobbs, d_stan, d_jags, "mu[1]")
})