Normal with SD 1

HOBBS form: x(i) ~ normal_sd1(mean);

The package test file performs:

normal_sd1 recovers its mean
normal_sd1 gives the correct normal posterior
normal_sd1 matches Stan and JAGS

Same model in HOBBS, Stan, and JAGS

param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) ~ normal_sd1(mu(1));
}

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

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

Run this test

From the documentation project itself:

library(hobbs)
library(testthat)
source("validation/source/tests/testthat/helper-distributions.R")
testthat::test_file("validation/source/tests/testthat/test-dist-normal-sd1.R")

From the HOBBS package source tree, the normal package test workflow is simpler:

devtools::test(filter = "dist-normal-sd1")

Download the test file · helper-distributions.R

Complete test file

test_that("normal_sd1 recovers its mean", {
  set.seed(103); truth <- 0.6; y <- rnorm(60, truth, 1)
  model <- 'param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) ~ normal_sd1(mu(1));
}'
  d <- hobbs_test_draws(model, list(y = y)); expect_posterior_near(d, "mu[1]", truth, 0.25)
})

test_that("normal_sd1 gives the correct normal posterior", {
  set.seed(103)
  truth <- 0.6
  sigma <- 1
  prior_sd <- 3
  n <- 60
  y <- rnorm(n, truth, sigma)

  model <- 'param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) ~ normal_sd1(mu(1));
}'

  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$`mu[1]`), posterior_mean, tolerance = 0.03)
  expect_equal(sd(d$`mu[1]`), posterior_sd, tolerance = 0.02)
})

test_that("normal_sd1 matches Stan and JAGS", {
  skip_if_reference_samplers_missing()
  set.seed(103)
  truth <- 0.6
  y <- rnorm(60, truth, 1)
  n <- length(y)

  hobbs_model <- 'param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) ~ normal_sd1(mu(1));
}'

  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]")
})