Normal

HOBBS form: x(i) ~ dnorm(mean, sd);

The package test file performs:

• dnorm recovers a normal location
• dnorm gives the correct normal posterior
• dnorm matches Stan and JAGS

Same model in HOBBS, Stan, and JAGS

HOBBS

param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) ~ dnorm(mu(1), 1.1);
}

Stan

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

JAGS

model {
  mu[1] ~ dnorm(0, 0.1111111111111111)
  tau <- 1 / pow(sigma, 2)
  for (i in 1:n) { y[i] ~ dnorm(mu[1], tau) }
}

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.R")

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

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

Download the test file · helper-distributions.R

Complete test file

test_that("dnorm recovers a normal location", {
  set.seed(101); truth <- 0.7; y <- rnorm(60, truth, 1.1)
  model <- 'param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) ~ dnorm(mu(1), 1.1);
}'
  d <- hobbs_test_draws(model, list(y = y)); expect_posterior_near(d, "mu[1]", truth, 0.28)
})

test_that("dnorm gives the correct normal posterior", {
    set.seed(101)
    
    truth <- 0.7
    sigma <- 1.1
    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) ~ dnorm(mu(1), 1.1);
  }
  '
    
    d <- hobbs_test_draws(model, list(y = y))
    
    # Exact conjugate posterior
    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("dnorm matches Stan and JAGS", {
  skip_if_reference_samplers_missing()
  set.seed(101)
  truth <- 0.7
  sigma <- 1.1
  y <- rnorm(60, truth, sigma)
  n <- length(y)

  hobbs_model <- 'param mu(1);
block mu(1) {
mu(1) ~ dnorm(0, 3);
for (i = 1:n) y(i) ~ dnorm(mu(1), 1.1);
}'

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

  jags_model <- '
model {
  mu[1] ~ dnorm(0, 0.1111111111111111)
  tau <- 1 / pow(sigma, 2)
  for (i in 1:n) { y[i] ~ dnorm(mu[1], tau) }
}'

  data <- list(n = n, y = y, sigma = sigma)
  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]")
})