Half-normal

HOBBS form: x(i) ~ dhalfnorm(sd);

The package test file performs:

dhalfnorm recovers its scale
dhalfnorm gives the correct posterior for its scale
dhalfnorm matches Stan and JAGS

Same model in HOBBS, Stan, and JAGS

param log_sd(1);
block log_sd(1) {
log_sd(1) ~ dnorm(0, 2);
for (i = 1:n) y(i) ~ dhalfnorm(exp(log_sd(1)));
}

data {
  int<lower=1> n;
  vector<lower=0>[n] y;
}
parameters {
  vector[1] log_sd;
}
model {
  log_sd[1] ~ normal(0, 2);
  y ~ normal(0, exp(log_sd[1]));
}

model {
  log_sd[1] ~ dnorm(0, 0.25)
  tau <- exp(-2 * log_sd[1])
  for (i in 1:n) { y[i] ~ dnorm(0, 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-halfnormal.R")

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

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

Download the test file · helper-distributions.R

Complete test file

test_that("dhalfnorm recovers its scale", {
  set.seed(117); truth <- 1.3; y <- r_halfnormal(80, truth)
  model <- 'param log_sd(1);
block log_sd(1) {
log_sd(1) ~ dnorm(0, 2);
for (i = 1:n) y(i) ~ dhalfnorm(exp(log_sd(1)));
}'
  d <- hobbs_test_draws(model, list(y = y)); testthat::expect_equal(exp(mean(d[, "log_sd[1]"])), truth, tolerance = 0.28)
})

test_that("dhalfnorm gives the correct posterior for its scale", {
  set.seed(117)
  truth <- 1.3
  y <- r_halfnormal(80, truth)

  model <- 'param log_sd(1);
block log_sd(1) {
log_sd(1) ~ dnorm(0, 2);
for (i = 1:n) y(i) ~ dhalfnorm(exp(log_sd(1)));
}'

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

  log_posterior <- function(log_sd) {
    sigma <- exp(log_sd)
    # The half-normal factor of 2 is constant in sigma and cancels.
    dnorm(log_sd, 0, 2, log = TRUE) +
      sum(dnorm(y, 0, sigma, log = TRUE))
  }

  expect_numerical_posterior(
    d, "log_sd[1]", log_posterior,
    lower = -2, upper = 2.5,
    mean_tolerance = 0.04
  )
})

test_that("dhalfnorm matches Stan and JAGS", {
  skip_if_reference_samplers_missing()
  set.seed(117)
  truth <- 1.3
  y <- r_halfnormal(80, truth)
  n <- length(y)

  hobbs_model <- 'param log_sd(1);
block log_sd(1) {
log_sd(1) ~ dnorm(0, 2);
for (i = 1:n) y(i) ~ dhalfnorm(exp(log_sd(1)));
}'

  stan_model <- '
data {
  int<lower=1> n;
  vector<lower=0>[n] y;
}
parameters {
  vector[1] log_sd;
}
model {
  log_sd[1] ~ normal(0, 2);
  y ~ normal(0, exp(log_sd[1]));
}'

  jags_model <- '
model {
  log_sd[1] ~ dnorm(0, 0.25)
  tau <- exp(-2 * log_sd[1])
  for (i in 1:n) { y[i] ~ dnorm(0, tau) }
}'

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

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