Using priorsense with Stan

library(cmdstanr)
library(posterior)
library(priorsense)

priorsense is compatible with models fit with either rstan and cmdstanr. To use priorsense with a Stan model, the log prior and log likelihood evaluations should be added to the model code.

Consider the univariate normal model with unknown mu and sigma available viaexample_powerscale_model("univariate_normal"). In Stan, lprior and log_lik variables can be defined as below. By also defining separate lprior_mu and lprior_sigma variables, it will be possible to check the sensitivity for each prior separately.

model <- example_powerscale_model("univariate_normal")

data {
  int<lower=1> N;
  array[N] real y;
}
parameters {
  real mu;
  real<lower=0> sigma;
}
transformed parameters {
  real lprior; // joint prior
  real lprior_mu = normal_lpdf(mu | 0, 1); // marginal prior density for mu
  real lprior_sigma = normal_lpdf(sigma | 0, 2.5); // marginal prior density for sigma
  lprior = lprior_mu + lprior_sigma;
}
model {
  // priors
  target += lprior;
  // likelihood
  target += normal_lpdf(y | mu, sigma);
}
generated quantities {
  vector[N] log_lik;
  // likelihood
  for (n in 1:N) log_lik[n] = normal_lpdf(y[n] | mu, sigma);
}

We first fit the model using Stan:

fit <- rstan::stan(
  model_code = model$model_code,
  data = model$data,
  refresh = FALSE,
  seed = 123
)

Then the priorsense functions will work as usual.

powerscale_sensitivity(fit)

Sensitivity based on cjs_dist
Prior selection: all priors
Likelihood selection: all data

 variable prior likelihood                           diagnosis
       mu 0.433      0.641 potential prior-likelihood conflict
    sigma 0.359      0.674 potential prior-likelihood conflict

powerscale_sensitivity(fit, prior_selection = "sigma")

Sensitivity based on cjs_dist
Prior selection: sigma
Likelihood selection: all data

 variable prior likelihood diagnosis
       mu 0.006      0.641         -
    sigma 0.010      0.674         -

powerscale_sensitivity(fit, prior_selection = "mu")

Sensitivity based on cjs_dist
Prior selection: mu
Likelihood selection: all data

 variable prior likelihood                           diagnosis
       mu 0.438      0.641 potential prior-likelihood conflict
    sigma 0.369      0.674 potential prior-likelihood conflict

powerscale_plot_dens(fit)

In some cases, setting moment_match = TRUE will improve unreliable estimates at the cost of some further computation. This requires the iwmm package.