priorsense provides tools for prior diagnostics and sensitivity analysis.
It currently includes functions for performing power-scaling sensitivity analysis on Stan models. This is a way to check how sensitive a posterior is to perturbations of the prior and likelihood and diagnose the cause of sensitivity. For efficient computation, power-scaling sensitivity analysis relies on Pareto smoothed importance sampling (Vehtari et al., 2021) and importance weighted moment matching (Paananen et al., 2021).
Power-scaling sensitivity analysis and priorsense are described in Kallioinen et al. (2022).
Download the development version from GitHub with:
# install.packages("remotes")
remotes::install_github("n-kall/priorsense")
priorsense currently works with models created with rstan, cmdstanr or brms. However, moment matching currently does not work with cmdstan models.
Consider a simple univariate model with unknown mu and sigma fit to some data y (available viaexample_powerscale_model("univariate_normal")
):
data {
int<lower=1> N;
real y[N];
}
parameters {
real mu;
real<lower=0> sigma;
}
model {
// priors
target += normal_lpdf(mu | 0, 1);
target += normal_lpdf(sigma | 0, 2.5);
// likelihood
target += normal_lpdf(y | mu, sigma);
}
generated quantities {
vector[N] log_lik;
// likelihood
real log_prior;
for (n in 1:N) log_lik[n] = normal_lpdf(y[n] | mu, sigma);
// joint prior specification
log_prior = normal_lpdf(mu | 0, 1) +
normal_lpdf(sigma | 0, 2.5);
}
We first fit the model using Stan:
library(priorsense)
normal_model <- example_powerscale_model("univariate_normal")
fit <- rstan::stan(
model_code = normal_model$model_code,
data = normal_model$data,
refresh = FALSE,
seed = 1234
)
Once fit, sensitivity can be checked as follows:
powerscale_sensitivity(fit)
#> Sensitivity based on cjs_dist:
#> # A tibble: 2 × 4
#> variable prior likelihood diagnosis
#> <chr> <dbl> <dbl> <chr>
#> 1 mu 0.368 0.519 prior-data conflict
#> 2 sigma 0.266 0.512 prior-data conflict
To visually inspect changes to the posterior, first create a power-scaling sequence.
pss <- powerscale_sequence(fit)
#> Warning: Some Pareto k diagnostic values are slightly high. See help('pareto-k-diagnostic') for details.
Then use a plotting function. Estimates that may be inaccurate (Pareto-k values > 0.5) are indicated.
powerscale_plot_ecdf(pss, variables = c("mu", "sigma"))
powerscale_plot_quantities(
pss,
quantities = c("mean", "sd"),
div_measure = "cjs_dist",
variables = c("mu", "sigma")
)
Noa Kallioinen, Topi Paananen, Paul-Christian Bürkner, Aki Vehtari (2022). Detecting and diagnosing prior and likelihood sensitivity with power-scaling. preprint arXiv:2107.14054
Topi Paananen, Juho Piironen, Paul-Christian Bürkner, Aki Vehtari (2021). Implicitly adaptive importance sampling. Statistics and Computing 31, 16. https://doi.org/10.1007/s11222-020-09982-2
Aki Vehtari, Daniel Simpson, Andrew Gelman, Yuling Yao, Jonah Gabry (2021). Pareto smoothed importance sampling. preprint arXiv:1507.02646