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Power-Scale Prior Sensitivity Diagnostics for Fitted HBMs

Source: R/prior-sensitivity.R
prior_sensitivity.Rd

Computes prior and likelihood power-scaling sensitivity diagnostics for a fitted hbmfit model using the priorsense package. Useful for assessing whether posterior conclusions are driven by the prior or the data – a critical step in any principled Bayesian SAE workflow.

Usage

prior_sensitivity(model, ...)

Arguments

model

An hbmfit object returned by hbm (or one of its wrappers) or a brmsfit object directly.

...

Additional arguments forwarded to priorsense::powerscale_sensitivity(), e.g.\ variable = c("b_x1", "sd_regency__Intercept") to restrict the report to specific parameters.

Value

A powerscale_sensitivity_summary object (data frame) with one row per monitored parameter and columns variable, prior, likelihood, diagnosis. NULL (with a message) when the priorsense package is not installed.

Details

Prior sensitivity analysis answers the question: “If I had used a slightly different prior, would the substantive conclusions change?”. The power-scaling approach of Kallioinen et al.\ (2023) detects:

  • Prior–likelihood conflict: the posterior moves non-negligibly when the prior is up- or down-weighted. Often indicates an overly informative or misspecified prior.

  • Weak likelihood: the posterior is dominated by the prior. Common in SAE for areas with few sampled units.

Reported diagnostics include the Kullback–Leibler divergence between the original posterior and the power-scaled posterior (prior, likelihood) and a categorical flag (prior-data conflict, strong prior, -).

Computational cost. No re-sampling is required: importance sampling reuses the existing posterior draws. Hence a typical run costs only a few seconds even for large hierarchical models.

When to run prior sensitivity

Always. Specifically:

  • After every model fit, before drawing substantive conclusions.

  • Whenever convergence diagnostics from convergence_check() are clean but the posterior seems implausibly narrow or implausibly wide.

  • When comparing models with shrinkage priors – horseshoe and R2D2 are both informative, and small differences in their hyperparameters can move estimates noticeably.

References

Kallioinen, N., Paananen, T., Burkner, P.-C., & Vehtari, A.\ (2024). Detecting and diagnosing prior and likelihood sensitivity with power-scaling. Statistics and Computing, 34, 57. doi:10.1007/s11222-023-10366-5

See also

prior_check, convergence_check, model_compare

Examples

# \donttest{
if (requireNamespace("priorsense", quietly = TRUE)) {
  data("data_fhnorm")
  fit <- hbm(brms::bf(y ~ x1 + x2),
             data = data_fhnorm, re = ~(1 | regency),
             chains = 4, iter = 2000, refresh = 0)
  ps  <- prior_sensitivity(fit)
  print(ps)
}
#> Compiling Stan program...
#> Error in .fun(model_code = .x1): Boost not found; call install.packages('BH')
# }