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Power-scaling prior / likelihood sensitivity

Source: R/priorsense.R
tulpa_powerscale_sensitivity.Rd

Local power-scaling sensitivity (Kallioinen et al. 2024): how much each fixed-effect posterior moves when the prior or the likelihood is raised to a power alpha near 1. The existing draws are importance-reweighted by exp((alpha - 1) * log_component) (PSIS-smoothed via tulpa_psis(); no refits), and the sensitivity is the gradient of the cumulative Jensen-Shannon distance between the base and power-scaled posteriors with respect to log2(alpha).

Values above threshold flag sensitivity. High on both the prior and likelihood components indicates potential prior-data conflict; high prior with low likelihood indicates a strong prior / weak likelihood.

When the fit recorded per-draw hyperparameter log-prior values at draw-synthesis time ($hyper_log_prior_draws, stored by the nested-Laplace mixture paths such as tulpa_re_cov_nested() and the tulpa() random-slope redirect), a hyperparameter column reports the power-scaling sensitivity of the hyperparameter prior by the same reweighting; NA otherwise.

Usage

tulpa_powerscale_sensitivity(
  fit,
  data,
  prior = NULL,
  lower_alpha = 0.99,
  upper_alpha = 1.01,
  threshold = 0.05
)

Arguments

fit

A tulpa_fit fitted through tulpa() (fixed-effect / GLMM; spatial / temporal-field fits are rejected).

data

The data frame the model was fit to.

prior

The Gaussian fixed-effect prior the fit used, as list(mean =, sd =) (scalars recycled). Required for the prior component; omit to compute the likelihood component only.

lower_alpha, upper_alpha

Power-scaling grid endpoints for the gradient (defaults 0.99 / 1.01, as in priorsense).

threshold

Sensitivity flag threshold (default 0.05).

Value

A data frame with one row per fixed-effect parameter and columns variable, prior, hyperparameter, likelihood, diagnosis.

References

Kallioinen, Paananen, Buerkner & Vehtari (2024). Detecting and diagnosing prior and likelihood sensitivity with power-scaling. Statistics and Computing 34:57. Nguyen & Vreeken (2015). Non-parametric Jensen-Shannon divergence. ECML PKDD.

See also

tulpa_psis(), tulpa_criteria().

Examples

# \donttest{
set.seed(1)
d <- data.frame(x = rnorm(150))
d$y <- rpois(150, exp(0.5 + 0.7 * d$x))
fit <- tulpa(y ~ x, data = d, family = "poisson", mode = "laplace",
             beta_prior = list(mean = 0, sd = 5))
tulpa_powerscale_sensitivity(fit, data = d, prior = list(mean = 0, sd = 5))
# }