Posterior Predictive Diagnostic Statistics

Computes a suite of predictive discrepancy statistics that quantify how well the posterior predictive distribution \(p(y^{rep} \mid y)\) matches the observed data \(y\). All statistics are scalar summaries derived from the \(S \times n\) replicated data matrix.

Usage

ppc_diagnostics(y_obs, y_rep, credible_mass = 0.95)

Arguments

y_obs

Numeric vector of length \(n\) containing the observed outcomes.

y_rep

Numeric matrix of dimension \(S \times n\) where each row is one posterior predictive replicate (e.g. the output of simulate_ppc()).

credible_mass

Numeric scalar in \((0, 1)\) specifying the credible interval mass used for the coverage calculation. Defaults to 0.95.

Value

An object of class "ppc_diagnostics" (a named list) with the following elements:

mean_diff

Difference between the mean of the replicated means and the observed mean: \(\bar{\mu}_{rep} - \bar{y}\).

var_diff

Difference between the mean of the replicated variances and the observed variance: \(\bar{v}_{rep} - \mathrm{Var}(y)\).

bayesian_p_value

Proportion of draws for which the replicated mean exceeds the observed mean. Values near 0.5 indicate good calibration.

rmse

Root mean squared error between the column-wise predictive means and the observed values: \(\sqrt{n^{-1}\sum_i (\bar{y}^{rep}_i - y_i)^2}\).

coverage

Proportion of observations whose value falls inside the credible_mass posterior predictive interval.

n_draws

Number of posterior draws \(S\).

n_obs

Number of observations \(n\).

credible_mass

The credible mass used for the coverage calculation.

See also

simulate_ppc(), plot_ppc_overlay()

Other ppc-workflow: compare_models_ppc(), plot_ppc_overlay(), plot_ppc_stat(), print.ppc_diagnostics(), simulate_ppc(), theme_ppc()

Examples

set.seed(1)
y     <- rnorm(50, mean = 2, sd = 1)
draws <- matrix(rnorm(200 * 50, mean = 2), nrow = 200, ncol = 50)
y_rep <- simulate_ppc(draws)
diag  <- ppc_diagnostics(y, y_rep)
print(diag)
#> 
#> -- Posterior Predictive Diagnostics (predictCheckR) --
#> 
#>   Draws  : 200
#>   Obs    : 50
#> 
#>   Discrepancy Statistics:
#>     Mean difference        : -0.1107
#>     Variance difference    : 1.353
#>     Bayesian p-value       : 0.28
#>     RMSE (pred vs. obs)    : 0.8518
#>     Coverage (95% CI)      : 1
#>