Classify overall posterior predictive fit from a discrepancy-statistics table

Does NOT classify from a single tail probability. Groups supported statistics into families (marginal, pairwise, profile [complete-profile and resistant-count statistics – both address joint multidrug-resistance burden], hospital_heterogeneity, cluster [admission and patient clustering]) and flags a family when either (a) any statistic in it is SEVERE (ppc_tail_probability < tail_severe or > 1 - tail_severe), or (b) the FRACTION of that family's supported statistics that are extreme exceeds max_fraction_core_extreme. Thresholds are configurable, not universal hardcoded truths, and are applied as discrepancy FLAGS, not frequentist rejection tests.

Usage

compute_posterior_predictive_status(ppc_statistics, thresholds = list())

Arguments

ppc_statistics

Tibble returned by compute_probit_ppc_statistics.

thresholds

Named list overriding any of the defaults: tail_warning = 0.025, tail_severe = 0.005, max_fraction_core_extreme = 0.20. These are INITIAL AMR-PROJECT DEFAULTS, not universal statistical truths – validated only against this package's own synthetic recovery scenarios (test-probit-predictive-synthetic-recovery.R). Expect to recalibrate them once real multi-pathogen experiment results are available; override via this argument rather than editing the defaults in place, so the thresholds actually used for any given run remain visible in $thresholds_used.

Value

List with status (one of "pass", "warning_marginal_ppc", "warning_pairwise_ppc", "warning_profile_ppc", "warning_hospital_heterogeneity_ppc", "warning_cluster_ppc", "fail_major_ppc_misfit", "insufficient_ppc_support"), reasons (character vector of every triggered family-level flag), thresholds_used, and family_status (per-family n/n_extreme/n_severe/fraction_extreme).

Details

Statistics with essentially ZERO posterior-predictive variance (replicated_sd at or near 0 – e.g. a discrete statistic that lands on the same value in every replicated state, such as max(resistant_count) pinned at its ceiling for a small class panel) are excluded from extreme/severe classification (though still returned in ppc_statistics with their true, unmodified ppc_tail_probability): mean(T_rep >= T_obs) is exactly 1 whenever every replicate exactly EQUALS the observed value, which is a well-known degeneracy of posterior-predictive tail probabilities for near-constant discrete statistics, not evidence of misfit – a discrepancy statistic that cannot vary under the posterior predictive distribution carries no discriminating information about model fit.