Exact discrete conflict p-value for a two-arm binomial target

The discrete counterpart of egidi_normal_conflict_pvalue(): the total prior-predictive probability of every pair of response counts whose probability is at or below that of the observed pair.

Usage

egidi_binomial_conflict_pvalue(
  table_informative,
  table_weak,
  psi,
  y_control,
  y_treatment,
  tolerance = 1e-09
)

Arguments

table_informative, table_weak

Component tables from binomial_rmp_predictive_tables().

psi

Weight on the weak component, one value.

y_control, y_treatment

Observed responder counts.

tolerance

Relative tolerance used when comparing probabilities.

Value

The conflict p-value.

Details

Ties are possible on a finite sample space and matter, because a cell excluded by a rounding difference removes its whole probability from the sum rather than an infinitesimal amount. The comparison therefore carries a relative tolerance.