 Posterior equality for proportional likelihoods

If every model's likelihood is multiplied by the same positive factor independent of its parameter or model index, Bayes theorem cancels that factor from the normalized posterior. Fixed-count Bernoulli sampling and sampling stopped at a specified positive head count give such proportional likelihoods for the same total heads and tails. This conclusion uses their actual sampling likelihoods; it is not a claim that every selection or stopping rule can be ignored.