Continuous Learning from Data: No Multiplicities from Computing and Using Bayesian Posterior Probabilities as Often as Desired

(In a Bayesian analysis) It is entirely appropriate to collect data until a point has been proven or disproven, or until the data collector runs out of time, money, or patience. Edwards, Lindman, Savage (1963) Introduction Bayesian inference, which follows the likelihood principle, is not affected by the experimental design or intentions of the investigator. P-values can only be computed if both of these are known, and as been described by Berry (1987) and others, it is almost never the case that the computation of the p-value at the end of a study takes into account all the changes in design that were necessitated when pure experimental designs encounter the real world.