Dynamic survival bias in optimal stopping problems

This paper studies the optimal inference from observing an ongoing experiment. An experimenter sequentially chooses whether to continue with costly trials that yield random payoffs. The experimenter sees the full history of the trial results, while an outside observer sees only the recent trial results, not the earlier prehistory. I contrast the optimal sophisticated posterior of the observer based on a full Bayesian inference that accounts for the prehistory and the naive posterior based solely on the observed history. The resulting dynamic bias grows with longer prehistory if we see enough early successes. Observing more failures may increase the sophisticated posterior if they come early. Revealing a success (failure) in the prehistory always increases (lowers) the sophisticated posterior. Uncovering a more recent signal leads to a larger change than an older one. Seeing a future failure may increase the sophisticated posterior.