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.

本文研究了观察正在进行的实验的最佳推理。实验者依次选择是否继续进行产生随机收益的代价高昂的试验。实验者可以看到试验结果的完整历史，而外部观察者只能看到最近的试验结果，而不是更早的史前史。我比较了基于完整贝叶斯推理的观察者的最佳复杂后验，该推理解释了史前和仅基于观察到的历史的朴素后验。如果我们看到足够多的早期成功，那么由此产生的动态偏差会随着史前历史的延长而增长。如果它们来得早，观察更多的失败可能会增加复杂的后验。揭示史前时代的成功（失败）总是会增加（降低）复杂的后验。发现更新的信号会导致比旧信号更大的变化。看到未来的失败可能会增加复杂的后验。