A rational analysis of confirmation with deterministic hypotheses

摘要: A Rational Analysis of Confirmation with Deterministic Hypotheses Joseph L. Austerweil (Joseph.Austerweil@gmail.com) Thomas Griffiths (Tom Griffiths@berkeley.edu) Department Psychology, University California, Berkeley, CA 94720-1650 USA Abstract Whether scientists test their hypotheses as they ought to has in- terested both cognitive psychologists and philosophers sci- ence. Classic analyses hypothesis testing assume that peo- ple should pick the largest probability falsi- fying current hypothesis, while experiments have shown people tend select tests consistent hypothesis. Using two different normative standards, we prove seek- ing evidence predicted by your is optimal when in question are deterministic other reasonable assumptions hold. We this account using a sequential prediction task, which guess next number sequence. Experiment 1 shows people’s predictions can be captured simple Bayesian model. 2 manipulates beliefs about probabilities hypotheses, con- firm whichever led believe most likely. Keywords: confirmation bias; rational analysis; testing; inference. How scientist seek help her find explains phenomenon? Does differ from how do evidence? Popper (1935/1990) ar- gued follow strategy falsifica- tion, seeking likely falsify the- ory. Interested whether adhere strategy, Wa- son (1960) investigated intuitively ories. In classic 2-4-6 participants were asked un- cover relational rule after being told one triplet, (2, 4, 6), conforms rule. The true rule, increasing numbers, sub- sumes potential rules (e.g., more than previous number) every triplet also valid under numbers Thus, only discovered not best at (negative or NTS). Rather NTS, choose triplets (the positive PTS) even though it impossi- ble way. For example, many partic- ipants task followed PTS entertaining each sequences hypothe- sis, such (1, 3, 5). tendency just instance what become known bias general human interpret ev- idence fitting theory differently against (Klayman & Ha, 1987). paper, outline set environmental conditions actually an strategy. Previ- ous work identified settings NTS yield falsification Klayman However, analysis produces quite behavior. still use situations where negative falsification, those encountered Wason’s experiment. complement showing optimally reduces uncertainty provided world herently (i.e., given true, there possible outcome). This suggests might explain result assumption determinism on part learners, recent results children causal relationships Schulz Sommerville, 2006; Gel- man, Coley, Gottfried, 1994). emphasis struc- ture environment parallels similar strategies pursued Oaksford Chater, plan paper follows, first introduce predicting event Under as- sumption (given sequence events, predicts event), situations. Next, define model for numeri- cal stimuli, behavioral experiment show captures predictions. If optimally, then verify num- ber second experiment, demonstrate changing per- son’s affects evidence-seeking conclude discussing our relate work. Sequence Given predict will oc- cur next? suppose you see woman outside airport security checkpoint. she stays checkpoint (she guard) walks gate passenger crewmember)? Clearly, depends explaining observed events these hy- potheses. Since no means complete certainty, inductive task. problem expressed terms objects (~ x = (x , . i−1 )) i ) P(x |~ x) ∑ |h,~ x)P(h|~ h pothesis h, P(h|~ posterior ~ x.