Teacakes, Trains, Taxicabs and Toxins: A Bayesian Account of Predicting the Future

摘要: Teacakes, Trains, Taxicabs and Toxins: A Bayesian Account of Predicting the Future Thomas L. Griffiths & Joshua B. Tenenbaum Department Psychology Stanford University Stanford, CA 94305-2130 USA {gruffydd ,jbt}@psych. stanford. edu Abstract This paper explores how people make predictions about future. Statistical approaches to predicting fu- ture are discussed, focussing on method for predict- ing future suggested by J. R. Gott (1993). gener- alized form Gott’s is presented, a specific psychological model suggested. Three experi- ments show that consistent with approach. Despite difficulty future, happily do it every day. We confident being able predict durations events, much time we will need get home after work, long take finish shopping. In many cases have great deal information guiding our judgments. How- ever, sometimes based upon less evidence. When faced new situations decisions longer can expect events last whatever evidence available. only possess concerns par- ticular event has lasted until now, becomes task induction. this explore question when told past. examine simple statistical consider such could be made sufficiently flexible useful in everyday situations. The resulting makes strong effects providing further information, symmetry reasoning, should affected prior knowledge. test these empirically. Copernican Anthropic Principle solution problem was recently proposed cosmologist Richard III founded what he calls “Copernican anthropic principle”, which holds ...the location your birth space Universe priveleged (or special) extent implied fact you an intelli- gent observer, among intelligent observers not special but rather picked at random (1993, p. 316) extends principle reasoning po- sition — given no contrary, assume “special” place time. means observer encounters phenomenon randomly located total duration phenomenon. Denoting since start tpast, its tt0m;, forms terms “delta t argument”. Define ratio T : past ttotal number between 0 1. It possible probabilistic value 7“. For example, 7“ 0.025 0.975 probability P 0.95, meaning Etpast l tfuture 39tpast 95% confidence, where tfutwe = tmm; —tpa3t. Sim- ilarly, than 0.5 0.5, so tpast 50% confidence. been used wide range phenomena. (1993) tells his visit Berlin Wall 1969 (tpast 8 years). Assuming period wall’s existence, confidence interval tfum,.e would 2.46 months 312 years. wall fell 20 years later, predictions. similar cal- culations Stonehenge, journal Nature, U.S.S.R., even human race. Subsequent tar- gets included Broadway musicals Conservative government Britain (Landsberg, Dewynne, Please, 1993). What’s Bayes got it? yields interesting simple, prove forming effective plans expectations events. On basis, plausible apply principles making judgments concerning attractiveness claim, there may good reasons why be- cognitive armory. One reason restrictive assumptions inference.