Some links related to understanding and estimating probabilities.
Nice video explanation from Julia Galef of the philosophical Sleeping Beauty problem.
For more information see the description in Quanta Magazine
Refers to analysis of streakiness in basketball shooting.
We find a subtle but substantial bias in a standard measure of the conditional dependence of present outcomes on streaks of past outcomes in sequential data. The mechanism is driven by a form of selection bias, which leads to an underestimate of the true conditional probability of a given outcome when conditioning on prior outcomes of the same kind. The biased measure has been used prominently in the literature that investigates incorrect beliefs in sequential decision making - most notably the Gambler's Fallacy and the Hot Hand Fallacy. Upon correcting for the bias, the conclusions of some prominent studies in the literature are reversed. The bias also provides a structural explanation of why the belief in the law of small numbers persists, as repeated experience with finite sequences can only reinforce these beliefs, on average.
Simpson's paradox occurs when groups of data show one particular trend, but this trend is reversed when the groups are combined together.
For example you and a friend do problems and your friend does better each day but that doesn't mean the friend does better when the two days are combined:
| Day | You | Friend |
| Saturday | 7⁄8 = 87.5% | 2⁄2 = 100% |
| Sunday | 1⁄2 = 50% | 5⁄8 = 62.5% |
| Total | 8⁄10 = 80% | 7⁄10 = 70% |
Predict which social and behavioral science studies will replicate and win cash prizes.