“examples of each?” Ibid.
(which has no strong pattern) In an email responding to fact-checking questions, Tenenbaum said that many of the examples they used were fairly complex, and “the reasons for the prediction functions having these shapes are the combination of (1) the priors, plus (2) a certain assumption about when an event is likely to be sampled (the ‘likelihood’), (3) Bayesian updating from priors to posteriors, and (4) using the 50th percentile of the posterior as the basis for prediction. What’s correct about what you have is that in our simple model, only (1) varies across domains—between movies, representatives, life spans, etc.—while (2–4) are the same for all the tasks. But [it’s] because of these causal processes (which vary across domains) together with the rest of the statistical computations (which are the same across domains) that the prediction functions have the shape they do.” It is important to note that the graphs in this text do not represent accurate empirical results, but rather patterns of predictions—the estimations that represent the 50th percentile of being right or wrong.
You read about a movie These are summaries of the questions asked. The direct wording of each question was: “Imagine you hear about a movie that has taken in 60 million dollars at the box office, but don’t know how long it has been running. What would you predict for the total amount of box office intake for that movie?” “Insurance agencies employ actuaries to make predictions about people’s life spans—the age at which they will die—based upon demographic information. If you were assessing an insurance case for a 39-year-old man, what would you predict for his life span?” “Imagine you are in somebody’s kitchen and notice that a cake is in the oven. The timer shows that it has been baking for 14 minutes. What would you predict for the total amount of time the cake needs to bake?” “If you heard a member of the House of Representatives had served for 11 years, what would you predict his total term in the House would be?”
variation of Bayes’ rule In an email responding to fact-checking questions, Tenenbaum wrote that “the most natural way to make these kinds of predictions in computers is to run algorithms which effectively implement the logic of Bayes’ rule. The computers typically don’t explicitly ‘use’ Bayes’ rule, because the direct computations of Bayes’ rule are typically intractable to carry out except in simple cases. Rather the programmers give the computers prediction algorithms whose predictions are made to be approximately consistent with Bayes’ rule in a wide range of cases, including these.”
data and your assumptions Sheldon M. Ross, Introduction to Probability and Statistics for Engineers and Scientists (San Diego: Academic Press, 2004).
skewed, as well “Base rate” typically refers to a yes-or-no question. In the Tenenbaum experiment, participants were asked to make numerical predictions, rather than answer a binary question, and so it’s most accurate to refer to this assumption as a “prior distribution.”
failures we’ve overlooked In an email responding to fact-checking questions, Tenenbaum wrote that “It’s not clear from our work that predictions for events in a certain class improve progressively with more experience with events of that type. Sometimes they might, sometimes they don’t. And this is not the only way to acquire a prior. As the pharaohs example shows, and other projects by us and other researchers, people can acquire a prior in various ways beyond direct experience with a class of events, including being told things, making analogies to other classes of events, forming analogies, and so on.”
“the Poker Brat” Eugene Kim, “Why Silicon Valley’s Elites Are Obsessed with Poker,” Business Insider, November 22, 2014, http://www.businessinsider.com/best-poker-players-in-silicon-valley-2014-11.
“bluff when it matters” In response to a fact-checking email, Hellmuth wrote: “Annie is a great poker player, and she has stood the test of time. I respect her, and I respect her Hold’em game.”
He folds In response to a fact-checking email, Hellmuth wrote: “I think she was trying to tilt me (get me emotional and upset) by showing a nine in that situation. A lot of players would have gone broke with my hand there (top pair) w[ith] a ‘Safe’ turn card, but I’ve made a living deviating from the norm and trusting my instincts (my white magic, my reading ability). I trusted it and folded.”
middle of the table In response to a fact-checking email, Hellmuth wrote: “With the chips I had at that time I had to go all in w[ith] 10–8 on that flop (I had top pair and there were flush draws, and straight draws possible). Completely standard. If you’re trying to imply that I put the money because I was emotionally tilted, you’re wrong. Nothing I could do there.”
Phil is out In response to a fact-checking email, Hellmuth contends that he and Annie had struck a deal when the tournament came down to the two of them in which they pledged to guarantee each other $750,000 regardless of the winner, and play for the last $500,000. Annie Duke confirmed this deal.
CHAPTER SEVEN: INNOVATION