“Bayes’ 1763 paper was an impeccable exercise in probability theory. The trouble and the subsequent busts came from overenthusiastic application of the theorem in the absence of genuine prior information, with Pierre-Simon Laplace as a prime violator. Suppose that in the twins example we lacked the prior knowledge that one-third of twins are identical. Laplace would have assumed a uniform distribution between zero and one for the unknown prior probability of identical twins, yielding 2/3 rather than 1/2 as the answer to the physicists’ question. In modern parlance, Laplace would be trying to assign an “uninformative prior” or “objective prior”, one having only neutral effects on the output of Bayes’ rule.”
“Academics who made the leap to Silicon Valley were rewarded with data unimaginable to most university researchers. Yahoo in the mid-2000s had roughly 500 million monthly visitors. Google presided over billions of AdWords auctions. Microsoft had millions of customers and hundreds of thousands of advertisers. “Economists have rarely had so much value to add in designing products and platforms that touch so many lives,” Athey said by email. “That was exhilarating—instead of hundreds of academics citing a research paper, my work could directly influence the economy as a whole.”
“Going against the advice of attorneys and confidantes, Levinson and Lapidus made an unusual offer that included a hefty upfront payment. Despite the Goelets’ wealth, Levinson said he knew the family would want to get back the cash they paid for L&L’s 33 percent stake quickly.
The move worked and L&L won the ground lease. It signed an 84-year deal valued at $320 million that included fixed rent for the first 39 years and then a rate based on an agreed formula for the remaining 45."
“It was the first time that the commercial side and the sporting side of Juventus came together in assessing the costs and benefits [of a signing],” says Mr Agnelli, a scion of the billionaire family that has owned the club for 95 years. “The opportunity of Ronaldo was thoroughly assessed and it made sense, both on and off the pitch.”"
“We see that X and Y have strong negative correlation. However, once we stratify by a confounder Z, encoded with color, the correlations flip to positive in each strata. The data is simulated, but we could see data like this if, for example, we looked at tutoring X and 9th grade test score Y data and then stratified students by their 8th grade test scores Z.”