Category Archives: Inference and choice

Historians and probability

Dice players

Dice players (detail, Georges de La Tour, 17th C.)

Bayesian probability theory is a formal method of reasoning about evidence. Its probabilities are typically subjective and personal measures. They represent either a real person’s felt confidence, or a hypothetical person’s theoretically justified confidence. Please do not be put off by the word subjective. Justified confidence is the foundation of prudent belief, action and behavior.

Richard Carrier is a serious independent scholar and internet celebrity who earned his doctorate in ancient history from Columbia University. He uses Bayesian methods to study history, especially the question of whether Jesus was a real historical person. Carrier professes serene assurance about the objectivity and validity of his Bayesian approach to history (link),

“I don’t think I’ll convince everyone, but the only people who won’t be convinced are people who are irrationally, dogmatically opposed to what I’m arguing.”

This post discusses how well Bayesian methods can resolve historical controversies, in the sense of achieving consensus founded on objective analysis of evidence. Within a community of Bayesians, objectivity and near-unanimity aren’t completely out of reach, but they tend to be elusive except when most people would be convinced whether or not they appeal to Bayes.

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BBC Big Data Month

“Big data” is the coming thing in buisness computing. Big data is also what Edward Snowden exposed the NSA to be gathering about you. It’s all in the three V’s:

Volume (the sheer amount of information retained by businesses and governments from their dealings with people),

Velocity (the speed with which information arrives, changes and can be moved around) and

Variety (of information sources, formats, and structure – if any),

a formulation that can be traced back to a 2001 report by Douglas Laney, Research Vice President at Gartner, a technology consulting firm.

The BBC website is presenting a month-long series of reports on the technical, social, legal and political challenges of living with big data. The first installment is here,

http://www.bbc.com/news/business-26383058

Check in through the month for what promises to be a painless introduction to an especially far-reaching technological development. Extra credit for working out how many zeroes appear in the number of bytes in a yottabyte.

Update: The March-April 2014 issue of Harvard Magazine also has a applications-oriented article on Big Data, from a university perspective, including public health, business and humanities projects. The article is “Why ‘Big Data’ is a big deal,” by Jonathan Show. It’s online here:

http://harvardmagazine.com/2014/03/why-big-data-is-a-big-deal

Click on the “continue reading” link for an index of the BBC stories, with direct links to each of them. Continue reading

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De Finetti’s conjecture: First broken, then fixed; but nobody noticed, Part 2

In the first part, we left Bruno de Finetti in 1949 as he established that for four distinct individual possibilities (like which team will win a championship), any usual ordering of “tickets” that was “quasi-additive” was also “probabilistic.” He conjectured that this would be true for any finite number of quasi-additively ordered propositions, and invited the community to help prove him right or wrong.

One who accepted de Finetti’s invitation was Leonard Savage, who later developed his own landmark axiomatization of subjective probability. Savage gave the obscure 1949 paper to Charles Kraft, John Pratt and Abraham Seidenberg. They showed in 1959 that de Finetti’s conjecture was wrong if there are five or more basic outcomes.

That’s the “broken” part of the story. De Finetti’s conjecture, scribbled in haste to rebut his friend George Polya, is false. Many people scrambled to fix it. The first were Kraft, Pratt and Seidenberg themselves in 1959. A famous second time was five years later, by Dana Scott. Oddly, neither solution was satisfactory to its authors. Odder still was that De Finetti himself may have come within a whisker of repairing it back at the beginning in 1949.  Continue reading

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De Finetti’s conjecture: First broken, then fixed; but nobody noticed, Part 1

Bruno de Finetti was an Italian statistician and probability theorist who contributed mightily to the Twentieth Century revival of Bayesian methods in statistics. One of his achievements was a gambling semantics for probability which explained Laplace’s observation that probability seemed to measure a person’s “degrees of belief” about uncertain prospects.

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Wily Self-interest

In the psychology lab, experimental versions of formal games often fail  to elicit the behavior which the experimenters expect based on their understanding of game theory. These results do not necessarily say much about the prevalence of cold, calculating, self-interested rationality. Some results might be occasions to think about what the player really gains by his or her behavior, and what problems reason is actually being asked to solve.  Continue reading

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Newcomb’s Problem

William Newcomb’s problem was reportedly first used as a conversational ice breaker at parties. It became an object of serious study largely thanks to the writing of the late Harvard philosophy professor Robert Nozick.

http://www.slate.com/id/2061419/

The situation is simple. You believe that somebody you know is a nearly faultless predictor of human behavior. Part of the fun is thinking about what it would take to convince you of that. Maybe a lengthy sterling record of successful past predictions, bolstered by a reputation of being a witch, a space alien, or an angel will suffice. But you are convinced. Then, this predictor offers you a very generous proposition.

“Here are two envelopes. One is transparent. It has a thousand dollars inside.” You see that it does. “The other is opaque. It contains either a cashier’s check for a million dollars, or no money at all, just a blank sheet of paper. Here, take them in your hands.” The predictor lets go of them. The envelopes are in your hands, and your hands alone.

“You have two choices. You may keep both envelopes, or you may keep just the opaque envelope and return the thousand dollars to me. Just drop it on the floor, I’ll pick it up later.

“But here’s the rub. I have predicted which way you are about to choose. If I thought you will keep just the one opaque envelope, then I put the check for a million dollars inside the envelope. If I thought you will keep both envelopes, including that thousand dollars for sure, then there is no money in the second envelope.”

So, which envelope(s) do you keep? Straight up, no tricks. You don’t get to flip a coin. You don’t think she’s a stage magician who can make her prediction come true by sleight of hand.

Do you take both envelopes, for a thousand dollars plus maybe much more, or just one envelope, for what you estimate is a far better chance of becoming a million dollars richer?  Continue reading

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