prior probability

Are we all Bayesians now?

Posted on October 1, 2014 by F. E. Guerra-Pujol

F. D. Flam’s essay “The Odds, Continually Updated” revisits the famous Monty Hall Problem and appears in this week’s Science Times. (The science section of the N.Y. Times, which appears every Tuesday, offers a fascinating glimpse into the wonderful world of contemporary science.) Here is an excerpt from Flam’s excellent essay (emphasis ours):

The essence of the frequentist technique is to apply probability to data. If you suspect your friend has a weighted coin, for example, and you observe that it came up heads nine times out of 10, a frequentist would calculate the probability of getting such a result with an unweighted coin. The answer (about 1 percent) is not a direct measure of the probability that the coin is weighted; it’s a measure of how improbable the nine-in-10 result is — a piece of information that can be useful in investigating your suspicion.

By contrast, Bayesian calculations go straight for the probability of the hypothesis, factoring in not just the data from the coin-toss experiment but any other relevant information — including whether you’ve previously seen your friend use a weighted coin.

Scientists who have learned Bayesian statistics often marvel that it propels them through a different kind of scientific reasoning than they’d experienced using classical [i.e. frequentist] methods. “Statistics sounds like this dry, technical subject, but it draws on deep philosophical debates about the nature of reality,” said the Princeton University astrophysicist Edwin Turner, who has witnessed a widespread conversion to Bayesian thinking in his field over the last 15 years.

Deborah Mayo reviews Flam’s essay here and retorts: “Yes, but … what many would like to know is how to cross check Bayesian methods—how do I test your beliefs?” We will give this important question some thought and respond in a future blog post (it’s way past our bedtime). In the meantime, whether you are a frequentist or a Bayesian (or something else altogether), why aren’t we teaching school children (or lawyers, for that matter) about the concepts of probability and error as well as the rudiments of probability theory?

Our hero.

Are “nudges” ethical?

Posted on September 30, 2014 by F. E. Guerra-Pujol

Moral philosopher Jeremy Waldron offers this powerful critique of “soft paternalism” or the use of state-sponsored “nudges” to change behavior (emphasis ours):

… it may help to think about a slightly different sort of nudge—an informational nudge, where we manipulate the information given to people who use certain heuristics, in order to achieve the behavioral change that we figure the proper processing of correct information would lead to.

For example: between 15 and 20 percent of regular smokers (let’s say men sixty years old, who have smoked a pack a day for forty years) will die of lung cancer. But regulators don’t publicize that number, even though it ought to frighten people away from smoking, because they figure that some smokers may irrationally take shelter in the complementary statistic of the 80–85 percent of smokers who will not die of lung cancer. So instead they say that smoking raises the chances of getting lung cancer. That will nudge many people toward the right behavior, even though it doesn’t in itself provide an assessment of how dangerous smoking actually is (at least not without a baseline percentage of nonsmokers who get cancer).

Or consider the way lawmakers nudge people away from drunk driving. There are about 112 million self-reported episodes of alcohol-impaired driving among adults in the US each year. Yet in 2010, the number of people who were killed in alcohol-impaired driving crashes (10,228) was an order of magnitude lower than that, i.e., almost one ten thousandth of the number of incidents of DWI. The lawmakers don’t say that 0.009 percent of drunk drivers cause fatal accidents (implying, correctly, that 99.991 percent of drunk drivers do not). They say instead that alcohol is responsible for nearly one third (31 percent) of all traffic-related deaths in the United States—which nudges people in the right direction, even though in itself it tells us next to nothing about how dangerous drunk driving is.

In other words, smoking and driving under the influence are, of course, risky activities — compared, that is, to not smoking and to not driving under the influence — but how great is the true risk? Is it ethical for our government to present a false or distorted picture of the actual magnitude of the true risk, as in the two examples above?

Thanks, but no thanks!

Posted in Bayesian Reasoning, Deception, Law, Questions Rarely Asked | Tagged Jeremy Waldron, Risk, Soft Paternalism | 4 Comments

Captain Kirk’s Constitution

Posted on September 29, 2014 by F. E. Guerra-Pujol

What theory of constitutional interpretation does Captain Kirk subscribe to? Hat tip: Will Baude. Addendum: At the end of the film clip, Dr Spock logically asks: “… but does our involvement here also constitute a violation of the Prime Directive?” (Note: The Prime Directive prohibits Starfleet personnel from interfering with the internal development of alien civilizations.) Captain Kirk, however, simply brushes off Spock’s question, arguing in essence that the ends of the mission justify the means. Is Kirk right? Whether or not he violated the Prime Directive, this particular episode of Star Trek raises a deep and difficult question about higher law.

Posted in Questions Rarely Asked, Science Fiction | Tagged Captain Kirk, Omega Glory, Star Trek | 1 Comment

Things that cost more than space exploration

Posted on September 28, 2014 by F. E. Guerra-Pujol

Pop Quiz: What do presidential libraries, advertisements for prescription drugs, and pennies (yes, pennies!) have in common? They are all things that cost more than space exploration! (Hat tip: Tyler Cowen.)

Posted in Bayesian Reasoning, Economics, Questions Rarely Asked | Leave a comment

Battle of the computer-chess engines

Posted on September 27, 2014 by F. E. Guerra-Pujol

Albert Silver recently conducted a fascinating computer experiment — a chess tournament between the Komodo 8 chess engine (running on an Android smart phone) playing against the Shredder chess engine (running on a much faster desktop computer — 50 times faster, to be exact). In Mr Silver’s words:

Since Komodo 8 exists on both the desktop as well as the Android smartphone, I decided to play a small match between it on a smartphone [an LG Optimus G Pro from 2013], facing Shredder on a modern, top of the line quad-core i7 processor.

Guess what happened?

Hat tip to Tyler Cowen for the pointer and for posing the question, “Is software outpacing hardware?“

Posted in Games, Science, Web/Tech | Tagged Chess, Experiments, Komodo 8, Shredder | 1 Comment

#2 Derek Jeter

Posted on September 26, 2014 by F. E. Guerra-Pujol

Posted in Sports | Tagged Derek Jeter | Leave a comment

“Visualizing Probabilistic Proof”

Posted on September 26, 2014 by F. E. Guerra-Pujol

That is the title of our latest paper on the blue bus problem, a favorite law-school hypothetical of torts and evidence professors. (We wrote up a first draft of our paper in Tarpon Springs, Florida during the summer of 2013 and made some stylistic as well as substantive revisions more recently in preparation for our paper’s forthcoming publication in volume 7 of the Washington University Jurisprudence Review.) Briefly, the main contribution of our paper is that we visualize the blue bus problem using Bayesian methods of probabilistic reasoning. By the way, although many legal scholars — most recently Edward Cheng — have applied Bayesian methods to the blue bus problem, none have taken a visual approach to the problem. Ironically, however, trial attorneys routinely rely on visual forms of evidence (e.g., pictures, objects, scale models, etc.) when presenting their cases to juries. In our blue bus paper, then, we follow the lead of trial lawyers and present a Bayesian approach to the blue bus problem in visual form using numerical frequencies instead of fractions or percentages. In addition to solving the blue bus problem, our larger aim is to reevaluate the problem of probabilistic proof and make the case for Bayesian methods in civil and criminal adjudication generally.

Posted in Bayesian Reasoning, Law, Truth | Tagged Blue Bus Problem, Evidence | 1 Comment

What ESPN doesn’t want you to hear

Posted on September 25, 2014 by F. E. Guerra-Pujol

Addendum: By the way, while we’re on the subject of ESPN’s three-week suspension of Bill Simmons, check out this original analysis of the economics of employee suspensions here. (Tyler Cowen offers two possible economic explanations of employee suspensions.) This part of Professor Cowen’s post in particular caught our attention: “If I were the commissioner, I would be insulted by the suspension of Simmons. It suggests these are words which cannot be said, perhaps because they will elicit audience assent. The suspension also signals that ESPN regards the commissioner as quite thin-skinned and presumably — especially if he is indeed thin-skinned! — he could be offended by that too.”