Results 1 
3 of
3
The WellPosed Problem
 Foundations of Physics
, 1973
"... distributions obtained from transformation groups, using as our main example the famous paradox of Bertrand. Bertrand's problem (Bertrand, 1889) was stated originally in terms of drawing a straight line "at random" intersecting a circle. It will be helpful to think of this in a more concrete way; p ..."
Abstract

Cited by 25 (0 self)
 Add to MetaCart
distributions obtained from transformation groups, using as our main example the famous paradox of Bertrand. Bertrand's problem (Bertrand, 1889) was stated originally in terms of drawing a straight line "at random" intersecting a circle. It will be helpful to think of this in a more concrete way; presumably, we do no violence to the problem (i.e., it is still just as "random") if we suppose that we are tossing straws onto the circle, without specifying how they are tossed. We therefore formulate the problem as follows. A long straw is tossed at random onto a circle; given that it falls so that it intersects the circle, what is the probability that the chord thus defined is longer than a side of the inscribed equilateral triangle? Since Bertrand proposed it in 1889 this problem has been cited to generations of students to demonstrate that Laplace's "principle of indifference" contains logical inconsistencies. For, there appear to be many ways of defining "equally possibl
Measures of Surprise in Bayesian Analysis
 Duke University
, 1997
"... Measures of surprise refer to quantifications of the degree of incompatibility of data with some hypothesized model H 0 without any reference to alternative models. Traditional measures of surprise have been the pvalues, which are however known to grossly overestimate the evidence against H 0 . Str ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Measures of surprise refer to quantifications of the degree of incompatibility of data with some hypothesized model H 0 without any reference to alternative models. Traditional measures of surprise have been the pvalues, which are however known to grossly overestimate the evidence against H 0 . Strict Bayesian analysis calls for an explicit specification of all possible alternatives to H 0 so Bayesians have not made routine use of measures of surprise. In this report we CRITICALLY REVIEw the proposals that have been made in this regard. We propose new modifications, stress the connections with robust Bayesian analysis and discuss the choice of suitable predictive distributions which allow surprise measures to play their intended role in the presence of nuisance parameters. We recommend either the use of appropriate likelihoodratio type measures or else the careful calibration of pvalues so that they are closer to Bayesian answers. Key words and phrases. Bayes factors; Bayesian pvalues; Bayesian robustness; Conditioning; Model checking; Predictive distributions. 1.
What’s Luck Got to Do with It?: The History, Mathematics, and Psychology behind the Gambler’s Illusion
"... The origin of the study of mathematical probability is often, though incorrectly, seen as arising in an exchange of letters between Antoine Gombauld (the Chevalier de Méré), Blaise Pascal, and Pierre Fermat in the midseventeenth century. This “origin ” was rooted in gambling, yet probability theory ..."
Abstract
 Add to MetaCart
The origin of the study of mathematical probability is often, though incorrectly, seen as arising in an exchange of letters between Antoine Gombauld (the Chevalier de Méré), Blaise Pascal, and Pierre Fermat in the midseventeenth century. This “origin ” was rooted in gambling, yet probability theory itself has had little, if any, effect on gamblers’ behavior. In What’s Luck Got to Do with It?, a book enlivened by numerous literary and personal anecdotes, Mazur explores various facets of gambling and luck in a manner that will appeal not only to the general reader but also to those who relish littleknown facts and tidbits. Divided into three parts, What’s Luck Got to Do with It? leads the reader through historical, mathematical, and psychological aspects of matters relating to gambling. The reader must draw his own conclusions about the wisdom of indulging in such a pastime, for Mazur does not sermonize. Although he no more preaches against gambling than he advocates it, one gets a distinct sense of the unreasonableness of gambling and of its obsessive and destructive nature. Authors of earlier centuries were less restrained in their opinions of gamblers. For instance, in 1785 Samuel Johnson, in his usual forthright and inimitable style, defined a gambler as “A knave