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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 ..."
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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 ..."
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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.
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"... In understanding behavior analysis as a natural science, we need to examine ties between behavior analysis and other natural sciences—this ..."
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In understanding behavior analysis as a natural science, we need to examine ties between behavior analysis and other natural sciences—this
Preface
"... The application of hydroacoustic measurements for preparation of spatial distribution maps of benthic communities is reported. For the present study common mussels (Mytilus edulis), neptune grass (Posidonia oceanica) and Cymodocea nodosa, serving as canonical species of many European marine ecosyst ..."
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The application of hydroacoustic measurements for preparation of spatial distribution maps of benthic communities is reported. For the present study common mussels (Mytilus edulis), neptune grass (Posidonia oceanica) and Cymodocea nodosa, serving as canonical species of many European marine ecosystems, were selected. These species are supposed to be good indicators of marine ecosystem health. The hydroacoustic measurements comprise preprocessed echo sounder recordings and sidescan sonar data forming a large and unique collection of datasets based on 4 field campaigns in resund and the Mediterranean. A combination of geostatistical methods for spatial interpolation of the echo sounder observations and a set of classification rules, based on discriminant analysis of the feature space of the observations, is found to yield reliable distribution maps when compared to groundtruth data. The datadriven methodology developed is shown to be adaptive to instationarities in the echo sounder observations and is recommended as a substantial improvement of existing methods of sea floor mapping based on echo sounder data. Elaborations of the developed methodology are studied, comprising the use of geostatistical simulation, Markov random fields and Boolean models. Geostatistical simulation provides a means of assessing the variability of random field functionals such as the estimated distribution area of a benthic species. The Markov random field allows the spatial distribution of the benthic communities to be modelled as a less smooth or regular phenomena than assumed when using geostatistical models. The use of Markov random fields in a Markov chain Monte Carlo simulation framework enables an alternative means of assessing variability of image functionals that is based on a sound...
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 ..."
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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