konrad scheffler tnqcnlmancalacbiouctacza hi rich analysis present frequentist bayesian approach arguing paradox exists frequentist case fair enough would like point frequentist approach orthodox hypothesis testing even problematic effectively makes assumptions claims frequentist exposition state idea whether population includes clairvoyants least want impose prior beliefs give us example circumstance would reject null hypothesis however example calculate bounds prior belief randomly chosen individual clairvoyant pclairvoyant 05 explain default belief null hypothesis pclairvoyant 110001 approximately 0001 otherwise would irrational reject null hypothesis observing success alternative would still less likely willing use commonly used p value threshold 001 get stronger bound pclairvoyant 1101 assuming willing believe hypothesis whenever probability 05 instead prefer build grey area accept beliefs bounds prior become stringent despite explicit denial method impose prior beliefs regards konrad tue 28 jun 2005 rich neapolitan wrote thank responded query discussed matter resolution first ill redescribe problem using numbers terminology provided francisco javier diez suppose task psuccess 0001 someone clairvoyant psuccess 1 someone clairvoyant idea whether population includes clairvoyants least want impose prior beliefs mike claims one null hypothesis succeeds unlikely event occurred 0001 null hypothesis true reject hypothesis believe mike probably one next 10000 people making claims clairvoyants null hypothesis none null hypothesis true probability least one succeeding 1999910000 63 mike alone succeeds reason reject null hypothesis need quite people succeeding reject little reason believing mike anyone else group clairvoyant way insist obtaining beliefs hypothesis testing however ij good said dont sweep prior beliefs carpet solve problem using bayes theorem suppose believe 01 probability individual say mike clairvoyant pclairvoyantsuccess psuccessclairvoyantpclairvoyantpsuccessclairvoyantpclairvoyant psuccessnot clairvoyantpnot clairvoyant 1 x 01 1x 01 0001 x 99 99 mike succeeds believe probably clairvoyant regardless many people attempt task succeed applications situations like buffet predicting stock performance think little analysis formulate reasonable priors etc analyze problem second way applications like coin tossing also assign extremely small priors someone special ability actually large group could see someone could talent forcing heads really mean random experiment control known tricks still could small probability someone psychic ability rich uai mailing list wed 06 aug 2008 150626 0200 uai luck skill resolution