Ruodu Wang’s contribution to the Discussion of ‘Testing by betting: A strategy for statistical and scientific communication’ by Glenn Shafer

=3131251 or http://dx.doi.org/10.2139/ssrn.3131251 . Dawid , A.P. , de Rooij , S. , Shafer , G. , Shen , A. , Vereshchagin , N. & Vovk , V. ( 2011 ) Insuring against loss of evidence in game-theoretic probability . Statistics and Probability Letters 81 ( 1 ), 157 – 162 . Fama , E.F. ( 1991 ). Efficient capital markets: II . The Journal of Finance 46 ( 5 ), 1575 – 1617 . Fisher , R.A. ( 1956 ). Statistical Methods and Scientific Inference . Edinburgh : Oliver and Boyd . Subsequent editions appeared in 1959 and 1973. Harvey , C.R. ( 2017 ). The scientific outlook in financial economics . Journal of Finance 72 ( 4 ), 1399 – 1440 . Jeffreys , H. ( 1961 ). Theory of Probability (3rd ed.). Oxford . Kass , R.E. & A.E. Raftery ( 1995 ). Bayes factors . Journal of the American Statistical Association 90 ( 430 ), 773 – 795 . Shafer , G. ( 1990 ) The unity and diversity of probability (with discussion) . Statistical Science 5 ( 4 ), 435 – 462 . Shafer , G. ( 2019a ) The language of betting as a strategy for statistical and scientific communication . arXiv:1903.06991 [math.ST]. Shafer , G. ( 2019b ) On the nineteenth century origins of significance testing and p-hacking . Working Paper 55, Available from: https://www.proba bilit yandf inance.com . Shafer , G. ( 2019c ) Pascal's and Huygens's game-theoretic foundations for probability . Sartoniana 32 , 117 – 145 . Shafer , G. & Vovk , V. ( 2001 ) Probability and finance: It's Only a Game! New York : Wiley . Shafer , G. & Vovk , V. ( 2006 ) The sources of Kolmogorov's Grundbegriffe . Statistical Science 21 ( 1 ), 70 – 98 . Shafer , G. & Vovk , V. ( 2019 ) Game-Theoretic Foundations for Probability and Finance . Hoboken, New Jersey : Wiley . Tamayo-Uria , I. , Mateu , J. & Diggle , P.J. ( 2014 ) Modelling of the spatio-temporal distribution of rat sightings in an urban environment . Spatial Statistics 9 , 192 – 206 . Ville , J. ( 1939 ). Étude critique de la notion de collectif . Paris : Gauthier-Villars . Vovk , V. ( 2019 ). Non-algorithmic theory of randomness . arXiv:1910.00585 [math.ST]. Vovk , V. & V’yugin , V.V. ( 1993 ) On the empirical validity of the Bayesian method . Journal of the Royal Statistical Society, Series B 55 ( 1 ), 253 – 266 . Vovk , V. & Wang , R. ( 2019 ) Combining e-values and p-values . arXiv:191206116v1 [math.ST], to appear in Annals of Statistics as “E-values: Calibration, combination, and applications”. Vovk , V. , Gammerman , A. & Shafer , G. ( 2005 ) Algorithmic learning in a random world . Berlin : Springer . Waudby-Smith , I. & Ramdas , A. ( 2020 ) Variance-adaptive confidence sequences by betting . arXiv:2010.09686 [math. ST]. Wu , W. & Shafer , G. ( 2007 ) Testing lead-lag effects under game-theoretic efficient market hypotheses . Working Paper 23, Available from: https://www.proba bilit yandf inance.com . How to cite this article: Shafer G. Author ' s reply to the Discussion of ‘Testing by betting: A strategy for statistical and scientific communication’ by Glenn Shafer. J R Stat Soc Series A. 2021;184:432–478. https://doi.org/10.1111/rssa.12672