We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on n independent samples from them. Curiously, we show that estimating the IPM itself between probability measures is not significantly easier than...

Ramsey’s complete and total ignorance of Keynes’s definition of “objective, logical, probability relations”, contained on pages 35-36 of the A Treatise on Probability, which was explicitly referenced and discussed by Edgeworth in his two reviews, can only be explained by the conclusion...

H. E. Kyburg never read beyond chapter 6 of Keynes’s A Treatise on Probability. From 1959 till his death in 2007, Kyburg continually based his assessment of Keynes’s accomplishments on pp. 30 and 34 of Chapter III of the A Treatise on Probability. Edgeworth’s careful and judicious reading...

F Y Edgeworth made the only correct assessment of Keynes’s Logical Theory of Probability, as presented in his A Treatise on Probability, among economists in the 100 years between 1921 and 2020. The reason is that he actually read the entire book with the exception of Part II, which he was able...

F. Y. Edgeworth made the only correct assessment of Keynes’s Logical Theory of Probability in his A Treatise on Probability among philosophers in the 100 years between 1921 and 2020. The reason is that he actually read the entire book, with the exception of Part II, which he was able to assess...

We propose probability and density forecast combination methods that are defined using the entropy regularized Wasserstein distance. First, we provide a theoretical characterization of the combined density forecast based on the regularized Wasserstein distance under the Gaus-sian assumption....

By the time that Keynes’s logical theory of probability appeared in 1921 in his A Treatise on Probability (1921), Keynes had already used it in his Indian Currency and Finance,1913, personally at the Treaty of Versailles negotiations as the official representative of the British Treasury...

Strategic models of auditor-inspectee interaction have neglected implementation details in multiple-inspectee settings. With multiple inspectees, the target audit probability derived from the standard analysis can be implemented with sampling plans differing in the budgets committed to support...

Retirees worry about depleting their portfolio, but a greater concern could be how long they might live without income from that portfolio. A retiree may accept a 4% probability of portfolio depletion, but object to the possibility of living five or six years afterwards without that income....

After the 2020 U.S. presidential election, counting votes and calling states took more time than usual, particularly in battleground states. In the days following the election, winning probabilities changed frequently as new results were tabulated. Based on the sensitivity of stocks to changes...