78 citations · 236 across the 18 of their papers we have counts for
7 papers · 1 filter
Indispensable monomials of toric ideals and Markov bases
Satoshi Aoki, Akimichi Takemura, Ruriko Yoshida
Extending the notion of indispensable binomials of a toric ideal, we define indispensable monomials of a toric ideal and establish some of their properties. They are useful for sea…
Capital process and optimality properties of a Bayesian Skeptic in coin-tossing games
Masayuki Kumon, Akimichi Takemura, Kei Takeuchi
We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic…
Game theoretic derivation of discrete distributions and discrete pricing formulas
Akimichi Takemura, Taiji Suzuki
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves t…
On a simple strategy weakly forcing the strong law of large numbers in the bounded forecasting game
Masayuki Kumon, Akimichi Takemura
In the framework of the game-theoretic probability of Shafer and Vovk (2001) it is of basic importance to construct an explicit strategy weakly forcing the strong law of large numb…
Validity of the expected Euler characteristic heuristic
Jonathan Taylor, Akimichi Takemura, Robert J. Adler
We study the accuracy of the expected Euler characteristic approximation to the distribution of the maximum of a smooth, centered, unit variance Gaussian process f. Using a point p…
Defensive forecasting for linear protocols
Vladimir Vovk, Ilia Nouretdinov, Akimichi Takemura +1
We consider a general class of forecasting protocols, called "linear protocols", and discuss several important special cases, including multi-class forecasting. Forecasting is form…