9 citations · 18 across the 13 of their papers we have counts for
13 papers
The explicit formulae for the distributions of nonoverlapping words and its applications to statistical tests for pseudo random numbers
Hayato Takahashi
The distributions of the number of occurrences of words (the distributions of words for short) play key roles in information theory, statistics, probability theory, ergodic theory,…
The distributions of sliding block patterns in finite samples and the inclusion-exclusion principles for partially ordered sets
Hayato Takahashi
In this paper we show the distributions of sliding block patterns for Bernoulli processes with finite alphabet, which is not based on the induction on sample size. We show a new in…
Recent progress on conditional randomness
Hayato Takahashi
In this article, recent progress on ML-randomness with respect to conditional probabilities is reviewed. In particular a new result of conditional randomness with respect to mutual…
Bayesian definition of random sequences with respect to conditional probabilities
Hayato Takahashi
We study Martin-Löf random (ML-random) points on computable probability measures on sample and parameter spaces (Bayes models). We consider variants of conditional randomness defin…
Conditional probabilities and van Lambalgen theorem revisited
Bruno Bauwens, Alexander Shen, Hayato Takahashi
The definition of conditional probability in case of continuous distributions was an important step in the development of mathematical theory of probabilities. How can we define th…
Universal test for Hippocratic randomness
Hayato Takahashi
Hippocratic randomness is defined in a similar way to Martin-Lof randomness, however it does not assume computability of the probability and the existence of universal test is not…
Generalization of van Lambalgen's theorem and blind randomness for conditional probabilities
Hayato Takahashi
Generalization of the Lambalgen's theorem is studied with the notion of Hippocratic (blind) randomness without assuming computability of conditional probabilities. In [Bauwence 201…
Algorithmic randomness and stochastic selection function
Hayato Takahashi
We show algorithmic randomness versions of the two classical theorems on subsequences of normal numbers. One is Kamae-Weiss theorem (Kamae 1973) on normal numbers, which characteri…
Algorithmic analogies to kamae-Weiss theorem on normal numbers
Hayato Takahashi
In this paper we study subsequences of random numbers. In Kamae (1973), selection functions that depend only on coordinates are studied, and their necessary and sufficient conditio…
Weak randomness and Kamae's theorem on normal numbers
Hayato Takahashi
A function from sequences to their subsequences is called selection function. A selection function is called admissible (with respect to normal numbers) if for all normal numbers,…
Some limits to nonparametric estimation for ergodic processes
Hayato Takahashi
A new negative result for nonparametric distribution estimation of binary ergodic processes is shown. The problem of estimation of distribution with any degree of accuracy is studi…
Computational limits to nonparametric estimation for ergodic processes
Hayato Takahashi
A new negative result for nonparametric estimation of binary ergodic processes is shown. I The problem of estimation of distribution with any degree of accuracy is studied. Then it…
Algorithmic randomness and monotone complexity on product space
Hayato Takahashi
We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space,…