I have updated the preprint (title has been changed).
Title: Universal parameterized family of distributions of runs.
Author: Hayato Takahashi
arxiv 2302.14356
I have uploaded Poster (IIBMP 2023 Tokyo Univ.).
Title: Explicit formulae for distributions of words and their computational complexity.
Author: Hayato Takahashi
Poster
I have uploaded Poster (ICIAM 2023 Waseda Univ.).
Title: Test of randomness with distributions of words.
Author: Hayato Takahashi
Poster
I have uploaded slides (ICIAM 2023 Waseda Univ.).
Title: The explicit formulae for the distributions of words.
Author: Hayato Takahashi
Slides
I have uploaded a preprint, which will be appear in Information and Computation.
Title: Bayesian definition of random sequences with respect to conditional probabilities.
Author: Hayato Takahashi
https://arxiv.org/pdf/1701.06342.pdf (Open access)
https://doi.org/10.1016/j.ic.2023.105041
I have uploaded a preprint, which will be appear in RIMS Kokyuroku.
Title: Some explicit formulae for the distributions of words
Author: Hayato Takahashi
someexplicitRims.pdf
I have uploaded a preprint.
Title: A unified approach to explicit formulae for the distributions of runs
Author: Hayato Takahashi
Abstract: Fu et.al (1994) studied five statistics of runs and showed explicit formulae for their distributions by Markov imbedding method.
We show new simple explicit formulae for distributions of these statistics for independent and identically distributed binary random variables by a unified manner.
https://arxiv.org/pdf/2302.14356.pdf
I have presented at Workshop Number theory and Ergodic theory, 11 Feb. 2023.
Workshop Number theory and Ergodic theory
Title: A unified approach to explicit formulae for the distributions of runs
Author: Hayato Takahashi
I have uploaded slides, which includes recent results.
I have presented at IEICE IT Maebashi 25 Jan. 2023.
IEICE IT Maebashi
Title: Explicit formulae for the distributions of runs.
Author: Hayato Takahashi
I have uploaded slides, which includes recent results.
I have presented at RIMS Kyoto Univ. 19 Dec. 2022.
Probability Symposium at RIMS Kyoto Univ 2022
Title: Some explicit formulae for the distributions of words.
Author: Hayato Takahashi
I have uploaded the abstract for MSJ 2023.
Title: Some explicit formulae for the distributions of words.
HayatoTakahashi20221118msj.pdf
Author: Hayato Takahashi
I have updated the preprint,
The explicit formulae for the distributions of nonoverlapping words and its applications to statistical tests for pseudo random numbers.
https://arxiv.org/pdf/2105.05172.pdf
In this revision, I have simplified statements and proofs.
I have updated the preprint,
Bayesian definition of random sequences with respect to conditional probabilities.
https://arxiv.org/pdf/1701.06342.pdf
In this revision, I have simplified statements and proofs.
I have presented at IEICE online 11 Mar 2022,
https://www.ieice.org/ken/paper/202203115CJU/
I have presented the explicit formula for the exact distributions of the number of the occurrences of the non overlapping words.
These distributions are very fundamental for information sciences, but, as far as I understand,
the mathematical formula for these distributions were not known before.
I have updated the preprint,
Bayesian definition of random sequences with respect to conditional probabilities.
https://arxiv.org/pdf/1701.06342.pdf
This paper studies algorithmic randomness in statistical models and conditional randomness.
In particular, we show equivalent conditions for consistent theorems for Bayes statistics and
parametric models with algorithmic notion of
randomness.
As a byproduct, 1. we give a new solution to classical problem in Bayes statistics,
i.e. the posterior distributions
weakly converges to ML-random parameters when the model is consistent.
2. There is a consistent estimator for uniformly computable parametric models if and only if the random sets are pairwise disjoint for different parameters.
The total number of three bit strings is 8, i.e., 000, 001, 010, 011, 100, 101, 110, 111.
In this set, 4 strings contain the word 10.
These numbers are computed from Corollary 1 in
https://h-takahashi.sakura.ne.jp/HayatoTakahashiPoster.pdf
It is impossible to check the all strings that contain the specific words if the string is large.
For example, the size of human DNA is 10^9 and the number of possible strings is 4^10^9.
Our algorithm computes the number of words within few seconds for human size DNA.
I have uploaded the poster,
https://h-takahashi.sakura.ne.jp/HayatoTakahashiPoster.pdf,
which will be presented at
https://www.worldsymposium2020.org/home
The poster demonstrates simple formula for the distributions of words and algorithm
that compute the distribution within few seconds for human DNA size 10^9.
I have updated the preprint,
Bayesian definition of random sequences with respect to conditional probabilities.
https://arxiv.org/pdf/1701.06342.pdf
In this version, I commented on a classical problem in statistics.
There are two types of parametric models,
frequentist models (parametric models without priors) and
Bayes models (parametric models with priors).
Frequentist studies models for which estimators converge to true models for all parameters,
while Bayesian studies models for which posterior distributions converge weakly
to the true models for almost all parameters.
The problem is to identify for which points the posterior distributions weakly converge.
The preprint demonstrate an algorithmic solution to this problem, i.e.,
the posterior distributions converges weakly to Martin Löf random sets.
I have been upgraded to IEEE Senior member.
I have updated the preprint,
“The distributions of the sliding block patterns in finite samples and
the inclusion-exclusion principles for partially ordered sets”, which is available from arXiv 1811.12037.
This preprint is based on the presentation at Probability Symposium 2018 RIMS Kyoto.
The preprint shows statistical tests and their properties of sliding block patterns.
These statistics are very common in information theory and ergodic theory.
However their non-asymptotic characters are not well studied.
In the preprint, it is shown that the power of tests based on sliding block patterns is
much larger compared to conventional methods, which implies that
we can make a statistically reasonable decision from the limited samples.
https://arxiv.org/pdf/1811.12037.pdf