2017/01/23 by Hayato Takahashi, Takahashi, Hayato
Computer Science · Mathematics · #03D32 #68Q30 #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.1701.06342
openalex publication_date 2017/01/23 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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 defined by ML-randomness on Bayes models and those of conditional blind randomness. We show that variants of conditional blind randomness are ill-defined from the Bayes statistical point of view. We prove that if the sets of random sequences of uniformly computable parametric models are pairwise disjoint then there is a consistent estimator for the model. Finally, we present an algorithmic solution to a classical problem in Bayes statistics, i.e., the posterior distributions converge weakly to almost all parameters if and only if the posterior distributions converge weakly to all ML-random parameters.