Generalization of van Lambalgen's theorem and blind randomness for conditional probabilities

2013/09/29 by Hayato Takahashi, Takahashi, Hayato
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Logic (math.LO) #Logic in Computer Science (cs.LO)

paper · pdf · doi:10.48550/arxiv.1310.0709

openalex publication_date 2013/09/29 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Generalization of the Lambalgen's theorem is studied with the notion of Hippocratic (blind) randomness without assuming computability of conditional probabilities. In [Bauwence 2014], a counter-example for the generalization of Lambalgen's theorem is shown when the conditional probability is not computable. In this paper, it is shown that (i) finiteness of martingale for blind randomness, (ii) classification of two blind randomness by likelihood ratio test, (iii) sufficient conditions for the generalization of the Lambalgen's theorem, and (iv) an example that satisfies the Lambalgen's theorem but the conditional probabilities are not computable for all random parameters.

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