On Empirical Meaning of Randomness with Respect to Parametric Families of Probability Distributions

作     者：V'yugin, Vladimir 

作者机构：Russian Acad Sci Inst Informat Transmiss Problems Moscow 127994 Russia 

出 版 物：《THEORY OF COMPUTING SYSTEMS》 (计算系统理论)

年 卷 期：2012年第50卷第2期

页      面：296-312页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：Russian foundation for fundamental research [09-07-00180a  09-01-00709a] 

主　　题：Martin-Lof random sequences A priory semimeasure Probabilistic machines Bernoully sequences Parametric families of probability distributions Algorithmic information theory Turing degrees 

摘      要：We study the a priori semimeasure of sets of P(theta)-random infinite sequences, where P(theta) is a family of probability distributions depending on a real parameter theta. In the case when for a computable probability distribution P(theta) an effectively strictly consistent estimator exists, we show that Levin s a priory semimeasure of the set of all P(theta)-random sequences is positive if and only if the parameter theta is a computable real number. We show that the a priory semimeasure of the set U(theta)I(theta), where I(theta) is the set of all P(theta)-random sequences and the union is taken over all algorithmically non-random theta, is positive.