Algorithmic randomness and monotone complexity on product space
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, Lambalgen's theorem for correlated probability, classification of random sets by likelihood ratio tests, decomposition of complexity and independence, and Bayesian statistics for individual random sequences. Formerly Lambalgen's theorem for correlated probability is shown under a uniform computability assumption in [H. Takahashi, Inform. Comput. 2008]. In this paper we show the theorem without the assumption. (C) 2010 Elsevier Inc. All rights reserved.
lambalgen's theorem bayesian statistics martin-lof randomness kolmogorov complexity consistency