Bayesian definition of random sequences with respect to conditional probabilities
Hayato Takahashi · 2017
We review the recent progress on the definition of randomness with respect to conditional probabilities and a generalization of van Lambalgen theorem (Takahashi 2006, 2008, 2009, 2011). In addition we generalize Kjos Hanssen theorem (2010) when the consistency of the posterior distributions holds. Finally we propose a definition of random sequences with respect to conditional probabilities as the section of the Martin-Lof random set at the random parameters and argue the validity of the definition from the Bayesian statistical point of view.