  We study Martin-L\"{o}f 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.
