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Algorithmic randomness and the weak merging of computable probability measures
Simon M. Huttegger, Sean Walsh, Francesca Zaffora Blando
We characterize Martin-Löf randomness and Schnorr randomness in terms of the merging of opinions, along the lines of the Blackwell-Dubins Theorem. After setting up a general framew…
Schnorr Randomness and Effective Bayesian Consistency and Inconsistency
Simon M. Huttegger, Sean Walsh, Francesca Zaffora Blando
We study Doob's Consistency Theorem and Freedman's Inconsistency Theorem from the vantage point of computable probability and algorithmic randomness. We show that the Schnorr rando…
Algorithmic Randomness, Effective Disintegrations, and Rates of Convergence to the Truth
Simon M. Huttegger, Sean Walsh, Francesca Zaffora Blando
Lévy's Upward Theorem says that the conditional expectation of an integrable random variable converges with probability one to its true value with increasing information. In this p…