Theory of Bayesian Multiscale Bootstrap and its Applications

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A resampling algorithm based on a scaling-law of randomness has been studied for computing a highly accurate confidence level of data analysis. In a previous study, we have proposed multiscale bootstrap method which computes an approximately unbiased confidence level (p-value) of statistical hypothesis testing in a frequentist sense. In this study, we proposed a method for computing the posterior probability in a Bayesian sense. We have shown a connection between the frequentist and the Bayesian confidence levels. We also studied a confidence level, as well as an active learning, for machine learning using the scaling-law of the randomness.