Frequentist and Bayesian measures of confidence via multiscale bootstrap for testing three regions
Abstract
A new computation method of frequentist -values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is represented as an arbitrary-shaped region. We introduce new parametric models for the scaling-law of bootstrap probability so that the multiscale bootstrap method, which was designed for one-sided test, can also computes confidence measures of two-sided test, extending applicability to a wider class of hypotheses. Parameter estimation is improved by the two-step multiscale bootstrap and also by including higher-order terms. Model selection is important not only as a motivating application of our method, but also as an essential ingredient in the method. A compromise between frequentist and Bayesian is attempted by showing that the Bayesian posterior probability with an noninformative prior is interpreted as a frequentist -value of ``zero-sided'' test.
Cite
@article{arxiv.0807.0053,
title = {Frequentist and Bayesian measures of confidence via multiscale bootstrap for testing three regions},
author = {Hidetoshi Shimodaira},
journal= {arXiv preprint arXiv:0807.0053},
year = {2013}
}