  A new computation method of frequentist $p$-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 $p$-value of
``zero-sided'' test.
