  Structural equation models and Bayesian networks have been widely used to
study causal relationships between continuous variables. Recently, a
non-Gaussian method called LiNGAM was proposed to discover such causal models
and has been extended in various directions. An important problem with LiNGAM
is that the results are affected by the random sampling of the data as with any
statistical method. Thus, some analysis of the statistical reliability or
confidence level should be conducted. A common method to evaluate a confidence
level is a bootstrap method. However, a confidence level computed by ordinary
bootstrap method is known to be biased as a probability-value ($p$-value) of
hypothesis testing. In this paper, we propose a new procedure to apply an
advanced bootstrap method called multiscale bootstrap to compute confidence
levels, i.e., p-values, of LiNGAM outputs. The multiscale bootstrap method
gives unbiased $p$-values with asymptotic much higher accuracy. Experiments on
artificial data demonstrate the utility of our approach.
