  This paper examines the effectiveness of a sparse Bayesian algorithm to
estimate multivariate autoregressive coefficients when a large amount of
background interference exists. This paper employs computer experiments to
compare two methods in the source-space causality analysis: the conventional
least-squares method and a sparse Bayesian method. Results of our computer
experiments show that the interference affects the least-squares method in a
very severe manner. It produces large false-positive results, unless the
signal-to-interference ratio is very high. On the other hand, the sparse
Bayesian method is relatively insensitive to the existence of interference.
However, this robustness of the sparse Bayesian method is attained on the
scarifies of the detectability of true causal relationship. Our experiments
also show that the surrogate data bootstrapping method tends to give a
statistical threshold that are too low for the sparse method.
  The permutation-test-based method gives a higher (more conservative)
threshold and it should be used with the sparse Bayesian method whenever the
control period is available.
