This paper provides a theoretical analysis on the classification accuracy of LDA-Bayesian based method with respect
to the data sample size in brain connectivity analysis. More specifically, we show that when the sample size increases, both the classification error probability and its upper bound decreases monotonically. However, we also show that due to the model limitation of the Bayesian classifier, the classification error probability is actually lower bounded as well, which implies that the error probability actually converges to a non-zero constant even if the data sample size tends to infinity. Our analysis is demonstrated through fMRI based numerical results.