  In this work a quantum analogue of Bayesian inference is considered. Based on
the notion of instrument, we propose a quantum analogue of Bayes' rule, which
elaborates how a prior normal state updates under observations. Besides, we
investigate the limit of posterior normal state as the number of observations
goes to infinity. After that, we generalize the fundamental notions and results
of Bayesian inference according to quantum Bayes' rule. It is noted that our
theory not only retains the classical one as a special case but possesses many
new features as well.
