  We investigate the discrimination of two candidates of an unknown parameter
in quantum systems with continuous weak measurement, inspired by the
application of hypothesis testing in distinguish-ing two Hamiltonians
[Kiilerich and M{\o}lmer, Phys. Rev. A, 98, 022103 (2018)]. Based on the
measurement output and stochastic master equation, temporal evolutions of
posterior probabilities of two hypotheses are given by Bayes' formula. The
Bayes criterion is presented by the likelihood ratio conditioned on the outcome
of measurements. Different from the calculation method based on maximum a
posteriori criterion, the Bayes criterion based method for calculating the
average prob-ability of making errors is more suitable and efficient in general
situation of binary discrimination. Finally, an example of distinguishing two
candidate Hamiltonians is given and the running times of calculating the
average probability of error under the Bayes criterion and the maximum a
posteriori criterion are compared to illustrate the feasibility of the
hypothesis testing in quickly distinguishing two candidates of the parameter to
be estimated.
