In radar target adaptive detection problems, parts of the samples in the reference data are missing, such case is as a result of the degradation of detection performance for conventional detectors. Being under no condition of a prior information, an expectation maximization based adaptive matched filter (EM-AMF) is obtained by the maximal likelihood estimate of the clutter covariance matrix. A prior information about the detection environment is utilized for obtaining Markov Chain Monte Carlo based adaptive matched filter (MCMC-AMF) under condition of using Gibbs sampler to obtain the posterior mean of the clutter covariance matrix. The computer simulation results show that both of the detectors perform well under condition of the missing samples. With less prior information, MCMC-AMF and EM-AMF possess the analogous detection performance. But the MCMC-AMF detection performance can be improved further by exploiting more prior information.