In this paper, we present a maximum a posteriori probability (MAP) approach to the problem of blind estimation of single-input, multiple-output (SIMO), finite impulse response (FIR) channels. A number of methods have been developed to date for this blind estimation problem. Some of those utilize prior knowledge on input signal statistics. However, there are very few that utilize channel statistics too. In this paper, the unknown channel to be estimated is assumed as the frequency-selective Rayleigh fading channel, and we incorporate the channel prior distributions (and hyperprior distributions) into our model in two different ways. Then for each case an iterative MAP estimator is derived approximately. Performance comparisons over existing methods are conducted via numerical simulation on randomly generated channel coefficients according to the Rayleigh fading channel model. It is shown that improved estimation performance can be achieved through the MAP approaches, especially for such channel realizations that have resulted in large estimation error with existing methods.