AR(2) estimation in Bayes from first principles involves writing an M-H sampler as full conditional distributions for some of the parameters does not belong to any standard form. However softwares like WinBUGS and JAGS make the life easy for a modeler. The following document contains some basic code to do Bayesian inference for AR(2) process using WinBUGS and JAGS

AR(2) parameter estimation in WinBUGS and JAGS