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This study develops Bayesian methods for estimating the parameters of a stochastic switching regression model. Markov Chain Monte Carlo methods, data augmentation, and Gibbs sampling are used to facilitate estimation of the posterior means. The main feature of these methods is that the posterior means are estimated by the ergodic averages of samples drawn from conditional distributions, which are relatively simple in form and more feasible to sample from than the complex joint posterior distribution. A simulation study is conducted comparing model estimates obtained using data augmentation, Gibbs sampling, and the maximum likelihood EM algorithm and determining the effects of the accuracy of and bias of the researcherʹs prior distributions on the parameter estimates.