This paper is directed at developing methods for delivering Bayesian estimates of dynamic system parameters, and functions of them (such as frequency response), for general problems. There are several motivations for the work. One is that due to computational load problems, such methods for Bayesian estimation do not currently exist. A second is that there are theoretical and practical motivations for considering adding Bayesian methods to the toolbox of system identification methods. A final one is that current advances in multi-core desktop processing are now making possible (via the algorithms discussed in this paper) the potential to compute Bayesian estimates for problems that have previously only been able to be addressed by prediction error, maximum-likelihood, and related techniques.