This paper takes a Bayesian approach to the problem of dynamic
system estimation, and illustrates how posterior densities for
rather arbitrary system parameters or properties (such a frequency
response, phase margin etc) may be numerically
computed. In achieving this, the key idea of constructing an
ergodic Markov chain with invariant distribution equal to the
desired posterior is one borrowed from the mathematical statistics
literature. An essential point of the work here is that, via the
associated posterior computation from the Markov chain, error bounds
on estimates are provided that do not rely on asymptotic in data
length arguments, and hence they apply with arbitrary accuracy
for arbitrarily short data
records.