  We present a parameter estimation procedure based on a Bayesian framework by
applying a Markov Chain Monte Carlo algorithm to the calibration of the
dynamical parameters of a space based gravitational wave detector. The method
is based on the Metropolis-Hastings algorithm and a two-stage annealing
treatment in order to ensure an effective exploration of the parameter space at
the beginning of the chain. We compare two versions of the algorithm with an
application to a LISA Pathfinder data analysis problem. The two algorithms
share the same heating strategy but with one moving in coordinate directions
using proposals from a multivariate Gaussian distribution, while the other uses
the natural logarithm of some parameters and proposes jumps in the eigen-space
of the Fisher Information matrix. The algorithm proposing jumps in the
eigen-space of the Fisher Information matrix demonstrates a higher acceptance
rate and a slightly better convergence towards the equilibrium parameter
distributions in the application to LISA Pathfinder data . For this experiment,
we return parameter values that are all within $\sim1\sigma$ of the injected
values. When we analyse the accuracy of our parameter estimation in terms of
the effect they have on the force-per-unit test mass noise estimate, we find
that the induced errors are three orders of magnitude less than the expected
experimental uncertainty in the power spectral density.
