To obtain a sample from the posterior distribution P (θ|y) we make use of the Markov Chain Monte Carlo method. In outline, this involves finding an approximation to the posterior distribution P (θ|y) by drawing a finite (but sufficiently large to be accurate) number of samples from this distribution. To do this we simulate a Markov Chain whose limiting distribution is the required posterior distribution using an efficient implementation of the Metropolis-Hastings algorithm, 20 within which candidate parameter sets are proposed from a proposal distribution q(θ cand |θ i ) which depends only on the previously accepted parameter set θ i ;