Appendix C. Markpv chain Monte Carlo (MCMC) and posterior distributions for real data.
For each of the three models, three simulations with different starting points were run to assess the convergence of the Markov chains. For each simulation, a burn-in of 10,000 iterations was used, and the next 30,000 (40,000 for model II) iterations were thinned by taking every third iteration.
In all cases, the MCMC mixed very well (shown for models I and II in Figs. C1 and C2). The prior distributions are essentially uninformative in the sense that the posteriors were much more concentrated than the priors (Fig. C1 and C2). And exception was given by the parameters _{}, _{}, for which the priors could be considered slightly informative, and especially the parameter _{ }in case of model II, for which posterior can be considered to depend essentially on the choice of the prior. The mixing of the MCMC and posterior distributions for model III are similar to that for model I.
FIG. C1. Left hand panels shows Monte Carlo Markov chains for the parameters _{}, _{}, _{}, and _{} for real data. The three independent chains of 30,000 iterations are shown in parallel. The right hand panels show the marginal posterior distributions (continuous lines) and the corresponding prior distributions (dotted lines). Results based on model I. |
FIG. C2. As Fig. C1, based on model II, and including a panel for the parameter _{}. |