Figure 3.

MCMC convergence. The convergence of posterior probabilities for loss, neutral, and gain of three representative probes--probe 1658, probe 1512, and probe 447 respectively--from the simulated dataset 63 are shown. For each probe, at first, the posterior probability of the corresponding HMM state, given the sampled parameters from the current MCMC iteration, is computed. The time-average of these posterior probabilities, starting from the first iteration to the current iteration, approximates the posterior of the HMM state given the data. The mean of the posterior probabilities over 10 MCMC chains are shown with error bars (mean ± one standard deviation)--loss probe in the bottom row, neutral probe in the middle, and the gain probe in the top row. The top figures show the outcomes of FBG sampling and the bottom figures show the outcomes of approximate sampling. Note that the reduction in standard deviation suggests that approximate sampling converges quicker than FBG sampling for these probes.