GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 3.3 749 the centre to the lateral edges of the models and is particularly high at the top and bottom of the model. Fig. 3c illustrates a comparison of the marginal prior and posterior distributions for a cell located in the centre of the model. All the methods yield similar predictions thus further confirming their successful convergence to a stable posterior. As expected, the posterior shows a lower uncertainty than the prior, thus proving that the considered model parameter is illuminated by the data. If we analyse the PSRF for the considered model parameter we note that RWM converge after 20000 iterations, the AM needs 12000 iterations to converge, while the DEMC reach the stationary regime just after 7000 iterations after the burn-in. This result confirms that the automatic adaptation of the proposal, but particularly the mixing of the chains, ensure far superior performances than those achieved by the standard RWM algorithm. Conclusions. We compared the performances of five different MCMC algorithms. The analytical and the seismic synthetic tests proved that the automatic adaptation of the proposal distribution and the mixing of the models sampled by the different MCMC chains often ensure superior performances with respect to the standard RWM algorithm. This means that AM, AM_ sd, DEMC, and DREAM often show faster convergence rates toward the stationary regime. However, only a proper mixing of the chains (as performed by DEMC and DREAM) can guarantee the convergence in cases of complex target pdfs characterized by multiple modes separated by low probability regions. In other terms, this work demonstrated that a proper Fig. 3 - a) Comparison of the true and the mean Vp models provided by RWM, AM, and DEMC. b) Standard deviation of the posterior model estimated by RWM, AM, and DEMC. c) Comparison of marginal prior and posterior PPDs and evolution of the PSRF for a model parameter located at the center of the model.