Moreover, around the search neighborhoods of the optimal solution, there are many local optimums.It can conclude that when considering the measurement error the common likelihood measures as in (1) and in (5) are weak to solve the problem of equifinality.In the second step, a new fitness measure is proposed, which can be seen as the informal likelihood measure under the framework of the generalized likelihood uncertainty estimation (GLUE) [12–14].
To solve higher dimensional problems, Muto and Beck  developed an adaptive Markov chain Monte Carlo (MCMC) simulation for the Bayesian model updating.
With Taylor’s expansion, the likelihood measure can be deduced as denote the bias between the MAP/ML estimator and each of the posterior samples.
The proposed Bayesian updating of the posterior samples using DREAM algorithm can be divided into two steps.
The surface of the formal log-likelihood measure is studied considering the uncertainty of measurement error to illustrate the problem of equifinality.
To overcome the problem of equifinality, the first two derivatives of the log-likelihood measure are proposed to formulate a new informal likelihood measure for the sake of improving the accuracy of the estimator.
From the surfaces of fitness measures, it can be concluded that the formal likelihood measure underestimates or overestimates the uncertain intervals of the posterior samples.