“…These techniques can be classified into Bayesian methods based on Markov chain Monte Carlo (MCMC) [Oliver et al, 1997;Efendiev et al, 2005;Elsheikh et al, 2012], gradient-based optimization methods [McLaughlin and Townley, 1996;Carrera et al, 2005;Altaf et al, 2013], stochastic search algorithms [Li and Reynolds, 2011;Elsheikh et al, 2013aElsheikh et al, , 2013bElsheikh et al, , 2013cElsheikh et al, , 2013d, and ensemble Kalman filter methods [Moradkhani et al, 2005;Naevdal et al, 2005;Oliver et al, 2008;Luo et al, 2012;Elsheikh et al, 2013e]. It is evident from these studies (among others) that Bayesian statistics provide a general framework for estimating the probability distribution functions of the unknown parameters (i.e., inverse uncertainty quantification).…”