Analysis of regression confidence intervals and Bayesian credible intervals for uncertainty quantification

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An adaptive sparse‐grid high‐order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling (2013, methodology): “To efficiently build the surrogate system for the PPDF with multiple significant modes, optimization techniques are used to identify the modes, for which high-probability regions are defined and components of the aSG-hSC approximation are constructed.”
Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods (2016, methodology): “…uncertainty estimation methods [Rojas et al., 2008], method of anchored distributions [Rubin et al., 2010], Markov chain Monte Carlo (MCMC) methods [Lu et al., 2011], maximum likelihood methods [Neuman et al., 2012; Lu et al., 2012b], and ensemble Kalman filter methods [Xue and Zhang, 2014].”
Assessment of parametric uncertainty for groundwater reactive transport modeling (2014, background): “…g(b), are sufficiently monotonic, (3) there is a single minimum in the objective function, and (4) the residuals are multivariate normal distributed to obtain a valid critical value, and (5) model intrinsic nonlinearity is small [Cooley and Naff, 1990; Hill and Tiedeman, 2007; Lu et al., 2012].”