Bayesian inference using generalized likelihood for non-traditional residuals

Abstract

In structural engineering, Bayesian inference has been widely used to quantify uncertainties associated with modeling and measurement. Based on quantified uncertainties, predictions can be made in terms of the probability statement to consider predictive uncertainties for reliable decision-making. Traditionally, residual is assumed to be an independent and identically distributed Gaussian distribution with zero-mean and constant variance. In some situations, the traditional residual assumption cannot be adequate and their predictive capability for quantity of interest may be questionable. Although the residual assumption is important for quantifying the uncertainties in parameter estimation, there is little research for structural engineering to investigate influence of the non-traditional residuals to Bayesian inference. As an illustrative study, this study investigates influence of the non-traditional residuals in a concrete creep prediction. Without an adequate statistical representation of the observed residuals, the predictive performances over extrapolation are unreliable and inconsistent. To address the non-traditional residuals, this study introduces a generalized likelihood function. The generalized likelihood function can accommodate heteroscedasticity, temporal correlation and non-normality in observed residuals. By introducing the generalized likelihood function, the predictive performance over extrapolation can be significantly improved by satisfying with observed residual distribution.