Bayesian Inference for Prediction of Carbonation Depth of Concrete Using MCMC

Bayesian inference of model parameters for the time dependent carbonation depth of concrete is presented. The statistical model is assumed to have a form of where implies the carbonation coefficient and stands for the modeling error which is assumed to have a normal distribution with zero mean and unknown variance. By the use of existing data for the natural outdoor exposed concrete, the posterior distributions of the parameters are obtained by the Markov Chain Monte Carlo (MCMC) method, the implementation of which is made using WinBUGS. The corresponding linear statistical model equation is also considered, where the effect of small variance of the error on the number of samples in MCMC is illustrated. The compatibility of probability distributions of the carbonation coefficient for different values of is examined. It is shown that the carbonation coefficient derived from the carbonation depth for each has a lognormal distribution if 0.5 (the square-root-t law), whereas, for 0.33, a normal distribution is a better approximation.