Construction of Bayesian Prediction Intervals for Smart Systems

In this paper, we employ adaptive Metropolis algorithms to construct densities for parameters and quantities of interest for models arising in the analysis of smart material structures. In the first step of the construction, MCMC algorithms are used to quantify the uncertainty in parameters due to measurement errors. We then combine uncertainties from the input parameters and measurement errors, and construct prediction intervals for the quantity of interest by propagating uncertainties through the models.