Bayesian inference calibration of the modulus of elasticity

This work uses the Bayesian inference technique to infer the Young modulus from the stochastic linear elasticity equation. The Young modulus is modeled by a finite Karhunen Lo\'{e}ve expansion, while the solution to the linear elasticity equation is approximated by the finite element method. The high-dimensional integral involving the posterior density and the quantity of interest is approximated by a higher-order quasi-Monte Carlo method.