Many Bayesian inference problems involve target distributions whose density functions are computationally expensive to evaluate. Replacing the with a local approximation based on small number of carefully chosen evaluations can significantly reduce computational expense Markov chain Monte Carlo (MCMC) sampling. Moreover, continual refinement guarantee asymptotically exact We devise new strategy...

We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/multiscale ansatz functions defined that can be combined time stepping schemes within model order reduction or multiscale methods. end, propose to perform several simulations of the PDE for a few steps parallel starting at differe...