Abstract: Engineering, material science, and biological models generally have a number of parameters which are nonidentifiable in the sense that they are not uniquely determined by measured responses. Furthermore, the computational cost of high-fidelity simulation codes often precludes their direct use for Bayesian model calibration and uncertainty propagation. In this presentation, we will discuss techniques to isolate influential parameters for subsequent surrogate model construction, Bayesian inference and uncertainty propagation. For parameter selection, we will discuss advantages and shortcomings of global sensitivity analysis to isolate influential inputs and detail the use of parameter subset selection and active subspace techniques as an alternative. We will also discuss the manner in which Bayesian calibration on active subspaces can be used to quantify uncertainties in physical parameters. These techniques will be illustrated for models arising in nuclear power plant design and quantitative systems pharmacology (QSP), as well as models for transductive materials