  A ubiquitous challenge in design space exploration or uncertainty
quantification of complex engineering problems is the minimization of
computational cost. A useful tool to ease the burden of solving such systems is
model reduction. This work considers a stochastic model reduction method (SMR),
in the context of polynomial chaos (PC) expansions, where low-fidelity (LF)
samples are leveraged to form a stochastic reduced basis. The reduced basis
enables the construction of a bi-fidelity (BF) estimate of a quantity of
interest from a small number of high-fidelity (HF) samples. A successful BF
estimate approximates the quantity of interest with accuracy comparable to the
HF model and computational expense close to the LF model. We develop new error
bounds for the SMR approach and present a procedure to practically utilize
these bounds in order to assess the appropriateness of a given pair of LF and
HF models for BF estimation. The effectiveness of the SMR approach, and the
utility of the error bound are presented in three numerical examples.
