  The recent direct observation of gravitational waves has further emphasized
the desire for fast, low-cost, and accurate methods to infer the parameters of
gravitational wave sources. Due to expense in waveform generation and data
handling, the cost of evaluating the likelihood function limits the
computational performance of these calculations. Building on recently developed
surrogate models and a novel parameter estimation pipeline, we show how to
quickly generate the likelihood function as an analytic, closed-form
expression. Using a straightforward variant of a production-scale parameter
estimation code, we demonstrate our method using surrogate models of
effective-one-body and numerical relativity waveforms. Our study is the first
time these models have been used for parameter estimation and one of the first
ever parameter estimation calculations with multi-modal numerical relativity
waveforms, which include all l <= 4 modes. Our grid-free method enables rapid
parameter estimation for any waveform with a suitable reduced-order model. The
methods described in this paper may also find use in other data analysis
studies, such as vetting coincident events or the computation of the
coalescing-compact-binary detection statistic.
