  Using the latest numerical simulations of rotating stellar core collapse, we
present a Bayesian framework to extract the physical information encoded in
noisy gravitational wave signals. We fit Bayesian principal component
regression models with known and unknown signal arrival times to reconstruct
gravitational wave signals, and subsequently fit known astrophysical parameters
on the posterior means of the principal component coefficients using a linear
model. We predict the ratio of rotational kinetic energy to gravitational
energy of the inner core at bounce by sampling from the posterior predictive
distribution, and find that these predictions are generally very close to the
true parameter values, with $90\%$ credible intervals $\sim 0.04$ and $\sim
0.06$ wide for the known and unknown arrival time models respectively. Two
supervised machine learning methods are implemented to classify precollapse
differential rotation, and we find that these methods discriminate rapidly
rotating progenitors particularly well. We also introduce a constrained
optimization approach to model selection to find an optimal number of principal
components in the signal reconstruction step. Using this approach, we select 14
principal components as the most parsimonious model.
