Abstract: In this talk, I describe a few workflows and algorithms used to interpret of gravitational wave observations of coalescing compact binaries, as a small-scale case study prototyping several challenges for future multimessenger investigations. These strategies statistically distinguish rare transient events from nongaussian noise, infer the distribution of sources consistent with each transient, and characterize the population of astrophysical sources responsible for the data. Focusing on the latter two challenges, I describe some recent progress using improved algorithms, several forms of surrogate modeling, and novel computing architectures and workflows to achieve these goals. I'll then describe new opportunities and challenges associated with rapid population identification and outlier detection; managing and propagating systematic errors in parameter inference; and computing-constrained exploration, approximation, and inference for astrophysical formation scenarios.