  We introduce Bilby-MCMC, a Markov-Chain Monte-Carlo sampling algorithm tuned
for the analysis of gravitational waves from merging compact objects.
Bilby-MCMC provides a parallel-tempered ensemble Metropolis-Hastings sampler
with access to a block-updating proposal library including problem-specific and
machine learning proposals. We demonstrate that learning proposals can produce
over a 10-fold improvement in efficiency by reducing the autocorrelation time.
Using a variety of standard and problem-specific tests, we validate the ability
of the Bilby-MCMC sampler to produce independent posterior samples and estimate
the Bayesian evidence. Compared to the widely-used dynesty nested sampling
algorithm, Bilby-MCMC is less efficient in producing independent posterior
samples and less accurate in its estimation of the evidence. However, we find
that posterior samples drawn from the Bilby-MCMC sampler are more robust: never
failing to pass our validation tests. Meanwhile, the dynesty sampler fails the
difficult-to-sample Rosenbrock likelihood test, over constraining the
posterior. For CBC problems, this highlights the importance of cross-sampler
comparisons to ensure results are robust to sampling error. Finally, Bilby-MCMC
can be embarrassingly and asynchronously parallelised making it highly suitable
for reducing the analysis wall-time using a High Throughput Computing
environment. Bilby-MCMC may be a useful tool for the rapid and robust analysis
of gravitational-wave signals during the advanced detector era and we expect it
to have utility throughout astrophysics.
