A Delayed Rejection Reversible Jump Markov Chain Monte Carlo Method for Multi-Resolution Maps of the Stochastic Gravitational Wave Background with Pulsar Timing Array Data

Pulsar timing array anisotropy analyses often use a naive counting argument to set resolutions of inferred maps of the stochastic gravitational wave background (GWB). We present a data-driven method in the form of a delayed rejection reversible jump sampler tailored to multi-resolution pixel decompositions of the angular power density of the GWB. We also consider a rapid, frequentist alternative based on information criteria statistics. We verify our methods with a series of injection-and-recovery simulations, finding that the standard counting argument would lead to drastic overfitting of the data and that our data-driven methods reduce the number of parameters in the models by one to three orders of magnitude yet can achieve higher resolution than the standard counting argument when justified by the data. We make our sampler and frequentist method implementation available on GitHub.