The excess of electron recoil events seen by the XENON1T experiment has been interpreted as a potential signal of axion-like particles (ALPs), either produced in the Sun, or constituting part of the dark matter halo of the Milky Way. We consider the evidence for the solar and dark-matter ALP hypotheses from the combination of XENON1T data and multiple astrophysical probes, including horizontal branch stars, red giants, and white dwarfs. We discuss the pros and cons of different statistical approaches to quantify the evidence, including Bayesian and frequentist methods. Lastly, we describe the computational methods used in the analysis, including a recently development cross-check of Bayesian computation.