Bayesian inference is having a major impact on the scientific method, especially with regard to the interpretation of astronomical observations (e.g., Gregory 2001). In a recent international exoplanet radial velocity fitting challenge, the top five solutions, including my own (Gregory 2016), employed a Bayesian framework (Dumusque et al., A&A, 598, p. 133, 2017).
We employed the Bayesian framework to develop a new method for the detection of periodic signals (Gregory & Loredo 1992) of unknown shape. For certain problems the new method is a major advance over existing techniques (see Gregory and Loredo, 1996). It is particularly suited to the problem of detecting rapidly rotating neutron stars (pulsars) at X-ray and gamma-ray wavelengths. We also used a Gaussian version of this method to detect a new super orbital period in the radio to TeV gamma-ray emitting binary star, LSI+61o 303 (Gregory 1999; Gregory et al. 1999; Gregory 2002).
More recently I have applied the Bayesian framework to separate planetary and stellar activity signals (Gregory 2016), which is discussed in the Exoplanet Section.