Reputability Statement: The article is online at the Cornell University Library, which has a very good reputation as a university, and its library is very dilligently maintained.
Comments: This thesis article details how the bayesian theories are applied to astrophysics, including in great detail the widespread use of bayesian techniques to analyze "inverse problems." I did not understand what these were but after reading more of the thesis paper it became (very) slightly more clear as to how the application was found.
The article brings up some very interesing points including how some of the problems mentioned can't be solved analytically, which I thought was the only option, but brought up Markov Chain Monte Carlo algorithms which I had no idea even existed or how they could be applied. Apparently there was some argument over whether or not Bayesian techniques should be used in the field of astrophysics, but after discovering their application and the degree of opportunities for new study they opened up based on accepting certain things as true because of certain degrees of validity, many people came around.