@article{02f29ca75dce4935ace36fec35adf6b0,

title = "How proper are Bayesian models in the astronomical literature?",

abstract = "The well-known Bayes theorem assumes that a posterior distribution is a probability distribution. However, the posterior distribution may no longer be a probability distribution if an improper prior distribution (non-probability measure) such as an unbounded uniform prior is used. Improper priors are often used in the astronomical literature to reflect a lack of prior knowledge, but checking whether the resulting posterior is a probability distribution is sometimes neglected. It turns out that 23 out of 75 articles (30.7 per cent) published online in two renowned astronomy journals (ApJ and MNRAS) between 2017 Jan 1 and Oct 15 make use of Bayesian analyses without rigorously establishing posterior propriety. A disturbing aspect is that a Gibbs-type Markov chain Monte Carlo (MCMC) method can produce a seemingly reasonable posterior sample even when the posterior is not a probability distribution (Hobert & Casella 1996). In such cases, researchers may erroneously make probabilistic inferences without noticing that the MCMC sample is from a non-existing probability distribution. We review why checking posterior propriety is fundamental in Bayesian analyses, and discuss how to set up scientifically motivated proper priors.",

author = "Hyungsuk Tak and Ghosh, {Sujit K.} and Ellis, {Justin A.}",

note = "Funding Information: HT and SKG acknowledge partial support from the National Science Foundation grant DMS 1127914 (and DMS 1638521 only for HT) given to the Statistical and Applied Mathematical Sciences Institute. JAE acknowledges supports from the National Science Foundation Physics Frontier Center Grant 1430284 and from the National Aeronautics and Space Administration through Einstein Fellowship Grant PF4-150120.We thank David E. Jones and David C. Stenning for a productive discussion at the International Centre for Theoretical Sciences in Bangalore, India, during a visit when participating in the program 'Time Series Analysis for Synoptic Surveys and Gravitational Wave Astronomy'. We also thank Eric B. Ford for insightful comments, Christian P. Robert and Peter Coles for their discussions in their personal blogs, and the referee for invaluable suggestions. Funding Information: HT and SKG acknowledge partial support from the National Science Foundation grant DMS 1127914 (and DMS 1638521 only for HT) given to the Statistical and Applied Mathematical Sciences Institute. JAE acknowledges supports from the National Science Foundation Physics Frontier Center Grant 1430284 and from the National Aeronautics and Space Administration through Einstein Fellowship Grant PF4-150120. We thank David E. Jones and David C. Stenning for a productive discussion at the International Centre for Theoretical Sciences in Bangalore, India, during a visit when participating in the program {\textquoteleft}Time Series Analysis for Synoptic Surveys and Gravitational Wave Astronomy{\textquoteright}. We also thank Eric B. Ford for insightful comments, Christian P. Robert and Peter Coles for their discussions in their personal blogs, and the referee for invaluable suggestions. Publisher Copyright: {\textcopyright} 2018 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society.",

year = "2018",

month = nov,

day = "21",

doi = "10.1093/mnras/sty2326",

language = "English (US)",

volume = "481",

pages = "277--285",

journal = "Monthly Notices of the Royal Astronomical Society",

issn = "0035-8711",

publisher = "Oxford University Press",

number = "1",

}