B.Sc., M.Sc. Queen's (63, 65)
E-mail: gregory `at' phas.ubc.ca
Bayesian Inference in Astronomy
Check out my text book from Cambridge University Press:
Bayesian Logical Data Analysis for the Physical Sciences
Also check out the free resources that accompany the book which includes solution sets, errata, supporting Mathematica software, and a Mathematica free interactive player,
plus New Supplement that includes two additional chapters (Dec. 2014),
plus Fusion Markov chain Monte Carlo code for Mathematica (Nov. 2014).
Excerpt from the book preface: "We are currently in the throes of a major paradigm shift in our understanding of statistical inference based on a powerful generalization of Aristotelian logic. For historical reasons, it is referred to as Bayesian Probability Theory or Bayesian statistic. To get a taste of how significant this development is, consider the following: probabilities are commonly quantified by a real number between 0 and 1. The end-points, corresponding to absolutely false and absolutely true, are simply the extreme limits of this infinity of real numbers. Deductive logic, which is based on axiomatic knowledge, corresponds to these two extremes of 0 and 1. Now try to imagine what you might achieve with a theory of extended logic that encompassed the whole range from 0 to 1. This is exactly what is needed in science and real life where we never know anything is absolutely true or false. Of course, the field of probability has been around for years, but what is new is the appreciation that the rules of probability are not merely rules for manipulating random variables. They are now recognized as uniquely valid principles of logic, for conducting inference about any proposition or hypothesis of interest. It is thus a mathematical theory that encompasses both inductive and deductive logic. Ordinary deductive logic is just a special case in the idealized limit of complete information."
This fundamental advance is having a major impact on the scientific method, especially with regard to the interpretation of observations (see Gregory 2001). With this approach we have developed a new method for the detection of periodic signals (Gregory & Loredo 1992; Gregory 1999) 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 have also used a new Gaussian version of this method to detect a new periodic phenomenon in the radio and X-ray emitting binary star, LSI+61o 303 (Gregory 1999; Gregory et al. 1999; Gregory 2002).
The discovery of multiple planets orbiting the Pulsar PSR B1257+12 (Wolszczan & Frail, 1992), ushered in an exciting new era of astronomy. Nineteen years later, over 500 extra-solar planets had been discovered by a variety of techniques, including precision radial velocity measurements which have detected the majority of planets to date. It is to be expected that continued monitoring and increased precision will permit the detection of lower amplitude planetary signatures. The increase in parameters needed to model multiple planetary systems is motivating efforts to improve the statistical tools for analyzing the radial velocity data. Much of the recent work has highlighted a Bayesian MCMC approach as a way to better understand parameter uncertainies and degeneracies.
I have developed (Gregory 2005, 2006, 2007, 2008, 2010) a Bayesian nonlinear model fitting program based on a new fusion MCMC algorithm. The algorithm incorporates parallel tempering, simulated annealing, and genetic crossover operations via a unique adaptive control system that automates the tuning of proposal distributions for efficient exploration of the parameter space even for highly correlated parameters. Each of these methods was designed to facilitate the detection of a global maximum in a fitness criteria. By combining all three the fusion MCMC greatly increases the probability of realizing this goal. When applied to the Kepler problem it acts as a powerful multi-planet Kepler periodogram which provides full Bayesian posterior parameter probability density distributions for for all the orbital elements that can be determined from precision radial velocity data. The various features of the algorithm makes it practical to attempt blind searches for multiple planets simultaneously.
The samples from the parallel chains can also be used to compute the marginal likelihood for a given model (see chapter 12 of Bayesian Logical Data Analysis for the Physical Sciences) for use in computing the model marginal likelihood that is needed to compare models with different numbers of planets. The development of alternative robust schemes for computing the marginal likelihoods is an active research topic (Ford & Gregory 2006). See the text book supplement for a discussion of a new but conceptually simple method called Nested Restricted Monte Carlo (NRMC), along with a detailed comparison to two other methods in an exoplanet application.
"Our Solar Grid-Tie System with Battery Backup"
Presented at the Bowen Island Solar Power Forum 4 Apr.
PDF file (2.9 MB)
Invited talk "Bayesian Planet Searches for the 10 cm/s
Radial Velocity Era"
to the Honolulu IAU Focus Meeting 8 on Statistics and Exoplanets, 4 Aug.
PDF file (3.4 MB)
Download 6 lectures on Bayesian Astrostatistics given
at the XXVI Canary Island Winter School in Astrophysics, Nov. 3-15, 2014.
PDF file (6.8 MB)
Download lecture 1 on Bayesian Astrostatistics given
at the Carnegie Observatories Nov. 8, 2011.
Lecture 1 PDF file (1.4 MB)
Download lecture 2 on Bayesian Astrostatistics given
at the CarnegieObservatories Nov. 9, 2011.
Lecture 2 PDF file (1.2 MB)
Download lecture 3 on Bayesian Astrostatistics given
at the Carnegie Observatories Nov. 9, 2011.
Lecture 3 PDF file (1.6 MB)
Download lecture on Bayesian Exoplanet Analysis given
at the Victoria University of Wellington in New Zealand March 2011.
PDF file (1.9 MB)
Gregory, P. C., "
An Apodized Keplerian Periodogram for Separating Planetary and Stellar
MNRAS in press 13 Jan 2016. PDF file (8.2 MB)
Gregory, P. C., "
Extra-solar Planets via Bayesian Fusion MCMC
2013, Chapter 7 in 'Astrostatistical Challenges for the New Astronomy', Springer Series in Astrostatistics, Hilbe, J. M. (ed) , New York:Springer. PDF file (2.2 MB)
Gregory, P. C., "Discussion on paper by Martin Weinberg
regarding "Bayesian Model Selection and Parameter Estimation."
2012, in Statistical Challenges in Modern Astronomy V, (ed) Eric Feigelson and Jogesh Babu, Springer, p. 117-125. PDF file (235 kB)
Gregory, P. C., "Bayesian Re-analysis of the Gliese 581 Exoplanet System
MNRAS, 415, 2523-2545, 2011 PDF file (2.4 MB)
Gregory, P. C., "Bayesian Exoplanet tests of a new method for MCMC
sampling in highly correlated model parameter spaces",
MNRAS 410, 94, 2010. PDF file (1.1 MB)
Gregory, P. C. and Fischer, D. A., "A Bayesian Periodogram Finds Evidence for Three
Planets in 47 Ursae Majoris",
MNRAS 403, 731, 2010. PDF file (3.1 MB)
Gregory, P. C., " Detecting Extra-solar Planets with a Bayesian
hybrid MCMC Kepler periodogram",
For publication in the Joint Statistical Meeting Proceedings, 2008. PDF file (2.5 MB)
Gregory, P. C., " A Bayesian re-analysis of HD 11964: evidence for
in `Bayesian Inference and Maximum Entropy Methods in Science and Engineering: 27th International Workshop', Kevin H. Knuth, Ariel Caticha, Julian L. Center, Adom Giffin, Carlos C. Rodríguez, eds, AIP Conference Proceedings, 954, 307-314, 2007. PDF file (249 kB)
Gregory, P. C., "A Bayesian Periodogram Finds Evidence for Three Planet in HD 11964",
MNRAS 381, 1607, 2007. PDF file (689 kB)
Gregory, P. C., "A Bayesian Kepler Periodogram Detects a Second Planet in HD 208487",
MNRAS 374, 1321, 2007. PDF file (923 kB)
Ford, E. B. & Gregory, P. C., "Bayesian Model Selection and Extrasolar Planet Detection",
Preprint, 2006. PDF file (498 kB)
Gregory, P. C., "A Bayesian Re-analysis of Extrasolar
Planet Data for HD 73526",
Ap.J. 631, 1198, 2005. PDF file (1.2 MB)
Gregory, P. C., "LSI+61o 303 Radio Outburst Ephemeris",
Preprint, 2004. PDF file (116 kB)
Gregory, P. C., and Neish, C., "Density and
Velocity Structure of the Be Star Equatorial Disk in the Binary, LSI+61o
303, a Probable Microquasar",
Ap.J.,580, 1133, 2002. PDF file (300 KB),gzip PostScript file (1.2 MB)
Wrobel, J. M., Taylor, G. B., and Gregory, P. C., "Phase calibration Sources in the Northern Sky at Galactic Latitudes |b|< 2o.5", A.J. 122, 1669, 2001. PostScript file (1.2 MB)
Gregory, P. C., Capak, P., Gasson,
D., & Scott, W. K., "The GB6 4.85 GHz Radio Variability Catalog",
IAU Symposium 205, 98, 2001, APS Conference Series, eds. R. T. Schilizzi, S. N. Vogel, F. Paresec, & M. S. Elvis,
PostScript file (375 KB)
Gregory, P. C., "A Bayesian Revolution in Spectral Analysis", in
Bayesian Inference and Maximum Entropy
Methods in Science and Engineering, Paris 2000, ed. A. Mohammad-Djafari,
American Institute of Physics Proceedings, 568, 557, 2001.
PDF file (216 KB)
Gregory, P. C., "Bayesian Periodic Signal Detection: Analysis of 20
Years of Radio Flux Measurements of the
X-ray Binary LSI+61o 303", Ap.J.,520, 361-375 (1999). PDF file (258 KB)
Gregory, P. C., Peracaula, M. & Taylor, A. R.,
"Discovery of Periodic Phase Modulation in LSI+61o 303
Radio Outbursts", Ap.J., 520, 376-390 (1999). PDF file (237 KB)
Gregory, P.C., and Loredo, T.J., "Bayesian
Periodic Signal Detection: Analysis of ROSAT Observations of
PSR 0540-693", Ap. J., 473, 1059 (1996). PDF file (155 KB)
Gregory, P.C., Scott, W.K., Douglas, K., and Condon, J.J., “The GB6
Catalog of Radio Sources”, Ap. J.
Supplement, 103, 427 (1996).
Emitting X-ray Binary LSI 61o 303," Astron. & Astrophys. 305, 817 (1996).
Gregory, P.C., and Loredo, T.J., "A New
Method for the Detection of a Periodic Signal of Unknown Shape
and Period", Ap. J., 398, 146 (1992). PDF file (491 KB)
ˇ Useful Bayesian links:
Edwin T. Jaynes
was one of the first people to realize that probability theory, as originated
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