Phil Gregory, Professor

B.Sc., M.Sc. Queen's (63, 65)
Ph.D., Manchester (69)
Post-doctoral Fellow, Manchester (69-70)
& Toronto (70-71)
Research Associate, Toronto (71-73)

E-mail: gregory `at' physics.ubc.ca

Research Interests

Bayesian Inference in Astronomy

Check out my new text book from Cambridge University Press:
    Bayesian Logical Data Analysis for the Physical Sciences

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).  

Extra-solar Planets

 The discovery of multiple planets orbiting the Pulsar PSR B1257+12 (Wolszczan & Frail, 1992), ushered in an exciting new era of astronomy. Fifteen years later, approximately 200 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.

We have developed (Gregory 2005, 2006 & 2007) a Bayesian MCMC algorithm that makes use of parallel tempering to efficiently explore the full range of model parameter space starting from a random location. It is able to identify any significant periodic signal component in the data that satisfies Kepler's laws, thus functions as a Kepler periodogram. This eliminates the need for a separate periodogram search for trial orbital periods which typical assume a sinusoidal model for the signal that is only correct for a circular orbit. In addition, the Bayesian MCMC algorithm provides full marginal parameters distributions for all the orbital elements that can be determined from radial velocity data. The parallel tempering MCMC algorithm employed in this work includes a control system that automates the selection of efficient Gaussian parameter proposal distributions. This feature makes it practical to carry out 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).

Radio Astronomy

 Current research strongly suggests that supper massive black holes are commonplace at the centers of active galaxies.  The radio images of these galaxies often contain highly collimated jets emanating from the nucleus.  Under high resolution these jets are observed to contain discrete ejecta or plasmons moving at highly relativistic velocities.  An outburst of radio emission is associated with the ejection of each new plasmon, the magnitude of which, is extremely sensitive to the angle between the jet axis and the direction of the observer.  For small angles the relativistic beaming of the radiation can amount to a brightness increase of greater than 105.  Thus radio variability is a powerful diagnostic for detecting super massive black holes with jets close to our line of sight.  They may also be some of the most distant objects observable in the universe.

Here at UBC  we have recently completed (Gregory et al. 2001) the world's largest study of radio source variability, based on a sample of 75,162 radio sources (Check out our online GB6 Radio Variability Catalog). One of the survey variables has been identified as a Be + neutron star binary, with a relativistic jet (a probable microquasar). In a theoretical study we have been developing a new method for mapping the wind structure associated with the Be star using the neutron star as a density and velocity probe (Gregory and Neish 2002).

Down load Newspaper Article on my Daughter's Ph.D. Research on Salmon
    PDF file (1.2 MB)

Recent References

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. PostScript file (3.3 MB),gzip PostScript file (1.2 MB)

Gregory, P. C., "Bayesian Analysis of Radio Observations of the Be X-ray Binary LSI+61o 303",
    Ap.J., 575, 427, 2002. PostScript file (1.6 MB),gzip PostScript file (568 KB)

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.
   gzip PostScript file (576 KB), PostScript file (5.7 MB)

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). PostScript file (362 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). PostScript file (440 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). PostScript file (407 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).

Taylor, A.R., Young, G., Peracaula, M., Kenny, H.T., and Gregory, P.C., "An X-ray Outburst from the Radio
    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). PostScript file (1.1 MB)

·  Useful Bayesian links:

Edwin T. Jaynes was one of the first people to realize that probability theory, as originated by Laplace, is a generalization of Aristotelian logic. This web site was established to help promote this interpretation of probability theory by distributing articles, books and related material.

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