Selected Papers

I've just started working on this part of my website, so only a few papers are listed below. If I have time I may put up some others for which I've had significant numbers of requests and which are not otherwise available on the web. To retrieve a fairly complete bibliography of my publications, click here. This information is provided to you courtesy of NASA's Astrophysics Data System (ADS). The papers retrieved in this way do not include articles published in non-astronomical journals, nor those published in most proceedings of conferences, workshops, etc. Nor, of course, will it include articles that have not yet appeared in print.

Papers on Astronomy

Here is a link to my Atlas of Surfaces of Section for the Restricted Problem of Three Bodies, now available on the web after being out of print for several years.

"Statistics for twenty-first century astrometry," charts for my invited Eichhorn Memorial Lecture delivered at the Fifth Alexander von Humboldt Colloquium, Bad Hofgastein, Austria, on March 20, 2000. Download PDF File of charts (312kB) and PDF File of T Mon results (2.3 MB). Also, the paper as submitted to the proceedings: Download Postscript File (1.3 MB) or PDF File (548 kB).

"Calibration of the Hubble Space Telescope fine guidance sensors: An application of seminal ideas of H. K. Eichhorn," invited paper presented at the International Colloquium on Modern Astrometry and Astrophysics, honoring Heinrich Eichhorn, Vienna, 1998 May 25-26. Download Postscript File (488kB) or PDF File (260kB)

"New results on the Cepheid distance scale," by Thomas G. Barnes, III and William H. Jefferys. This is a continuation of the work described in the following paper. It was presented as a poster paper at the "Harmonizing Cosmic Distance Scales in a Post-Hipparcos Era" meeting held in Strasbourg, France 14-16 September, 1998 (I'm getting the details from Tom, who actually went to the meeting). Download Postscript File (33kB) or PDF File (33kB). There are five figures, unfortunately available only as separate downloads. Download Postscript (each 33kB): Figures 1, 2, 3, 4, 5 or PDF (each 33kB): Figures 1, 2, 3, 4, 5.

Papers on Statistics

"Bayesian Analysis of RR Lyrae Distances and Kinematics" by Jefferys, Jefferys and Barnes. This is a presentation that was given at ISBA 2004 in Vina del Mar, Chile, and at the Canadian Statistical Society meeting in Montreal, 2004. PDF File (724 KB) or Postscript File (5 MB).

"Bayes's Theorem," a review of a collection of papers from a meeting held at the British Academy. Download PDF File (92 KB).

"Model Selection for Cepheid Star Oscillations", by William H. Jefferys, Thomas G. Barnes, III, and Raquel Rodrigues (U Texas) and James O. Berger and Peter Müller (Duke University). Invited paper given at the meeting of the International Society for Bayesian Analysis, Hersonissos, Crete, May 28-June 2, 2000. Further research on Bayesian model selection and model averaging. Download Postscript File (1.1 MB) or PDF File (408 kB).

"Bayesian Model Selection and Model Averaging, With Applications to the Cepheid Distance Scale" (talk given at UT Stellar Astronomy seminar, 10/13/99, reporting on research being done with Tom Barnes, Jim Berger and Peter Müller, the latter two of Duke University). Download Postscript File (515kB) or PDF File (260kB).

"Bayesian analysis of cepheid variable data," by William H. Jefferys and Thomas G. Barnes, III. We investigate Bayesian analysis as a tool for understanding velocity and photometric data for the determination of the zero-point of the Cepheid period-luminosity relationship. The principal question addressed in this paper is determining the best representation of the velocity curve without overfitting. This paper was presented at the Sixth Valencia International Meeting on Bayesian Statistics, Alcossebre, Spain, May 30-June 4, 1998, and was accepted to appear in the proceedings. Download Postscript File (423kB) or PDF File (130kB).

"Bayesian analysis of lunar laser ranging data," by William H. Jefferys and Judit Gyorgyey Ries, describes a new approach for finding the very small number of actual laser returns from a retroreflector placed on the Moon amongst the very large number of "noise" photons present in the background. It uses a Markov Chain Monte Carlo (MCMC) method to marginalize the nuisance variables. This paper was an invited paper at the Statistical Challenges in Modern Astronomy II conference held at Penn State University in June, 1996 and will be found in the proceedings volume on pp. 49-65 (including a discussion by Steven F. Arnold of Penn State University). Download Postscript File (1453kB) or PDF File (308kB). The postscript file is extra-long because of several large figures. You can also download a shortened version of the Postscript File (248kB) without the three large figures.

"Discussion by William H. Jefferys of Michael Akritas' paper, 'Astronomical (heteroskedastic) measurement errors: Statistical issues and problems," which also appeared in the Statistical Challenges in Modern Astronomy II proceedings volume (1996). This shows how some of the problems noted in Professor Akritas' paper are solved naturally by a Bayesian approach that cannot result in the ambiguities and incorrect results that the frequentist method is prone to. Download Postscript File (119kB) or PDF File (73kB).

"On p-values and chance" and "Further comments on p-values and chance" were two letters to the editor published in Journal of Scientific Exploration, 9, pp. 121-122 and 595-597 (1995). They point out a commonly held misconception on the nature of p-values. Bob Jahn and York Dobyns, of the Princeton PEAR lab, wrote responses to each of these letters; in my opinion, they reveal a lack of understanding on the part of the PEAR team, of exactly the nature I pointed out in these letters. Download Postscript File (32kB) or PDF File(17kB).

"Sharpening Ockham's razor on a Bayesian strop," by William H. Jefferys and James O. Berger. Ockham's Razor, an established principle used every day in science, has deep connections with Bayesian reasoning, which traces directly back to Sir Harold Jeffreys' pioneering work on statistics during the 1920s and 30s. In this paper we shall explore the connection between Ockham's Razor and Bayesian statistics, and present an objective quantification of Ockham's Razor. Download Postscript File (384kB) or PDF File (260kB). This paper is a Purdue University technical report which was later published in edited form and with a different title in American Scientist (89, 64-72, January 1992). A more technical version appears in "The application of robust Bayesian analysis to hypothesis testing and Occam's Razor," by James O. Berger and W.H. Jefferys, Journal of the Italian Statistical Society 1, 17-32 (1992). I do not have a postable version of the latter paper.

"Bayesian Analysis of Random Event Generator Data," by William H. Jefferys. Journal of Scientific Exploration, 4, pp. 153-169 (1990). This paper gives a real-life example of the statistical phenomenon of the Jeffreys-Lindley "paradox," wherein a (near)-point null hypothesis may be rejected by a classical (frequentist) hypothesis test with a very small p-value at the same time that a Bayesian test convinces us that the null hypothesis is almost certainly true. It is also an example of the Bayesian Ockham's Razor (see the Jefferys/Berger work above). The example is taken from the parapsychological literature, and in my opinion demonstrates that certain claims made in the parapsychological literature are not nearly as strong as claimed. Download Postscript File (429kB) or PDF File (120kB). York Dobyns, of the PEAR group where the research that produced this example was done, responded in an article in Journal of Scientific Exploration, 6, no. 1 (1992). I published a response to that article in "Response to Dobyns", which appeared in the same issue of Journal of Scientific Exploration, 6, pp. 47-57 (1992). Download Postscript File (165kb) or PDF File (227kb).

"Robust estimation when more than one variable per equation of condition has error," by William H. Jefferys. Develops a robust errors-in-variables procedure with equality constraints that is embodied in the GaussFit software (below). The refereed version appeared in Biometrika, 77, 3, pp. 597-607 (1990) and can be read at Download Postscript File (163kB) or PDF File (98kB).

"GaussFit---A system for least squares and robust estimation," by W.H. Jefferys, M.J. Fitzpatrick, and B.E. McArthur, describes our very easy-to-use program for solving such problems. It has a number of unique features, including a complete programming language for expressing estimation problems, a built-in compiler and interpreter to support the programming language, and a built-in algebraic manipulator for calculating the required partial derivatives analytically. It can handle heteroskedastic nonlinear models with equality constraints, and errors-in-variables problems where more than one observation appears in an equation of condition. This was an invited talk at the 18th meeting of the Division on Dynamical Astronomy of the American Astronomical Society. Download Postscript File (98kB) or PDF File (65kB). The refereed paper appeared in Celestial Mechanics, 41 (1988), 39-49. Copies of the software for UNIX or Macintosh platforms can be retrieved from the Hubble Space Telescope Astrometry Science Team website.

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