Bayes' Theorem Logo

Probability Theory as Extended Logic Local Reference List

"Scientific inference is concerned, necessarily, not with empty assertions of 'objectivity' but with information processing; how to extract the best conclusions possible from the incomplete information available to us."

E.T. Jaynes, in Commentary on Two Articles by C.A. Los

I have set up this web page in order to make available to the Dě collaboration some papers I have found to useful in my study of probability theory.

If you know of other papers available online which you consider important, please let me know; I'll add them to the list. Especially useful are web sites with new material. Note that I have not included many references to the literature; this page is intended merely as a guide to online resources. For an excellent annotated bibliography, see Jaynes's book.


Downloadable Books and Papers:

This is just a small subset of what is available on the web. I have found these to be especially clear and cogent introductions to the subject.

E. T. Jaynes, "Probability Theory: The Logic of Science"

Jaynes's masterpiece, still under construction. This is the  major work in this field. Jaynes has graciously made it available, in TeX or PostScript form, before publication. It can be retrieved from the Web from the Washington University (St. Louis) ftp server. They are GZIPed tar archives. Please note that these are LARGE files; the book (in the last version I printed out) is about 2 inches thick. If you'd like to see a copy, before downloading the whole thing, come to my office in PK 173, room 22. You can download the book in one of three forms; PostScript, TeX source, or DVI file.

G. Larry Bretthorst, "Bayesian Spectrum Analysis and Parameter Estimation"

This is an enlargement of Bretthorst's thesis. This book was published by Springer-Verlag, but is now out of print. Springer-Verlag has allowed Bretthorst to distribute it in electronic form. You can obtain the PostScript (compressed) from the ftp site at <ftp://bayes.wustl.edu/pub/Bretthorst/book>, or you can get the Adobe PDF.

T. J. Loredo "From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics"

64 pages. This is an excellent introduction, covering everything from the definition of probability to examples of parameter estimation and model comparison. Includes a critique of frequentist statistics, noting when and why it works, and when and why it fails. It is certainly not only of interest to astrophysicists. It also contains an excellent example of the study of a source strength of a Poisson process, in the presence of a background source: what we call cross section measurements in the presence of background. PostScript here. DVI file here.


Probability Theory as Extended Logic Web Sites

Probability Theory As Extended Logic

Located at Washington University, St. Louis. This site is home to Jaynes's book, as well as a number of other papers, some of which are included in the lists above. This WUSTL web site can be found at http://bayes.wustl.edu.

International Society for Bayesian Analysis

The ISBA web site can be found at http://www.bayesian.org.

Data Understanding Group (previously Bayesian Model-Based Learning Group)

This is the home page of a group at the NASA Ames Research Center. It contains links for a few of their interesting projects. They are located at http://ic-www.arc.nasa.gov/ic/projects/bayes-group.


Local Documents and Notes

These are some very short notes written by Dě collaborators.

Iain Bertram, G. Landsberg, R. Partridge, M. Paterno, H.B. Prosper, and J. Linnemann, "A Recipe for the Construction of Confidence Limits" -- D0 Note 2775a

This is (so far) the "official" D0 recipe for the construction of cross section limits. As the title states, this note contains only the recipe, and nothing in the way of explanation why this is the way to do it. Get the DVI file here. Get the PostScript file here. Note that the authors are reconsidering one aspect of the suggested recipe, specifically the use of a truncated gaussian to represent the knowledge of efficiencies. This is an adequate approximation for those cases in which the fractional error in the efficiency is small (less than 20-30%), but is a poor approximation when the fractional error in the efficiency is large.

Marc Paterno, "Calculating Efficiencies and Their Uncertainties" -- D0 Note 2861

This is a note which gives the details of the calculation of an efficiency, given no prior information (other than that the efficiency is between 0%and 100%) and given data of k events passing, out of a total N events examined. Get the DVI file here. Get the PostScript file here. A C++ program that performs the calculation discussed in the note is also available, as a gzipped tar file. Please note that the GNUmakefile assumes the use of the KAI C++ compiler (and gmake, of course). The program is simple enough that the makefile really is not necessary.

Harrison Prosper, "Poisson Signal on a Gaussian Background: A Failure of Orthodox confidence intervals"

This is a Mathcad document (in RTF form) that analyses the calculation of cross section confidence intervals from the Orthodox point of view, and which includes a description of when and why they fail to satisfy their own criteria. Get it here. You need an RTF viewer to read this file. You can get the PostScript version here.

Marc Paterno, "Calculating an Upper Limit on a Branching Fraction"

This is a Mathcad document (in RTF form or PostScript form) that sketches the calculation of an upper limit on the branching fraction for a rare decay mode (top -> charm + photon).

Harrison Prosper, "Statistical Issues in Data Analysis", lectures at the NATO/ASI St. Croix Summer School, 1996

This is a series of four lectures given by Prof. Harrison Prosper. It is available in HTML and PDF form.

Lecture 1: Basic Notions and Orthodox Statistics (html)
Lecture 2: A Word or Two About Errors (html)
Lecture 3: The World According To The Rev. Thomas Bayes (html)
Lecture 4: Data Analysis (html)
All lectures in one file (PDF)


This page is maintained by Marc Paterno paterno@fnal.gov

It was last modified 12/10/98 07:55 AM.