Archive for Augustus de Morgan

Théorie analytique des probabilités

Posted in Books, Statistics, University life with tags , , , , , , on March 26, 2012 by xi'an

The Brazilian society for Bayesian Analysis (ISBrA, whose annual meeting is taking place at this very time!) asked me to write a review on Pierre Simon Laplace’s book, Théorie Analytique des Probabilités, a book that was initially published in 1812, exactly two centuries ago. I promptly accepted this request as (a) I had never looked at this book and so this provided me with a perfect opportunity to do so, (b) while in Vancouver, Julien Cornebise had bought for me a 1967 reproduction of the 1812 edition,  (c) I was curious to see how much of the book had permeated modern probability and statistics or, conversely, how much of Laplace’s perspective was still understandable by modern day standards. (Note that the link on the book leads to a free version of the 1814, not 1812, edition of the book, as free as the kindle version on amazon.)

Je m’attache surtout, à déterminer la probabilité des causes et des résultats indiqués par événemens considérés en grand nombre.” P.S. Laplace, Théorie Analytique des Probabilités, page 3

First, I must acknowledge I found the book rather difficult to read and this for several reasons: (a) as is the case for books from older times, the ratio text-to-formulae is very high, with an inconvenient typography and page layout (ar least for actual standards), so speed-reading is impossible; (b) the themes offered in succession are often abruptly brought and uncorrelated with the previous ones; (c) the mathematical notations are 18th-century, so sums are indicated by S, exponentials by c, and so on, which again slows down reading and understanding; (d) for all of the above reasons, I often missed the big picture and got mired into technical details until they made sense or I gave up; (e) I never quite understood whether or not Laplace was interested in the analytics like generating functions only to provide precise numerical approximations or for their own sake. Hence a form of disappointment by the end of the book, most likely due to my insufficient investment in the project (on which I mostly spent an Amsterdam/Calgary flight and jet-lagged nights at BIRS…), even though I got excited by finding the bits and pieces about Bayesian estimation and testing. Continue reading