Sunday, August 5, 2007

Assorted on Probablity and Statistics

Probability Theory With Applications in Science and Engineering by E. T. Jaynes

Materials for the History of Statistics

Thomas Bayes, F.R.S.: A biography to celebrate the tercentenary of his birth

PROBABILITY THEORY: THE LOGIC OF SCIENCE

Venn Diagrams

How Euler Did it

An Intuitive Explanation of Bayesian Reasoning;
Q. Who originally discovered Bayes' Theorem?
A. The Reverend Thomas Bayes, by far the most enigmatic figure in mathematical history. Almost nothing is known of Bayes's life, and very few of his manuscripts survived. Thomas Bayes was born in 1701 or 1702 to Joshua Bayes and Ann Carpenter, and his date of death is listed as 1761. The exact date of Thomas Bayes's birth is not known for certain because Joshua Bayes, though a surprisingly wealthy man, was a member of an unusual, esoteric, and even heretical religious sect, the "Nonconformists". The Nonconformists kept their birth registers secret, supposedly from fear of religious discrimination; whatever the reason, no true record exists of Thomas Bayes's birth. Thomas Bayes was raised a Nonconformist and was soon promoted into the higher ranks of the Nonconformist theosophers, whence comes the "Reverend" in his name.

In 1742 Bayes was elected a Fellow of the Royal Society of London, the most prestigious scientific body of its day, despite Bayes having published no scientific or mathematical works at that time. Bayes's nomination certificate was signed by sponsors including the President and the Secretary of the Society, making his election almost certain. Even today, however, it remains a mystery why such weighty names sponsored an unknown into the Royal Society.

Bayes's sole publication during his known lifetime was allegedly a mystical book entitled Divine Benevolence, laying forth the original causation and ultimate purpose of the universe. The book is commonly attributed to Bayes, though it is said that no author appeared on the title page, and the entire work is sometimes considered to be of dubious provenance.

Most mysterious of all, Bayes' Theorem itself appears in a Bayes manuscript presented to the Royal Society of London in 1764, three years after Bayes's supposed death in 1761!

Despite the shocking circumstances of its presentation, Bayes' Theorem was soon forgotten, and was popularized within the scientific community only by the later efforts of the great mathematician Pierre-Simon Laplace. Laplace himself is almost as enigmatic as Bayes; we don't even know whether it was "Pierre" or "Simon" that was his actual first name. Laplace's papers are said to have contained a design for an AI capable of predicting all future events, the so-called "Laplacian superintelligence". While it is generally believed that Laplace never tried to implement his design, there remains the fact that Laplace presciently fled the guillotine that claimed many of his colleagues during the Reign of Terror. Even today, physicists sometimes attribute unusual effects to a "Laplacian Operator" intervening in their experiments.

In summary, we do not know the real circumstances of Bayes's birth, the ultimate origins of Bayes' Theorem, Bayes's actual year of death, or even whether Bayes ever really died. Nonetheless "Reverend Thomas Bayes", whatever his true identity, has the greatest fondness and gratitude of Earth's scientific community.


Bayesians Worldwide - Personal Web Pages

Multimedia;
Imaginary Numbers

From BBC, In Our Time;
The Calendar - a history of the Calendar
Infinity - a brief history.

Zero - everything about nothing
Pi - the number that doesn't add up
Prime Numbers - the building blocks of mathematics
Negative numbers - how they spread across civilizations

Renaissance Maths - the birth of modern mathematics?

Mathematics and Music - the science behind sound and composition

1 comment:

Anonymous said...

thank you very much for that Bayes link