CHAPTER XIV. 



BAYES. 



589. The name of Bayes is associated with one of the most 

 important parts of our subject, namely, the method of estimating 

 the probabihties of the causes by which an observed event may 

 have been produced. As we shall see, Bayes commenced the in- 

 vestigation, and Laplace developed it and enunciated the general 

 principle in the form which it has since retained. 



540. We have to notice two memoirs which bear the fol- 

 lowing titles : 



An Essay towards solving a Prohlem in the Doctrine of Chances. 

 By the late Rev. Mr. Bayes^ F.R.S. communicated hy Mr Price in a 

 Letter to John Canton^ A.M. F.R.S. A Demonstration of the Second 

 Rule in the Essay towards the Solution of a Prohlem in the Doctrine of 

 Chances, published in the Philosoi')hical Transactions, Vol. liii. Com- 

 municated hy the Rev. Mr. Richard Price, in a Letter to Mr. John 

 Canton, M. A. F.R.S. 



The first of these memoirs occupies pages 870 — 418 of Vol. Liii. 

 of the Philosophical Transactions ; it is the volume for 1763, and 

 the date of publication is 1764. 



The second memoir occupies pages 296 — 825 of Vol. Liv. of the 

 Philosophical Transactions; it is the volume for 1764, and the 

 date of publication is 1765. 



541. Bayes proposes to establish the following theorem : If 



