Born in London as the son of a Nonconformist minister, I eventually enrolled in the University of Edinburgh where my studies focused on logic and theology.

I became a Presbyterian minister in Tunbridge Wells, but also dabbled in mathematics.

I was the first to use probability inductively, which led to my establishing a mathematical basis for probability inference (i.e. a technique for calculating, from the number of times an event has not occured, the probability that it will occur in future trials).

I published only two works in my lifetime, a religious tome and An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst, which was a defense of Isaac Newton's calculus against the criticism of philosopher George Berkeley.

A posthmous publication solved an "inverse probability" problem and contained a statement of the Theorem that is now my eponym.