Foreword

In 1814, Pierre-Simon Laplace wrote, “Life’s most important questions are, for the most part, nothing but probability problems.” For well over a hundred years after that, the only way to answer such questions (while remaining true to the dictum) was to analyze each problem with pen and paper, obtain a formula for the result, and evaluate the formula by plugging in the numbers by hand. The advent of computers did not change this very much. It simply meant that more-complicated formulas could be evaluated, with more numbers, and the pen-and-paper analyses became more ambitious, often stretching to hundreds of pages.

The analysis of a probability problem requires the formulation of a probability model that lays out the space of possibilities and, in some fashion, assigns a numerical probability to each of them. In the past, probability models were written down using a combination of natural language text and semi-formal mathematical notation. From the model, a formula or algorithm for calculating answers was derived by further mathematical manipulation. Each of these stages was laborious, error-prone, and problem-specific, placing severe practical limits on the applicability of probability theory. Despite Laplace, life’s most important questions remained unanswered.