This book gives a clear comprehensive explanation and defense of the Bayesian account of scientific reasoning. It will be read not only by philosophers and theorists of scientific method but also by working scientists, uneasy about the justification of the statistical methods now in use. Since the book is designed to explain to the uninitiated the controversial theories it discusses, it can serve as an introduction to the role of statistics and probability in science. Confronting the problems of induction and the confirmation of scientific theories, Howson and Urbach reject the "objectivist ideal" and the fashionable non-probabilistic standard of scientific worth (Popper, Lakatos, Fisher, Neyman and Pearson). The authors contend that "scientific reasoning is reasoning in accordance with the calculus of probabilities", and (using nothing more advanced that elementary algebra) they give a concise introduction to this calculus. Howson and Urbach examine the way in which scientists actually appeal to probability arguments, and explain the "classical" approach to statistical inference, which they demonstrate to be full of flaws. They then present the Bayesian approach, showing that it avoids the difficulties of the classical system. Finally, they reply to all the major criticisms levelled against the Bayesian method, especially the charge that it is "too subjective".