This is a history of the use of Bayes theoremfrom its discovery by Thomas Bayes to the rise of the statistical competitors in the first part of the twentieth century. The book focuses particularly on the development of one of the fundamental aspects of Bayesian statistics, and in this new edition readers will find new sections on contributors to the theory. In addition, this edition includes amplified discussion of relevant work.

The modern theory of Sequential Analysis came into existence simultaneously in the United States and Great Britain in response to demands for more efficient sampling inspection procedures during World War II. The develop ments were admirably summarized by their principal architect, A. Wald, in his book Sequential Analysis (1947). In spite of the extraordinary accomplishments of this period, there remained some dissatisfaction with the sequential probability ratio test and Wald's analysis of it. (i) The open-ended continuation region with the concomitant possibility of taking an arbitrarily...

One of the main reasons we cannot tell what the weather will be tomorrow is that we do not know accurately enough what the weather is today. Mathematically speaking, numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear partial differential equations in which the necessary initial values are known only incompletely and inaccurately. Data at the initial time of a numerical forecast can be supplemented, however, by observations of the atmos- phere over a time interval preceding it. New observing systems, in particular polar-orbiting and geostationary...

Given a series of wind speeds and directions from the port of Fremantle the aim of this monograph is to detect general weather patterns and seasonal characteristics. To separate the daily land and sea breeze cycle and other short-term disturbances from the general wind, the series is divided into a daily and a longer term, synoptic component. The latter is related to the atmospheric pressure field, while the former is studied in order i) to isolate particular short-term events such as calms, storms and oscillating winds, and ii) to determine the land and sea breeze cycle which dominates the...

This book attempts to present the concepts which underlie the various optimization procedures which are commonly used. It is written primarily for those scientists such as economists, operations researchers, and en gineers whose main tools of analysis involve optimization techniques and who possess a (not very sharp) knowledge of one or one-and-a-half year's calculus through partial differentiation and Taylor's theorem and some acquaintance with elementary vector and matrix terminology. Such a scientist is frequently confronted with expressions such as Lagrange multi pliers, first-and...

Ptolemy's Almagest shares with Euclid's Elements the glory of being the scientific text longest in use. From its conception in the second century up to the late Renaissance, this work determined astronomy as a science. During this time the Almagest was not only a work on astronomy; the subject was defined as what is described in the Almagest. The cautious emancipation of the late middle ages and the revolutionary creation of the new science in the 16th century are not conceivable without reference to the Almagest. This text lifted European astronomy to the high standard of knowledge on which...

When I first laid out the framework for A History of Ancient Mathe- matical Astronomy, I intended to carry the discussion down to the last applications of Greek astronomical methodology, i. e. Copernicus, Brahe, and Kepler. But as the work proceeded, it became evident that this plan was much too ambitious, and so I decided to terminate my History with late antiquity, well before Islam. Nevertheless, I did not discard the running commentary that I had prepared when studying De revolutionibus in its relation to the methodology of the Almagest. Only recently, E. S. Kennedy and his collaborators...

It would seem that S. Munk was the first modern scholar to draw attention to the significance of Levi ben Gerson's Astronomy, surely the most original work on astronomy written in Hebrew in the Middle Ages. Munk (1859, p. 500) called for a specialist to undertake a serious study of this work, but there was little response to his plea in the succeeding century. Indeed, this is the first edition of the Hebrew text of any part of Levi's Astronomy but for the table of contents (Renan, 1893, pp. 624-32), and the poems celebrating the invention of the Jacob Staff that appear in chapter 9...

Kepler's Physical Astronomy is an account of Kepler's reformulation of astronomy as a physical science, and of his successful use of (incorrect) physics as a guide in his astronomical discoveries. It presents the only reliable account of the internal logic of Kepler's so-called first and second laws, showing how and to what extent Kepler thought he had derived them from his physical principles. It explains for the first time Kepler's attempt to use an obscure discovery of Tycho Brahe to unify and confirm all of his own physical theories. It also describes the intricate (and neglected)...

The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last...