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This is the first book on the maximum entropy and Bayesian methods aimed at senior undergraduates in science and engineering. It takes the mystery out of statistics by showing how a few fundamental rules can be used to tackle a wide variety of problems in data analysis. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. Other topics covered include reliability analysis, multivariate optimization, least squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy, and experimental design. As a logical and unified approach to the subject of data analysis, with a self-contained tutorial approach, this work will be valued by instructors and students alike.