This book provides a multi-level introduction to Bayesian reasoning (as opposed to “conventional statistics”) and its applications to data analysis. The basic ideas of this “new” approach to the quantification of uncertainty are presented using examples from research and everyday life. Applications covered include: parametric inference; combination of results; treatment of uncertainty due to systematic errors and background; comparison of hypotheses; unfolding of experimental distributions; upper/lower bounds in frontier-type measurements. Approximate methods for routine use are derived and are shown often to coincide — under well-defined assumptions! — with “standard” methods, which can therefore be seen as special cases of the more general Bayesian methods. In dealing with uncertainty in measurements, modern metrological ideas are utilized, including the ISO classification of uncertainty into type A and type B. These are shown to fit well into the Bayesian framework.Contents: Critical Review and Outline of the Bayesian Alternative:Uncertainty in Physics and the Usual Methods of Handling ItA Probabilistic Theory of Measurement UncertaintyA Bayesian Primer:Subjective Probability and Bayes' TheoremProbability Distributions (A Concise Reminder)Bayesian Inference of Continuous QuantitiesGaussian LikelihoodCounting ExperimentsBypassing Bayes' Theorem for Routine ApplicationsBayesian UnfoldingFurther Comments, Examples and Applications:Miscellanea on General Issues in Probability and InferenceCombination of Experimental Results: A Closer LookAsymmetric Uncertainties and Nonlinear PropagationWhich Priors for Frontier Physics?Conclusion:Conclusions and BibliographyReadership: Graduate students and researchers interested in probability and statistics and their applications in science, particularly the evaluation of uncertainty in measurements.