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This book describes the Bayesian approach to statistics at a level suitable for final year undergraduate and Masters students. It is unique in presenting Bayesian statistics with a practical flavor and an emphasis on mainstream statistics, showing how to infer scientific, medical, and social conclusions from numerical data. The authors draw on many years of experience with practical and research programs and describe many new statistical methods, not available elsewhere. A first chapter on Fisherian methods, together with a strong overall emphasis on likelihood, makes the text suitable for mainstream statistics courses whose instructors wish to follow mixed or comparative philosophies. The other chapters contain important sections relating to many areas of statistics such as the linear model, categorical data analysis, time series and forecasting, mixture models, survival analysis, Bayesian smoothing, and non-linear random effects models. The text includes a large number of practical examples, worked examples, and exercises. It will be essential reading for all statisticians, statistics students, and related interdisciplinary researchers.