A Bayesian "posterior distribution" or "predictive distribution" summarizes everything you need to know about an unknown parameter, or future observations. This unique book shows how to use Bayesian statistical techniques in a sound and practically relevant manner. It will guide the reader on inferring scientific, medical, and social conclusions from numerical data. The authors explain the subtle assumptions needed for Bayesian methodology and show how to use them to obtain good-quality conclusions. The methods also perform remarkably well in terms of computer-simulated frequency properties. The lively introductory chapter on Fisherian methods (the frequency approach), 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. A chapter on advances in utility theory, and several sections on time series and forecasting, makes the text also suitable for quantitative economics students. The other chapters contain material on the linear model, categorical data analysis, survival analysis, random-effects models, and nonlinear smoothing. The book contains numerous worked examples, self-study exercises, and practical applications. It provides essential reading for final-year undergraduates, Masters-degree and graduate students, statisticians, and other interdisciplinary researchers wishing to develop good-quality conclusions from their data and to pursue the notion of scientific truth.