This exposition of the Bayesian approach to statistics at a level suitable for final year undergraduate and Masters students is unique in presenting its subject with a practical flavor and an emphasis on mainstream statistics. It shows 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. It will be essential reading for all statisticians, statistics students, and related interdisciplinary researchers.