Lectures presented at the XXVI Canary Islands Winter School of Astrophysics, held in La Laguna, Tenerife, Spain, Nov. 3-14, 2014.

Includes bibliographical references and index.

Bayesian methods are being increasingly employed in many different areas of research in the physical sciences. In astrophysics, models are used to make predictions to be compared to observations. These observations offer information that is incomplete and uncertain, so the comparison has to be pursued by following a probabilistic approach. With contributions from leading experts, this volume covers the foundations of Bayesian inference, a description of computational methods, and recent results from their application to areas such as exoplanet detection and characterisation, image reconstruction, and cosmology. It appeals to both young researchers seeking to learn about Bayesian methods as well as to astronomers wishing to incorporate these approaches in their research areas. It provides the next generation of researchers with the tools of modern data analysis that are already becoming standard in current astrophysical research. Contains beginners' how-to guides and advanced computational tools for Bayesian computation giving direct access into Bayesian computations right from the start. Explains both the fundamentals and state-of-the-art applications in astrophysics, appealing to students and researchers of different levels of experience. Covers a wide range of astrophysical applications as real examples for researchers wishing to implement Bayesian tools in their own areas.