Preface Pattern recognition has its origins in engineering,whereas machine learning grew out of computer science.However,these activities can be viewed as two facets of the same field,and together they have undergone substantial development over the past ten years.In particular,Bayesian methods have grown from a specialist niche to become mainstream,while graphical models have emerged as a general framework for describing and applying probabilistic models.Also,the practical applicability of Bayesian methods has been greatly enhanced through the development of a range of approximate inference algorithms such as variational Bayes and expectation propa- gation.Similarly,new models based on kernels have had significant impact on both algorithms and applications. This new textbook reflects these recent developments while providing a compre- hensive introduction to the fields of pattern recognition and machine learning.It is aimed at advanced undergraduates or first year PhD students,as well as researchers and practitioners,and assumes no previous knowledge of pattern recognition or ma- chine learning concepts.Knowledge of multivariate calculus and basic linear algebra is required,and some familiarity with probabilities would be helpful though not es- sential as the book includes a self-contained introduction to basic probability theory. Because this book has broad scope,it is impossible to provide a complete list of references,and in particular no attempt has been made to provide accurate historical attribution of ideas.Instead,the aim has been to give references that offer greater detail than is possible here and that hopefully provide entry points into what,in some cases,is a very extensive literature.For this reason,the references are often to more recent textbooks and review articles rather than to original sources. The book is supported by a great deal of additional material,including lecture slides as well as the complete set of figures used in the book,and the reader is encouraged to visit the book web site for the latest information: http://research.microsoft.com/~cmbishop/PRML viiPreface Pattern recognition has its origins in engineering, whereas machine learning grew out of computer science. However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years. In particular, Bayesian methods have grown from a specialist niche to become mainstream, while graphical models have emerged as a general framework for describing and applying probabilistic models. Also, the practical applicability of Bayesian methods has been greatly enhanced through the development of a range of approximate inference algorithms such as variational Bayes and expectation propa￾gation. Similarly, new models based on kernels have had significant impact on both algorithms and applications. This new textbook reflects these recent developments while providing a compre￾hensive introduction to the fields of pattern recognition and machine learning. It is aimed at advanced undergraduates or first year PhD students, as well as researchers and practitioners, and assumes no previous knowledge of pattern recognition or ma￾chine learning concepts. Knowledge of multivariate calculus and basic linear algebra is required, and some familiarity with probabilities would be helpful though not es￾sential as the book includes a self-contained introduction to basic probability theory. Because this book has broad scope, it is impossible to provide a complete list of references, and in particular no attempt has been made to provide accurate historical attribution of ideas. Instead, the aim has been to give references that offer greater detail than is possible here and that hopefully provide entry points into what, in some cases, is a very extensive literature. For this reason, the references are often to more recent textbooks and review articles rather than to original sources. The book is supported by a great deal of additional material, including lecture slides as well as the complete set of figures used in the book, and the reader is encouraged to visit the book web site for the latest information: http://research.microsoft.com/∼cmbishop/PRML vii