## Decision Theory: Principles and ApproachesDecision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice. The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decision making and presenting ideas in a unified framework and notation while respecting and highlighting the different and sometimes conflicting perspectives. This book: * Provides a rich collection of techniques and procedures. * Discusses the foundational aspects and modern day practice. * Links foundations to practical applications in biostatistics, computer science, engineering and economics. * Presents different perspectives and controversies to encourage readers to form their own opinion of decision making and statistics. Decision Theory is fundamental to all scientific disciplines, including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book. |

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action additional admissible alternative Analysis Applications approach assume Axiom Bayes Bayes rule Bayesian called Chapter choice choose coherence complete computing condition consider continuous cost decision maker decision problem decision rule define definition denote depends discussion distribution Edition equation equivalent error estimator evaluate event example expected loss expected utility experiment experimental Figure forecaster formal given gives hypothesis illustrate implies independent interested loss function lottery mean measure Methods minimax nature observed obtain optimal outcome parameter patients perfect information positive possible posterior prediction preferences principle prior probability proof Prove provides random reasonable relation represented requires respect result risk sample Savage scoring rule Second selected sequential shows simple solution specific stage Statistical stopping subjective Suppose Table Theorem theory unknown utility function variables