By Giovanni Parmigiani, Lurdes Inoue
Choice thought presents a proper framework for making logical offerings within the face of uncertainty. Given a collection of choices, a suite of effects, and a correspondence among these units, selection thought deals conceptually easy techniques for selection. This booklet provides an summary of the elemental suggestions and results of rational choice making below uncertainty, highlighting the consequences for statistical practice.The authors have built a chain of self contained chapters concentrating on bridging the gaps among the various fields that experience contributed to rational determination making and providing rules in a unified framework and notation whereas respecting and highlighting the various and infrequently conflicting perspectives.This book:Provides a wealthy selection of suggestions and procedures.Discusses the foundational elements and modern-day practice.Links foundations to sensible purposes in biostatistics, machine technology, engineering and economics.Presents diversified views and controversies to motivate readers to shape their very own opinion of selection making and statistics.Decision concept is prime to all medical disciplines, together with biostatistics, desktop technology, economics and engineering. someone attracted to the whys and wherefores of statistical technology will locate a lot to get pleasure from during this ebook.
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Extra resources for Decision Theory: Principles and Approaches (Wiley Series in Probability and Statistics)
Savage (1954) comments on an exchange between Gabriel Cramer and Daniel Bernoulli’s uncle Nicholas Bernoulli on this issue: Daniel Bernoulli’s paper reproduces portions of a letter from Gabriel Cramer to Nicholas Bernoulli, which establishes Cramer’s chronological priority to the idea of utility and most of the other main ideas of Bernoulli’s paper. . Cramer pointed out in his aforementioned letter, the logarithm has a serious disadvantage; for, if the logarithm were the utility of wealth, the St.
Several statistics books have good chapters on decision-theoretic topics. Excellent examples are Schervish (1995) and Robert (1994), both very rigorous and rich in insightful examples. Bernardo and Smith (1994) is also rich in foundational discussions presented in the context of both statistical inference and decision theory. French (1988), Smith (1987), and Bather (2000) cover decision-analytic topics very well. Kreps (1988) is an accessible and very insightful discussion of foundations, covered in good technical detail.
The birthplace of utility theory is usually considered to be St. Petersburg. In 1738, Daniel Bernoulli, a Swiss mathematician who held a chair at the local Academy of Science, published a very influential paper on decision making (Bernoulli 1738). Bernoulli analyzed the behavior of rational individuals in the face of uncertainty from a Newtonian perspective, viewing science as an operational model of the human mind. His empirical observation, that thoughtful individuals do not necessarily take the financial actions that maximize their expected monetary return, led him to investigate a formal model of individual choices based on the direct quantification of value, and to develop a prototypical utility function for wealth.