Mathematics

Decision Theory: Principles and Approaches by Giovanni Parmigiani, Lurdes Inoue

By Giovanni Parmigiani, Lurdes Inoue

Selection concept presents a proper framework for making logical offerings within the face of uncertainty. Given a collection of choices, a collection of results, and a correspondence among these units, choice idea bargains conceptually easy techniques for selection. This e-book provides an outline of the basic thoughts and results of rational choice making lower than uncertainty, highlighting the consequences for statistical practice.

The authors have built a chain of self contained chapters targeting bridging the gaps among the various fields that experience contributed to rational selection making and providing principles in a unified framework and notation whereas respecting and highlighting different and infrequently conflicting perspectives.

This book:
• presents a wealthy selection of options and procedures.
• Discusses the foundational points and modern-day practice.
• hyperlinks foundations to sensible purposes in biostatistics, machine technology, engineering and economics.
• offers varied views and controversies to inspire readers to shape their very own opinion of determination making and statistics.

Decision Theory is prime to all medical disciplines, together with biostatistics, machine technology, economics and engineering. someone drawn to the whys and wherefores of statistical technology will locate a lot to take pleasure in during this e-book.

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Extra info for Decision Theory: Principles and Approaches

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One of your clients is especially concerned about tree damage (θ1 ) and flood damage (θ2 ). In order to state the policies he is asked to elicit (personal) rates for the following events: θ1 , θ2 , θ1 | θ2 , and θ2 | θ1 . 9 Show that your client can be made a sure loser. 3 Utility Broadly defined, the goal of decision theory is to help choose among actions whose consequences cannot be completely anticipated, typically because they depend on some future or unknown state of the world. Expected utility theory handles this choice by assigning a quantitative utility to each consequence, a probability to each state of the world, and then selecting an action that maximizes the expected value of the resulting utility.

1 15 The “Dutch Book” theorem Betting odds De Finetti’s theory of subjective probability is usually described using the metaphor of betting on the outcome of an as yet unknown event, say a sports event. This is a stylized situation, but it is representative of many simple decision situations, such as setting insurance premiums. The odds offered by a sports bookmaker, or the premiums set by an insurance company, reflect their judgment about the probabilities of events. So this seems like a natural place to start thinking about quantification of uncertainty.

However, in the lottery example, we could work out properties of the relevant frequencies on the basis of plausible approximations of the physical properties of the draw, such as independence and equal chance. With patients, that is not so straightforward, and we would have to rely on observed populations. Patients in a population are more different from one another than repeated games of the lottery, and differ in ways we may not understand. To trust the applicability of observed relative frequencies to our decision we have to introduce an element of judgment about the comparability of Decision Theory: Principles and Approaches G.

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