chapter seven

7 From inference to choice: Howard Raiffa, Robert Schlaifer, and the Bayesian revolution

This chapter covers

Raiffa and Schalifer’s Applied Statistical Decision Theory (1961) and the birth of modern Bayesian decision analysis
How Bayes’ Theorem evolved into a framework for rational choice under uncertainty
The structure of decisions under uncertainty, expressed through decision trees
Key concepts such as expected utility, opportunity loss, and the value of information
The enduring influence of Raiffa and Schlaifer on decision science, economics, and artificial intelligence

Two centuries after Thomas Bayes’ An Essay Towards Solving a Problem in the Doctrine of Chances, the problem of reasoning under uncertainty remained incomplete. Bayes had shown how evidence could update belief—how an observation could shift our confidence in competing causes of a single effect—but he left open the question that ultimately matters most: once we have updated our beliefs, what action should we take—or not take?

7.1 Revisiting Bayes: From Posterior Probabilities to Rational Action

7.1.1 From posterior probability to expected utility

7.1.2 Decision trees: visualizing choice under uncertainty

7.1.3 The value of information

7.2 The decision framework of Raiffa and Schlaifer

7.2.1 Structure of decision problems

7.2.2 The expected utility formulation

7.2.3 Terminal versus preposterior analysis

7.2.4 Synthesis and enduring impact

7.3 Opportunity loss, regret, and expected utility

7.3.1 From utility to loss

7.3.2 The intuition of regret

7.3.3 From regret to refinement

7.4 Conjugate priors and computable Bayesian learning

7.3.4 From algebraic burden to reusable structure

7.3.5 Conjugacy as a design principle

7.3.6 Worked example: Beta-Binomial updating

7.4 The enduring value of a rational framework

7.4.1 Decision analysis as a managerial discipline

7.4.2 Decision architecture in AI

7.4.3 Enduring value and modern applications

7.4.4 Closing reflection: from belief to action

7.5 Summary