chapter seven

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

 

This chapter covers

  • Raiffa and Schlaifer’s Applied Statistical Decision Theory (1961) and how it extended Bayesian inference into a framework for rational decision-making
  • How posterior probabilities and subjective utilities combine to govern optimal decisions
  • How decision trees structure and clarify choices under uncertainty
  • How expected utility, opportunity loss, and value of information are used to evaluate and compare alternative actions
  • Why Raiffa and Schlaifer’s framework continues to shape decision science, economics, and artificial intelligence

Two centuries after Thomas Bayes published An Essay Towards Solving a Problem in the Doctrine of Chances, the problem of reasoning under uncertainty remained incomplete. Bayes showed how evidence updates belief—how an observation changes the probability assigned to competing explanations through what is now called Bayes’ Theorem. But this framework stops at inference. It answers what is likely, not what should be done.

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

7.4.1 From algebraic burden to reusable structure

7.4.2 Conjugacy as a design principle

7.4.3 Worked example: Beta-Binomial updating

7.5 The enduring value of a rational framework

7.5.1 Decision analysis as a managerial discipline

7.5.2 Decision architecture in AI

7.5.3 Enduring value and modern applications

7.5.4 Closing reflection: from belief to action

7.6 Summary