Bayesian Decision Theory

Marcel van Oijen

Chapter Chapter 19 in Bayesian Compendium, 2024, pp 157-164 from Springer

Abstract: Abstract Risk analysis (Chap. 18 ) is useful to summarise the implications of predictive uncertainty for risk, but for decision-making a wider framework is required, Bayesian decision theory (BDT) (Berger, Statistical decision theory and Bayesian analysis (2nd ed.). Springer Series in Statistics. Springer, 1985; Jaynes, Probability theory: The logic of science. Cambridge University Press, 2003; Lindley, Making decisions (2nd ed.). Wiley, 1991; Van Oijen and Brewer, Probabilistic Risk analysis and Bayesian decision theory, SpringerBriefs in Statistics. Springer International Publishing, 2022; Williams and Hooten (Ecol Appl 26:1930–1942, 2016). In BDT, every decision problem has three main ingredients: 1. A list or continuum of possible actions a ∈ A $$a \in A$$ : exactly one action is to be decided upon. 2. A list or continuum of possible external conditions x ∈ X $$x \in X$$ . These are uncertain, so we have p [ x ] $$p[x]$$ , possibly p [ x | a ] $$p[x|a]$$ . 3. A utility function u ( a , x ) $$u(a,x)$$ that can be evaluated for every combination of a and x.

Date: 2024
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DOI: 10.1007/978-3-031-66085-6_19

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