Bayesian Decision Theory

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: