决策理论与方法4_（Decision theory and method 4_）.docVIP

决策理论与方法4_（Decision theory and method 4_） Chapter 4 bayesian analysis Bayesean Analysis § 4.0 introduction 1. Table representation of decision - loss matrix No observation (No - data) problem a = delta Alternative decision tree (loss matrix) can be used to describe the consequences of decision making (loss) : ... ... PI () ... PI () ... PI () or PI () ... PI () ... PI () ... ... The loss matrix is intuitive and convenient Ii. Decision principles Usually, the decision rule delta is chosen according to some principle, and the result is optimal (or satisfactory), and this principle is called decision making The decision principle of bayesian analysis, however, is to make the expected utility extremely high. This chapter introduces bayesian analysis before introducing her decision The principle. Iii. Classification of decision-making problems: 1. Indeterminate form (non-deterministic) The state of nature is uncertain and the probabilities of various states cannot be estimated. 2. The type of risk The natural state is uncertain, but the probabilities of various states can be estimated. Four, press the state better: Or less? I, at least for some I strict inequality, says that the action is better than the state § 4.1 uncertain decision problems 1. Principle of wald (rule, criterion) L (,) or Ex. : 10 8 7 9 4 one 9 2 13 16 12 14 6 9 8 10 The biggest loss of action: 13, 16, 12, 14 The smallest loss corresponds to action. Those who adopt this principle are extremely conservative and pessimistic, believing that god always opposes himself. Two, minimum minimization L () or Ex. : 10 8 7 9 4 one 9 2 13 16 12 14 6 9 8 10 Minimize loss of action: 4, 1, 7, 2 The smallest loss is action. The principle is an extreme risk, an optimist, who thinks it will always be good. Hurwitz guidelines The last two methods of compromise, take the optimism coefficient in [lambda l (,) + (1 - lambda) l (,)] For example, lambda = 0.5 Lambda: 2.53.5 1 (1 - lambda) : 6.5, 8, 6, 7 The sum of the two: 8.5,