10 Section 10. Decision analysis
2021-11-15
10.1 Resources
- reading
- BDA3 chapter 9
- reading instructions
- lectures:
- slides:
- Assignment 9
10.2 Notes
10.2.1 Reading instructions
- outline of chapter 9
- 9.1 Context and basic steps (most important part)
- 9.2 Example
- 9.3 Multistage decision analysis (you may skip this example)
- 9.4 Hierarchical decision analysis (you may skip this example)
- 9.5 Personal vs. institutional decision analysis (important)
- the lectures have simpler examples and discuss some challenges in selecting utilities or costs
- ch 7 discusses how model selection con be considered as a decision problem
10.2.2 Chapter 9. Decision analysis
- how can inferences be used in decision making?
- examples in this chapter:
- section 9.2: simple example with hierarchical model on how incentives affect survey response rates
- compare expected response rates of various incentive structures to their expected cost
- section 9.3: option of performing a diagnostic test before deciding on a treatment for cancer
- example of “value of information” and balancing risks of the screening test against the information it would provide
- section 9.4: decision and utility analysis of the risk of radon exposure
- cost of measurement and fixing high exposure
- example of a full integration if inference with decision analysis
9.1 Bayesian decision theory in difference contexts
- use Bayesian inference in two ways when balancing costs and benefits of decision options under uncertainty:
- a decision depends on the predicted quantities which depend on the parameters of the model and type of data
- use Bayesian inference within a decisions analysis to estimate outcomes conditional on information from previous decisions
Bayesian inference and decision trees
- decision analysis involves optimization over decisions and uncertainties
- Bayesian decision analysis is defined as the following steps:
- Enumerate the space of all possible decisions \(d\) and outcomes \(x\).
- Determine the probability distribution of \(x\) for each decision option \(d\).
- Define a utility function \(U(x)\) mapping outcomes onto real numbers (values of interest).
- Compute the expected utility \(\text{E}(U(x)|d)\) as a function of the decision \(d\) and choose the decision with the highest expected utility.
- often, we only do the first two steps and the rest is left to the “decision makers”
10.2.3 Lecture notes
10.1 Decision analysis
(no new notes)