The term “decision analysis” has multiple meanings in Bayesian statistics. When we use the term here, we are not talking about problems of parameter estimation, squared error loss, etc. Rather, we use “decision analysis” to refer to the solution of particular decision problems (such as in medicine, public health, or business) by averaging over uncertainties as estimated from a probability model. (See here for an example.)

That said, decision analysis has fundamental difficulties, most notably that it requires one to set up a utility function, which on one hand can be said to represent subjective feelings but on the other hand is presumably solid enough that it is worth using as the basis for potentially elaborate calculations.

From a foundational perspective, this problem can be resolved using the concept of *institutional decision analysis*.

**Personal vs. institutional decision analysis**

Statistical inference has an ambiguous role in decision making. Under a “subjective” view of probability (which I do not generally

find useful; see Chapter 1 of Bayesian Data Analysis), posterior inferences represent the personal beliefs of the analyst, given his or her prior information and data. These can then be combined with a subjective utility function and input into a decision tree to determine the optimal decision, or sequence of decisions, so as to maximize subjective expected utility. This approach has serious drawbacks as a procedure for personal decision making, however. It can be more difficult to define a utility function and subjective probabilities than to simply choose the most appealing decision. The formal decision-making procedure has an element of circular reasoning, in that one can typically come to any desired decision by appropriately setting the subjective inputs to the analysis.

In practice, then, personal decision analysis is most useful when the inputs (utilities and probabilities) are well defined. For example, in a decision problem of the costs and benefits of screening for cancer, the utility function is noncontroversial–years of life, with a slight adjustment for quality of life–and the relevant probabilities are estimated from the medical literature. Bayesian decision analysis then serves as a mathematical tool for calculating the expected value of the information that would come from the screening.

In institutional settings–for example, businesses, governments, or research organizations–decisions need to be justified, and formal decision analysis has a role to play in clarifying the relation between the assumptions required to build and apply a relevant probability model and the resulting estimates of costs and benefits.

We introduce the term “institutional decision analysis” to refer to the process of transparently setting up a probability model, utility function, and an inferential framework leading to cost estimates and decision recommendations. Depending on the institutional setting, the decision analysis can be formalized to different extents.

In general, there are many ways in which statistical inferences can be used to inform decision-making. The essence of the “objective” or “institutional” Bayesian approach is to clearly identify the model assumptions and data used to form the inferences, evaluate the reasonableness and the fit of the model’s predictions (which include decision recommendations as a special case), and then expand the model as appropriate to be more realistic. The most useful model expansions are typically those that allow more information to be incorporated into the inferences.

Further discussion and several examples appear in Chapter 22 of “Bayesian Data Analysis.”

David K. Park commented:

couple of q's:

– you say that institutional decision analysis refers to process of transparently setting up a probability model, utility function, but isn't the personal decision analysis as transparent. you may disagree w/their probability model and utility function, but isn't it just as explicit as the institutional model.

– how does decision analysis handle strategic behavior of the individual, or institutionss? more generally, how where does decision analysis and game theory intersect? is decision analysis purely for non-strategic behavior?

Andrew commented:

in response to David:

1. Yes, personal and institutional decision analysis have the same mathematical structure. The difference is that in the institutional version, models and utilities must be justified in some way (whether by scientific argument or by a negotiation or political process), whereas in personal decision analysis, one can just retreat to the tautology of "personal preferences."

For example, in evaluate public health interventions, one can make institutional decisions based on a specified value of dollars per life, or dollars per qaly (quality-adjusted-life-years). The value for dollars per qualy has an arbitrariness to it, and it may be set by negotiation, but it can be used as a standard when evaluating a range of potential risks and interventions. On a personal level, however, the qaly calculation won't work so well since we have different tolerances for risk in different settings. Which doesn't leave so much room for decision analysis.

The point of the "institutional" idea is to think like an institution that needs to justify its choices to various "stakeholders." An institution cannot simply say "this is my taste" and shortcut the decision-making process.

2. Decision theory can be viewed as a special case of game theory when all the other players are deciding at random. In settings with a lot of other "players," I think decision theory makes sense, since my decision won't really be affecting what others will do. When others are behaving strategically, then game theory makes more sense. To me, it's usually clear, in any particular example, what is the right model to use.