level: research
value-of-information analysis typically assumes a single probability measure. but real evidence often only narrows things down to a set of possible measures. this paper looks at how to handle that imprecision. it introduces two main ideas. one is a rule-specific value of information that fixes a decision rule for acting under imprecision, like gamma-maximin. this measures what information is worth to someone using that rule. the other is a fixed-measure envelope that evaluates the classical value-of-information functional over all admissible precise measures.
the paper explains the difference between these two approaches. it also works out what they mean for expected perfect, partial, and sample information. a key finding is that the expected value of perfect information is concave over the credal set. when the set comes from a finite number of measures, the lower endpoint of the envelope is exactly given by those generators. the upper endpoint may need more work to find.
this work gives a formal way to do value-of-information analysis when probabilities are not precise. it shows how to get bounds on the value of information by looking at the whole set of possible measures. the results can help decision makers who face uncertainty about probabilities. they can see how much information is worth under different rules for dealing with imprecision.
why it matters: it provides a method to quantify the worth of data when probabilities are uncertain, which is common in real-world ai and data science decisions.