VOI is a measure of how much observing something changes your action if you are a rational agent.

The value of information a measure for how much observing an additional variable is expected to **increase** our utility. VOI can never be negative, and does not take into account the **COST** of performing the observation.

## constituents

- \(o\): an observation
- \(O’\): a possible observation to run which yield \(o’_{j}\) different outcomes

## requirements

\begin{equation} VOI(O’|o) = (\sum_{o’} P(o’|o) EU^{*}(o, o’)) - EU^{*}(o) \end{equation}

where, \(EU^{*}(o_{1} \dots o_{n})\) is the maximum expected utility given observations \(o_1, …, o_{n}\), that is:

\begin{equation} EU^{*}(o_1, \dots, o_{n}) = \max_{a} EU(o_1, \dots, o_{n}) \end{equation}

“the value of an observation is the sum of the MEU of each possible outcome from that new observation, time their probability of occurance, subtracted by the MEU of the current observation”

## additional information

### process of observation selection

Here’s how you would select what variables to observe.

- make observation
- determine value of information of anything you haven’t observed yet
- select the next feature to observe
- repeat 1-3
- wait until its no longer beneficial to observe any more variables
- make decision based on observations

This is not the true optimum: its only a heuristic!