Value of Information

[andersrm]

I've created an influence diagram and am trying to compute value of information associated with the Node "Downstream Water Clarity". The VOI would be computed in "value" or "utility" units. When the value of this node is known with certainty, the decision changes; yet, VOI is computed as zero. Does someone know why?

[shooltz[BayesFusion]]

I can't really answer your question - I don't have the theoretical background on VOI calculation. Unfortunately, the person who could help won't be available until the end of the month. However, I examined the internals of our VOI code. The output is calculated in the following way, using the copy of the original model:

1. add single decision node D
2. add arc from D to POV node
3. add arc from D to single chosen utility node (any will do)
4. run inference and get P1 = matrix of policy values for D
5. add arcs from each of the selected chance nodes to selected decision node
6. run inference and get P2 = matrix of policy values for D
7. P2 = P2 - P1
8. decrease the last dimension size of P2; P2 is then the VOI output

In your case (assuming that only 'Downstream Water Clarity' is selected) step 5 is a no-op, because adding an arc would result in a cycle. P1 is equal to P2 and VOI is zero.

I also tested the VOI on 'Oyster Density'. This chance node can be connected to 'Harvest' or 'Initial Ref Height', so step 5 works, but the VOI output is also zero

[andersrm]

Actually, your response answered most of my questions. The one remaining is: does GeNIe compute VOI for nonlinear utility/value functions?

[shooltz[BayesFusion]]

The one remaining is: does GeNIe compute VOI for nonlinear utility/value functions?

Yes.

[andersrm]

The one remaining is: does GeNIe compute VOI for nonlinear utility/value functions?

Yes.

Actually, I doubt this. Remember that for a nonlinear utility/value function, you cannot simply take the difference of the utilities and infer VOI. Can GeNIe compute certainty equivalents? For a utility function with constant risk aversion, this could provide the answer.

[marek [BayesFusion]]

The one remaining is: does GeNIe compute VOI for nonlinear utility/value functions?

Yes.

Actually, I doubt this. Remember that for a nonlinear utility/value function, you cannot simply take the difference of the utilities and infer VOI. Can GeNIe compute certainty equivalents? For a utility function with constant risk aversion, this could provide the answer.

I believe that Tomek was right. Why would the form of the utility function have any impact on the VOI calculation? GeNIe does not have CE computation built in -- you will have to do it outside of the program. Do you find CE of any value outside of its obvious theoretical appeal? It is easy to demonstrate on a single-attribute utility curve, but less straightforward on a MAU function and not that straightforward to compute exactly, I think, as you need the reverse of the utility function. Cheers,

Marek

[andersrm]

The reason is that VOI is calculated as the difference between the expected utility or expected monetary value of the information-gathering alternative (info) and the non-info gathering alternative (no_info). For linear value functions, which are equivalent to expected monetary value this difference can be calculated directly. However, if the value functions are non-linear, then CE(u(info - no_info)) is not equal to CE(u(info)) - CE(u(no_info)). So, you cannot simply compute CE for the different alternatives separately and subtract. Instead, you must determine a "cost" such that the utiility of the info alternative reduces until it equates to the utility of the no_info alternative. The "cost" is your VOI.

[marek [BayesFusion]]

The reason is that VOI is calculated as the difference between the expected utility or expected monetary value of the information-gathering alternative (info) and the non-info gathering alternative (no_info). For linear value functions, which are equivalent to expected monetary value this difference can be calculated directly. However, if the value functions are non-linear, then CE(u(info - no_info)) is not equal to CE(u(info)) - CE(u(no_info)). So, you cannot simply compute CE for the different alternatives separately and subtract. Instead, you must determine a "cost" such that the utiility of the info alternative reduces until it equates to the utility of the no_info alternative. The "cost" is your VOI.

I see. If you want to express VOI on the same scale as the original value, you need to be able to go back from utility to the value. You are right in that is indeed quite easy to compute in the risk-neutral case. I'm afraid we have no immediate plans for adding this computation to GeNIe , unless, of course a student is very interested in this or we get some kind of research or development grant that will finance this .
Cheers,

Marek