Assume the following problem: You're deciding whether to invest into an opportunity with uncertain cost $c$ and value $v$. The cost has been estimated to be normally distributed with 90% CI between 1 and 5 million. Similarly, the value has been estimated to be normally distributed with 90% CI between 1 and 20 million. The default decision is to invest. However, you're interested in finding the value of reducing the uncertainty about both the cost and value in order to be certain about your decision.
I intuitively understand that here we're after the Expected Value of Perfect Information or $EVPI$ which is equal to the potential loss in case we take the wrong decision.
Questions:
- How do we represent the problem above mathematically? Intuitively, I would write something like: $EVPI=\int_c\int_v(v-c)p(c)p(v)$
- How do we solve the problem for a generic case? Is MCMC or a simple Monte Carlo a good choice here?
I would prefer a layman-level answer as I'm not very strong with stats.