Before revision: The utility from the optimal decision based only on the prior, without making any further observations, is given by If the decision-maker could gain access to a single sample, , the optimal posterior utility would be : where is obtained from Bayes' rule: Since they don't know what sample would actually be obtained if one were obtained, they must average over all possible samples to obtain the expected utility given a sample: The expected value of sample information is then defined as : Computation It is seldom feasible to carry out the integration over the space of possible observations in E[U|SI] analytically, so the computation of EVSI usually requires a Monte Carlo simulation.
After revision: The utility from the optimal decision based only on the prior, without making any further observations, is given by If the decision-maker could gain access to a single sample, , the optimal posterior utility would be where is obtained from Bayes' rule Since they don't know what sample would actually be obtained if one were obtained, they must average over all possible samples to obtain the expected utility given a sample: The expected value of sample information is then defined as : Computation It is seldom feasible to carry out the integration over the space of possible observations in E[U|SI] analytically, so the computation of EVSI usually requires a Monte Carlo simulation.