Before revision: The utility from the optimal decision based only on your prior, without making any further observations, is given by If you could gain access to a single sample, , the optimal posterior utility would be: where is obtained from Bayes' rule: Since you don't know what sample would actually be obtained if you were to obtain a sample, you 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.