In decision theory, the expected value of sample information (EVSI) is the expected increase in utility that a decision-maker could obtain from gaining access to a sample of additional observations before making a decision. The additional information obtained from the sample may allow them to make a more informed, and thus better, decision, thus resulting in an increase in expected utility. EVSI attempts to estimate what this improvement would be before seeing actual sample data; hence, EVSI is a form of what is known as preposterior analysis. The use of EVSI in decision theory was popularized by Robert Schlaifer and Howard Raiffa in the 1960s.

Let

It is common (but not essential) in EVSI scenarios for ${\displaystyle Z_{i}=X}$, ${\displaystyle p(z|x)=\prod p(z_{i}|x)}$ and ${\displaystyle \int zp(z|x)dz=x}$, which is to say that each observation is an unbiased sensor reading of the underlying state ${\displaystyle x}$, with each sensor reading being independent and identically distributed.

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, ${\displaystyle z}$, the optimal posterior utility would be

where ${\displaystyle p(x|z)}$ 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