Expected value of sample information

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.

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.

...
Wikipedia