Question

I’m trying to figure out the best split of time between measuring either background or signal+background in a counting experiment in the case where we have prior estimates for the signal and background rates and then in the case where we have no prior knowledge about the mean signal count rate. The goal is to get the statistically best measurement of the background-subtracted signal rate.

Assuming we have only a limited time T to perform measurements and there is no timing uncertainty. What’s a good way to approach this problem?

Answer 1

To optimize the measurement in a counting experiment, allocate more time to the component with higher uncertainty. If there is prior knowledge about signal and background rates, allocate more time to measure the component with higher uncertainty. If there is no prior knowledge, allocate equal time to background and signal+background measurements.

Step-by-step explanation:

To determine the best split of time between measuring background or signal+background in a counting experiment, we can use a statistical approach. If we have prior estimates for the signal and background rates, we can optimize the measurement by allocating more time for the component with higher uncertainty. For example, if we have a high level of certainty for the background rate, we can allocate more time to measure the signal+background. On the other hand, if we have no prior knowledge about the mean signal count rate, we can allocate equal time for measuring both background and signal+background, as it gives us the statistically best measurement of the background-subtracted signal rate.