This is a power-type calculation for a Bernoulli/binomial question in two stages.

Suppose you are planning an experiment which starts with a test for an event on $N$ experimental units. The event occurs with probability $p$ and you first record the number of times it occurs, $n \in \{ 0, 1, 2, \ldots, N \}$.

Suppose further that the full experiment can only continue if the number or events is less or equal to some limit $n_L$, that is $n \le n_L$.

The probability of being able to carry out the full experiment will thus depend on the probability of a single event $p$ which we can estimate independently in a separate experiment by a sequence of Bernoulli trials.

How may Bernoulli trials is this initial separate experiment, and with what results, would we need to ensure a $1-\beta$ chance of having $n \le n_L$ in the full experiment? Is there a simple way of doing this? Is there a sequential testing framework I could use?

Working forward is easy from a Bayesian prior of $p \sim Beta(1,1)$ to $Pr(n \le n_L)$ but it would be nice to have a way of working backwards.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.