Is it sensible to use estimates of an efficiency which are a little larger than unity, or should unphysical values be excluded?
A question is whether the efficiency has been correctly estimated, in that some procedures cannot yield unphysical values (e.g. binomial procedures of selecting a sample, and then finding the fraction satisfying the requirement). Others however can (e.g. independent Poissons to estimate the total number and the number satisfying the requirement), and we assume that this is the case here. Deciding to reject efficiencies larger than unity while accepting those that are physical will clearly result in a bias if the true efficiency is close to unity. If the ultimate aim of the experiment is to measure the efficiency, there is an argument in favour of using a procedure that keeps the answer physical. However, because it is only a step in determining the quantity of interest, it is better to avoid bias. So it is possible either (i) to use the estimate, even if it is larger than unity; or (ii) to confine it to be physical, but to attempt to estimate the bias that this introduces. This bias, o
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