Interpreting null results from measurements with uncertain correlations: an info-gap approach

Null events—not detecting a pernicious agent—are the basis for declaring the agent is absent. Repeated nulls strengthen confidence in the declaration. However, correlations between observations are difficult to assess in many situations and introduce uncertainty in interpreting repeated nulls. We quantify uncertain correlations using an info-gap model, which is an unbounded family of nested sets of possible probabilities. An info-gap model is nonprobabilistic and entails no assumption about a worst case. We then evaluate the robustness, to uncertain correlations, of estimates of the probability of a null event. This is then the basis for evaluating a nonprobabilistic robustness-based confidence interval for the probability of a null.