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A false positive would be a case, for example, in which a decision is made that
mitigation action is needed, when in fact it is not. A false negative would be a case where a mitigation action is not triggered, when in fact it should have been. It can be proven mathematically that,
on the average, more and better data will result in lower false positive and false negative error rates when the decision rule optimizes the expected costs of the outcome. In other words, on the average the costs of the consequences of wise risk management will be lower if the input information is better.
The cost-benefit analysis of the value of the additional information hinges on whether the direct cost of obtaining that information is larger or smaller than the cost savings expected from its use in a decision process that relies on the results of a risk assessment based on that information.