Given a profit matrix, we can calculate an optimal policy for decision-making. In general, we should grant a loan if and only if the expected profit from granting is greater than the expected profit from refusing. Clearly the task of data mining is now to estimate the probability p that a person would repay a loan. But in general the costs and benefits will be different for different individuals and we really need a classifier that gives actual probabilities. Unfortunately there are no known data mining methods that directly give realistic probabilities in a reliable way.
Many classifiers give numerical scores to examples.
For example, a naive Bayesian classifier gives numbers between 0 and 1. These numbers are accurate probabilities if the assumption of conditional independence is true, but almost always this assumption is false. Luckily, naive Bayesian scores are empirically correlated positively with true probabilities. A higher score corresponds usually to a higher probability. Therefore, it is possible in principle to find a transformation function that is monotonic increasing and that maps a naive Bayesian score to a true probability approximately.