Sensitivity Analysis in Bayesian Classification Models: Multiplicative Deviations

The sensitivity of Bayesian pattern recognition models to multiplicative deviations in the prior and conditional probabilities is investigated for the two-class case. Explicit formulas are obtained for the factor K by which the computed posterior probabilities should be divided in order to eliminate the deviation effect. Numerical results for the case of binary features indicate that the Bayesian model tolerates large deviations in the prior and conditional probabilities. In fact, the a priori ratio and the likelihood ratio may deviate within a range of 65-135 percent and still produce posterior probabilities in accurate proximity of at most ±0.10. The main implication is that Bayesian systems which are based on limited data or subjective probabilities are expected to have a high percentage of correct classification despite the fact that the prior and conditional probabilities they use may deviate rather significantly from the true values.