A learning distributed detection system is investigated. It is comprised of a bank of local detectors and a data fusion center (DFC). Each local detector chooses one of two hypotheses on the basis of collected measurements to minimize a local Bayesian cost. The data fusion center combines the local decisions into a central decision with the objective of minimizing a centralized Bayesian cost. The optimal decision rules require that the local detectors and the DFC know the a priori probabilities of the hypotheses. The DFC should also know the probabilities of false alarm and missed detection for each local detector. These, however, are often unknown. In this study recursive estimators are developed that approximate the probabilities on line. The estimators are based on the evaluation of the unconditional and conditional means of the local and central decisions (conditioned on the hypothesis). Bias correction is applied to the estimates to account partially for the fact that all decision-makers in the system are occasionally erroneous. For ’ignorant’ distributed detection systems in low signal-to-noise ratios, the bias reduction is shown to significantly improve the overall detection performance.