Recovering Decay Rates from Noisy Measurements with Maximum Entropy in the Mean

We present a new method, based on the method of maximum entropy in the mean, which builds upon the standard method of maximum entropy, to improve the parametric estimation of a decay rate when the measurements are corrupted by large level of noise and, more importantly, when the number of measurements is small. The method is developed in the context on a concrete example: that of estimation of the parameter in an exponential distribution. We show how to obtain an estimator with the noise filtered out, and using simulated data, we compare the performance of our method with the Bayesian and maximum likelihood approaches.