Rethinking Maximum Likelihood

This paper argues that Maximum Likelihood Estimation (MLE) is the wrong approach for parameter estimation, both conceptually and in its results. We propose a new estimation method, called PLE, that offers four benefits over MLE: 1) PLE produces less biased estimates of the true parameters 2) PLE reduces overfitting 3) PLE more fairly represents minority (low-frequency) data and 4) PLE is more resilient to MAD collapse. We show how these benefits result from PLE's incorporation of counterfactual samples.