Some hot topics of maximum entropy research in economics and statistics

Maximum entropy is often used for solving ill-posed problems that occur in diverse areas of science (e.g., physics, informatics, biology, medicine, communication engineering, statistics and economics). The works of Kullback, Leibler, Lindley and Jaynes in the fifties of the last century were fundamental to connect the areas of maximum entropy and information theory with statistical inference. Jaynes states that the maximum entropy principle is a simple and straightforward idea. Indeed, it provides a simple tool to make the best prediction (i.e., the one that is the most strongly indicated) from the available information and it can be seen as an extension of the Bernoulli's principle of insufficient reason. The maximum entropy principle provides an unambiguous solution for ill-posed problems by choosing the distribution of probabilities that maximizes the Shannon entropy measure. Some recent research in regularization (e.g., ridGME and MERGE estimators), variable selection (e.g., normalized entropy with information from the ridge trace), inhomogeneous large-scale data (e.g., normalized entropy as an alternative to maximin aggregation) and stochastic frontier analysis (e.g., generalized maximum entropy and generalized cross-entropy with data envelopment analysis as an alternative to maximum likelihood estimation) will be presented, along with several real-world applications in engineering, medicine and economics.