Maximum Entropy

A major goal of ecology is to predict patterns and changes in the abundance, distribution, and energetics of individuals and species in ecosystems. The maximum entropy theory of ecology (METE) predicts the functional forms and parameter values describing the central metrics of macroecology, including the distribution of abundances over all the species, metabolic rates over all individuals, spatial aggregation of individuals within species, and the dependence of species diversity on areas of habitat. In METE, the maximum entropy inference procedure is implemented using the constraints imposed by a few macroscopic state variables, including the number of species, total abundance, and total metabolic rate in an ecological community. Although the theory adequately predicts pervasive empirical patterns in relatively static ecosystems, there is mounting evidence that in ecosystems in which the state variables are changing rapidly, many of the predictions of METE systematically fail. Here we discuss the underlying logic and predictions of the static theory and then describe progress toward achieving a dynamic theory (DynaMETE) of macroecology capable of describing ecosystems undergoing rapid change as a result of disturbance. An emphasis throughout is on the tension between, and reconciliation of, two legitimate perspectives on ecology: that of the natural historian who studies the uniqueness of every ecosystem and the theorist seeking unification and generality.

An Entropy-Based Machine Learning Algorithm for Combining Macroeconomic Forecasts

This paper applies a Machine Learning approach with the aim of providing a single aggregated prediction from a set of individual predictions. Departing from the well-known maximum-entropy inference methodology, a new factor capturing the distance between the true and the estimated aggregated predictions presents a new problem. Algorithms such as ridge, lasso or elastic net help in finding a new methodology to tackle this issue. We carry out a simulation study to evaluate the performance of such a procedure and apply it in order to forecast and measure predictive ability using a dataset of predictions on Spanish gross domestic product.