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According to the theorem, in making inferences on the basis of partial information, we must use the probability distribution which has maximum entropy subject to whatever is known.
The main modeling method used was MAXENT, a machine-learning method that estimates a species' distribution across a study area by calculating the probability distribution of maximum entropy subject to the constraint that the expected value of each feature under this estimated distribution should match its empirical average [50].
Given a set of records of species occurrences and values of selected environmental variables defined over a chosen geographical region, Maxent predicts the distribution of species in that space by finding the distribution of maximum entropy subject to the constraint that the expectation of the distribution of each species matches its observed average over the sample locations [11].
Niche models were generated using the Maxent algorithm [ 80], which estimates a target probability distribution by finding the probability distribution of maximum entropy subject to a set of constraints that represent the incomplete information about the target distribution [ 81].
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The paper presents a distribution free method for estimating the quantile function of a non-negative random variable using the principle of maximum entropy (MaxEnt) subject to constraints specified in terms of the probability-weighted moments estimated from observed data.
The main assumption is that the incomplete empirical probability distribution (determined by occurrence data) can be approximated with a probability distribution of maximum entropy (the Maxent distribution) subject to certain environmental constraints, and that this distribution approximates the potential geographic distribution of the group of interest [56].
The software finds the distribution that is closest to uniform, or of maximum entropy, within the study area, and it does so subject to the constraints imposed by variations in the environmental variables at the species' occurrence localities [ 35].
The proposed model, named hidden maximum entropy model (HMEM), estimates a distribution that maximizes entropy subject to multiple moment-based constraints.
The goal of Maxent is to estimate a probability distribution for species' occurrences by finding the distribution of maximum entropy (i.e., closest to uniform), subject to constraints defined by the environmental features being analyzed [21].
Maxent is also a machine-learning method that estimates a probability distribution for species' occurrences by finding the distribution of maximum entropy (that which is closest to uniform), subject to constraints defined by the environmental parameters input into the model [34].
It estimates species' distributions by finding the distribution of maximum entropy (i.e. closest to uniform) subject to the constraint that the expected value of each environmental variable (or its transform and/or interactions) under the distribution matches its empirical average [ 34].
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