Abstract
The diversity of a community that cannot be fully counted must be inferred. The two preeminent inference methods are the MaxEnt method, which uses information in the form of constraints and Bayes’ rule which uses information in the form of data. It has been shown that these two methods are special cases of the method of Maximum (relative) Entropy (ME). We demonstrate how this method can be used as a measure of diversity that not only reproduces the features of Shannon’s index but exceeds them by allowing more types of information to be included in the inference. A specific example is solved in detail. Additionally, the entropy that is found is the same form as the thermodynamic entropy.
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Bibliography
C. E. Shannon, “A Mathematical Theory of Communication”, Bell System Technical Journal, 27, 379 (1948).
E. H. Simpson, “Measurement of Diversity”, Nature, 163, 688 (1949).
R. Guiasu and S. Guiasu, “Conditional and Weighted Measures of Ecological Diversity”, International J. of Uncertainty, 11, 283 (2002).
E. T. Jaynes, Phys. Rev. 106, 620 and 108, 171 (1957); R. D. Rosenkrantz (ed.), E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics (Reidel, Dordrecht, 1983); E. T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press, Cambridge, 2003).
J. E. Shore and R. W. Johnson, IEEE Trans. Inf. Theory IT-26, 26 (1980); IEEE Trans. Inf. Theory IT-27, 26 (1981).
J. Skilling, “The Axioms of Maximum Entropy”, Maximum-Entropy and Bayesian Methods in Science and Engineering, G. J. Erickson and C. R. Smith (eds.) (Kluwer, Dordrecht, 1988).
A. Caticha and A. Giffin, “Updating Probabilities”, Bayesian Infer-ence and Maximum Entropy Methods in Science and Engineering, ed. by Ali Mohammad-Djafari (ed.), AIP Conf. Proc. 872, 31 (2006) (http://arxiv.org/abs/physics/0608185).
A. Giffin and A. Caticha, “Updating Probabilities with Data and Moments”, Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by Kevin Knuth, et all, AIP Conf. Proc. 954, 74 (2007) (http://arxiv.org/abs/0708.1593).
D. S. Sivia, Data Analysis: A Bayesian Tutorial (Oxford U. Press, 1996).
A. Gelman, et al., Bayesian Data Analysis, 2nd edition (CRC Press, 2004).
E. Pielou. Ecological Diversity (Wiley, New York 1975).
A. Giffin, “Updating Probabilities with Data and Moments: An Econo-metric Example”, presented at the 3rd Econophysics Colloquium, Ancona, Italy, 2007 (http://arxiv.org/abs/0710.2912).
A. Giffin, “Updating Probabilities with Data and Moments: A Complex Agent Based Example”, presented at the 7th International Conference on Complex Systems, Boston, 2007.
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Giffin, A. (2012). Inferring Diversity: Life After Shannon. In: Minai, A.A., Braha, D., Bar-Yam, Y. (eds) Unifying Themes in Complex Systems VII. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18003-3_11
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DOI: https://doi.org/10.1007/978-3-642-18003-3_11
Publisher Name: Springer, Berlin, Heidelberg
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