Table of Contentsįor the discrete case, consider \(N\) different possibilities, e.g.
MAXIMUM ENTROPY HOW TO
Here are some common probability distributions and how to derive them from the principle of maximum entropy. (NB throughout this answer, Im following your usage of as the specified 'mean value' of the energy any casual readers should note that it is not the chemical potential). So even as a way to understand the world, maximum entropy is a very useful and deep tool. 2,382 3 16 26 Add a comment 1 Answer Sorted by: 8 Your target formula 1 /, where is the average energy, is wrong.
Moreover, many physical patterns found in nature tend toward maximum entropy probability distributions. But from an information-theoretic perspective, these will be the least biased prior distributions (we maximize our ignorance) so subsequent experiments a la Bayes’ theorem will maximize the information gained. For me that alone is worth the cost of entry. A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. The cool thing is that these maximum entropy distributions are quite common, so this is a neat way of re-deriving many of the distibutions we encounter day-to-day.
You take a few knowns or constraints, and then maximize information entropy subject to these conditions and voila! you have a unique probability distribution. I think the method of maximum entropy to obtain probability distributions is so cool. This book presents an introduction to the maximum entropy method and some misconceptions about entropy, as well as a review of the literature on X-ray.
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