The Principle of Maximum Entropy
<p>When we toss a die the observed result can range between 1 and 6. Suppose that we are given a die and we are told that it was tossed multiple times yielding an average of 4.7 rather than 3.5 that someone would expect from a fair regular symmetrical die. <strong>Given this information how one should update their beliefs about each side occurring in a single toss?</strong></p>
<p>In the case of a regular die with probability 1/6 of each side occurring, we would expect the count histogram to look something like this:</p>
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