Example of how Shannon’s formula measures information - Wenglish Outcomes that are very unexpected give us more information, while expected outcomes give us little information. Remember that we are thinking of probability distributions as being due to human ignorance. Information is quantified using the Shannon measure, which says that the information contained in an observation is given by: The Shannon entropy gives the average information that we expect to obtain from sampling the distribution. The principle of maximum entropy tells us how to extend the principle of indifference to such cases.īy entropy, we mean the Shannon entropy of the distribution: But what about if we know some information about \(P(x)\) such as the average or variance of the distribution? This tells us how to assign a prior if we have zero knowledge of a distribution like \(P(x)\). This may be the case, but if we are ignorant of reasons, we cannot say that one outcome will be more likely than any other. This principle says that if we have no reason for suspecting one outcome over any other, than all outcomes must be considered equally likely. Jakob Bernoulli called this the “principle of insufficient reason”, a play on the “principle of sufficient reason”, which asserts that everything must have a reason or cause. If we don’t have any prior knowledge, then the obvious solution is to use the principle of indifference. Bayesian inference machine learning python How do we assign priors?
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