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In Bayesian statistics a prior distribution formalizes information or knowledge (often subjective), available before a sample is seen, in the form of a probability distribution. A distribution with large spread is used when little is known about the parameter(s), while a more narrow prior distribution represents a greater degree of information.

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Normal-inverse-Wishart distribution

One application is the Gibbs Sampling from a Dirichlet Process mixture model, where a conjugate prior is required. See page 33 of the pdf below https://www.cs.cmu.edu/~kbe/dp_tutorial.pdf …
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