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→A more complex example: Remove dispute tag (see talk page Equation correctness for explanation) + add comma |
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==A more complex example==
[[File:bayesian-gaussian-mixture-vb.svg|right|300px|thumb|Bayesian Gaussian mixture model using [[plate notation]]. Smaller squares indicate fixed parameters; larger circles indicate random variables. Filled-in shapes indicate known values. The indication [K] means a vector of size ''K''; [''D'',''D''] means a matrix of size ''D''×''D''; ''K'' alone means a [[categorical variable]] with ''K'' outcomes. The squiggly line coming from ''z'' ending in a crossbar indicates a ''switch'' — the value of this variable selects, for the other incoming variables, which value to use out of the size-''K'' array of possible values.]]
Imagine a Bayesian [[Gaussian mixture model]] described as follows:<ref name=bishop/>
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*SymDir() is the symmetric [[Dirichlet distribution]] of dimension <math>K</math>, with the hyperparameter for each component set to <math>\alpha_0</math>. The Dirichlet distribution is the [[conjugate prior]] of the [[categorical distribution]] or [[multinomial distribution]].
*<math>\mathcal{W}()</math> is the [[Wishart distribution]], which is the conjugate prior of the [[precision matrix]] (inverse [[covariance matrix]]) for a [[multivariate Gaussian distribution]].
*Mult() is a [[multinomial distribution]] over a single observation (equivalent to a [[categorical distribution]]). The state space is a "one-of-K" representation, i.e., a <math>K</math>-dimensional vector in which one of the elements is 1 (specifying the identity of the observation) and all other elements are 0.
*<math>\mathcal{N}()</math> is the [[Gaussian distribution]], in this case specifically the [[multivariate Gaussian distribution]].
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