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Chapter 13 The Multivariate Gaussian - People

Chapter 13 The Multivariate GaussianIn this Chapter we present some basic facts regarding the Multivariate Gaussian discuss the two major parameterizations of the Multivariate Gaussian themomentparameterizationand thecanonical parameterization, and we show how the basic operationsof marginalization and conditioning are carried out in thesetwo parameterizations. We alsodiscuss maximum likelihood estimation for the Multivariate ParameterizationsThe Multivariate Gaussian distribution is commonly expressed interms of the parameters and , where is ann 1 vector and is ann n, symmetric matrix. (We will assumefor now that is also positive definite, but later on we will haveoccasion to relax thatconstraint). We have the following form for the density function:p(x| , ) =1(2 )n/2| |1/2exp{ 12(x )T 1(x )},( )wherexis a vector in n.

The multivariate Gaussian distribution is commonly expressed in terms of the parameters µ for now that Σ is also positive definite, but later on we will have occasion to relax that constraint).

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