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Imagine I have a set of measures and I want to model my data as a multivariate normal distribution. For every measure I have a different mean vector and covariance matrix. So, how can I be sure about what are the parameters that fit better my data? Do I have to compute the log-likelihood for every set of parameters and see when this is minimum?

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You can't compute log-likelihood's for each pair of $(\mu, \Sigma)$ since both of those parameters are real numbers, so both can take infinite number of possible values (even if you had multiple discrete-valued parameters, it might not be possible to use brute-force search in a limited time). Assuming that you don't have a closed form solution for finding the optimal parameters, otherwise you would need an optimizer (see Wikipedia article on optimization), i.e. a black-box function that takes your function and returns an optimal set of parameters.

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  • $\begingroup$ I have a set of multiple measures and I want to model this data as multidimensional gaussian, but the problem arises because I don't know what mean and covariance matrix use. Is there any function in matlab that could do this? $\endgroup$ – Moltimor Aug 14 '17 at 10:48
  • $\begingroup$ @Moltimor I don't know Matlab and such question would be off-topic in here, but I'm sure that Matlab has to have implemented optimization algorithms (otherwise it would be useless for most of the applications). $\endgroup$ – Tim Aug 14 '17 at 10:50

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