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?
Asked
Active
Viewed 278 times
1 Answers
1
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.
Tim
- 108,699
- 20
- 212
- 390
-
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? – Moltimor Aug 14 '17 at 10:48
-
@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). – Tim Aug 14 '17 at 10:50