I have a set of 2D positions, obtained by tracking an object with an rgb camera. For various reasons, I want to train a model so that given a new position I can estimate how likely it is that it was generated by the same underlying process as the original set.
I've modeled the distribution as a 2D normal and for the system I'm building it works fine, but I'm being asked to perform a normality test on the set of 2D positions to ensure this is indeed reasonable, or if for example I should be using a GMM.
I've found the Peacock Test for multivariate ks testing. However from what I could understand, it was developed to test two sets of samples come from the same distribution, or to check the fit of a single set of samples to a normal distribution with known parameters ($\mu$ and $\Sigma$).
- How could I test for the hypothesis that it comes from some normal distribution, even if I don't know $\mu$?
- I though about estimating $\mu$ and $\Sigma$ from the datapoints, then generating samples with the estimated parameters for a 2D normal, and performing the peacock test on the two sets of samples (the original and generated). This is intuitive but hardly rigorous.
- Would it be better to use BIC or similar and try to estimate the number of gaussians for a GMM, even if in most cases there would be just a single one?