I'm pretty new to Bayesian statistics and I want to use Bayesian regression on a 2D data set (frequency on x-axis and measurement data on the y-axis) to quantify the uncertainties. The model is a simple sum of multiple Gaussians (number of Gaussians = 10) with unknown parameters (amplitude, position, and width of the Gaussians). I am trying my hands on Bayesian Inference for Gaussian mixture models using PyMC3.

I am not sure if this is the right approach to proceed. Any leads on the same would be highly appreciated. Thanks.

  • 2
    $\begingroup$ The term "sum of Gaussians" is ambiguous : the sum of independent Gaussian random variables is yet again a Gaussian random variable. The weighted sum of Gaussian probability densities is a mixture of Gaussian densities and the number of entries on X validated only is enormous. $\endgroup$
    – Xi'an
    Sep 14 at 13:35
  • $\begingroup$ Hey Xi'an, thanks for your comment. However, I am aware that I can use EM-algo to fit the mixture of Gaussians but I tend to focus more on Bayesian side of the problem. Do you think carrying out Bayesian inference on multivariate Gaussian mixtures would be useful in this case? $\endgroup$
    – leo31
    Sep 14 at 14:04

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