DAG - Bayesian mixture of Gaussians

#1
Dear all,

as a part of a theoretical homework I should draw a graphical model for bayesian inference of a mixture of gaussians. Besides this I should make sure that the model is in the exponential family such that Gibbs sampling and Variational Bayesian inference can be applied.

What does this mean? Can someone pls explain to me in an easy way what's the theoretical background behind this question?

Additionally I should identify the conjugate exponential family distributions for univariate and multivariate gaussians.
How should I start solving this question?
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
DAGs are a way to draw out hypothesized relationships between variables. They are likely asking you to draw out the data generating process between the Gaussian mixture and the dependent variable you are modeling.
 
#3
Thanks for your fast reply. So, of course I basically know what DAGs are and how they look like.
But from this job description, how do I know which variables do I have/are need? Where should I know from, how they are related to each other?

I saw a low of examples but in all these examples they had concrete values and situation like the relationship between e.g. weather and mood.
Here it is only written 'a mixture of gaussians'. Thats my biggest problem.
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
What are you self-studying from - text? I have not ran a mixture or variational Bayes myself yet. They are on my never ending list of things to review that I haven't gotten to. I would be interest in how you are trying to figure this stuff out.

Perhaps when McElreath releases his 2022 Winter lectures, that may be a good introduction.
 
#7
We got some lecture slides but they are very generic and consist mostly of formulars and key words which we can search for.
Thanks a lot for the hint, I will go more into detail in this topic for sure but at the moment I am running out of time as I should hand in a solution for this task until wednesday.