By Rohit D•
Jun 19, 2020
Bayesian Statistics: Mixture Models (BS3 for short)
In June 2020, BS3 is a new class. It appears that this class came to Coursera circa April 2020.
The class creators (Prof. Abel Rodriguez and others) have done an excellent job of pulling-together the requisite theory (video lectures) and practice (assignments in R).
For most people, including those with a modest amount of training in statistics or computer science, this class will feel like an advanced class. To reasonably comprehend the material, one needs to be familiar with Monte Carlo simulations (specifically Gibbs Sampling) and a broad spectrum of probability distributions (Poisson, Beta, Gamma, Inverse-Gamma, Log-Normal, Dirichlet) used in Bayesian statistics. The first two Bayesian Statistics classes cover most of these pre-requisites well.
BS3 delves into two ways of estimating mixtures, namely Expectation-Maximization (EM) and Gibbs sampling, and comparing results from the alternate approaches. BS3 does not stop at a "Gaussian Mixture of two Univariate distributions." Through its assignments, this class motivates the need for other mixture models such as zero-inflated Poisson distribution, a mixture of exponential and Log-Normal distribution, and a mixture of multivariate Gaussian distributions.
Some assignments require manipulation of hierarchical probability distributions using multiple techniques - Maximum Likelihood Estimation, detecting Conjugate Priors, Simulations - simultaneously. Since the manipulations are coded in R and need to achieve a numerical result, typos and algebraic manipulation errors are unforgiving.
The class organizers chose to have graded assignments (six in all) peer-reviewed. The peer review requirement can feel like a constraint for a class that is relatively new and advanced, and thus has low attendance.
It took me ~60 hours to complete this class over approximately two weeks. Ideally, I would have preferred to spread the course out over the recommended five-weeks. Life constraints dictated otherwise. Even so, the effort is well worth it. I am walking away with a much better appreciation of Bayesian Statistics in general and Mixture Models in particular.