Probabilistic Modelling Tutorial Series
Self-Directed Tutorial Series, GitHub (Open Access), 2022
Developed and published an open-access tutorial series covering probabilistic modelling techniques, aimed at graduate students and researchers in quantitative fields.
Topics Covered
Probabilistic Programming in PyMC3
- Fitting a Gaussian distribution
- Bayesian Linear Regression
- Changepoint modelling
- Poisson changepoint
- Bernoulli changepoint
- Gaussian changepoint for mean and variance
- Advanced: multi-changepoint model with mixture emissions for repeated timeseries
Gaussian Mixture Models and Hidden Markov Models
- Unsupervised clustering using GMMs
- Introduction to Hidden Markov Models
Additional Resources
Handwritten Analytical Derivations
A recurring frustration with textbooks is that they assume too much about how intuitive each step in a derivation is for the reader — often skipping over algebraic manipulations that are non-obvious, especially to those newer to the material. These handwritten derivations are intended to provide an exhaustive, step-by-step breakdown that is (hopefully) easy to follow, with no steps omitted.
| Document | Description |
|---|---|
| Gaussian MLE (1D) | Full derivation of the maximum likelihood estimates for the mean and variance of a 1D Gaussian distribution, starting from the log-likelihood and working through each calculus step explicitly. |
| Linear Regression MLE | Step-by-step derivation of the ordinary least squares solution via maximum likelihood estimation, including the matrix calculus needed to arrive at the normal equations. |
| GMM Expectation-Maximization | Detailed derivation of the EM algorithm for Gaussian Mixture Models, covering the E-step (responsibility computation) and M-step (parameter updates) with all intermediate algebra shown. |