Bayesian Statistics

This repository contain Bayesian statistics implementation in R and Python. The directories available are:

Non-parametric Bayesian inference

• DPMM: contains the R code to implement Dirichlet Process Mixture Model (DPMM) using NIMBLE on the iris dataset. The primary reference to understand the theory behind DPMMs are the Bayesian non-parametric tutorials by Tamara Broderick.
• nature_of_priors: Examined the nature of a popular non-parametric bayesian prior called Dirichlet process. Primary reference for this file is the DP density estimation tutorial by PyMC.

Statistical software for Bayesian Statistics

• Nimble: Understanding NIMBLE syntax using a simple bayesian capture-recapture model example taken from the NIMBLE tutorial by Olivier Gimenez.
• STAN: Learning to perform posterior inference using RStan while following Chapters 6,7, and 8 of Bayes Rules! by Alicia A. Johnson, Miles Q. Ott, and Mine Dogucu.
• PyMC: Learning to perform bayesian posterior inference using PyMC module. The primary reference for this folder are:
  • PyMC's example gallery
  • Martin Osvaldo A, Kumar Ravin; Lao Junpeng, Bayesian Modeling and Computation in Python Boca Ratón, 2021. ISBN 978-0-367-89436-8
  • Paper introducing PyMC3: Salvatier J, Wiecki TV, Fonnesbeck C. 2016. Probabilistic programming in Python using PyMC3. PeerJ Computer Science 2:e55 https://doi.org/10.7717/peerj-cs.55

Miscellaneous

• hare_lynx_dynamics: Performed likelihood estimation in R to estimate the parameters associated with the Lotka–Volterra system of differential equations.
• some_plots: Examined the nature of two popular priors used in Bayesian Statistics - beta and Dirichlet priors. Analyzed the effect of parameter choices on the nature of the resulting distributions.

Some useful resources

1. PyMC Github page:: https://github.com/pymc-devs/pymc
2. Course resource on PyMC3: https://people.duke.edu/~ccc14/sta-663-2017/19A_PyMC3.html
3. Course resource on PyStan