Just a repository for understanding the basics of Bayesian linear regression by applying it to a simple polynomial fitting problem.
Clone the repository and install the dependencies using the python package manager poetry as
git clone https://github.com/ShantanuKodgirwar/bayesreg.git
cd bayesreg
poetry install --with dev --syncThis installs the package in a virtual environment and can be accessed with poetry shell.
Implementations here mainly involve topics in Bayesian inference which are explained with some derivations under here. The following topics must also be reviewed,
- Markov chain Monte Carlo sampling to quantify the uncertainty of model parameters
- Sparsity prior, gradient-based priors
The following literature is considered in order of the level of complexity, mainly focusing on imaging.
- Bishop: Chapter 1 of "Pattern Recognition and Machine Learning"
- Ribes: Background on applications in imaging
- Hansen: Deconvolution and regularization
- MacKay: Bayesian perspective
- Minka: Bayesian linear regression