# LinearRegression package

Bayesian linear regression model with conjugate normal-inverse-gamma prior.

This package is open source software.

## Getting started

To build, use:

birch build


To run, use:

birch sample --config config/linear_regression.json


## Details

The model is given by:

\begin{align} \sigma^2 &\sim \mathrm{Inv\text{-}Gamma}(3, 4/10) \\ \boldsymbol{\beta} &\sim \mathcal{N}(0, I\sigma^2) \\ y_n &\sim \mathcal{N}(\mathbf{x}_n^{\top}\boldsymbol{\beta}, \sigma^2) \end{align}

The parameters are the noise variance $\sigma^2$ and vector of coefficients $\boldsymbol{\beta}$. The data consists of observations $y_n$ and explanatory variables $\mathbf{x}_n$ for $n=1,\ldots,N$.

## Acknowledgements

This package contains a bike sharing data set from the Capital Bikeshare system in Washington D.C., studied in Fanaee-T and Gama (2014), and prepared in JSON format for Birch.

## References

1. H. Fanaee-T and J. Gama (2014). Event labeling combining ensemble detectors and background knowledge. Progress in Artificial Intelligence. 2:113-127.