Skip to main content

Linear Regression by Gibbs Sampling

Project description

ascl:1602.005 PyPi MIT

LRGS: Linear Regression by Gibbs Sampling

Code implementing a Gibbs sampler to deal with the problem of multivariate linear regression with uncertainties in all measured quantities and intrinsic scatter. Full details can be found in this paper (1509.00908), the abstract of which appears below. (The paper describes an implementation in the R language, while this package is a port of the method to Python.)

Kelly (2007, hereafter K07) described an efficient algorithm, using Gibbs sampling, for performing linear regression in the fairly general case where non-zero measurement errors exist for both the covariates and response variables, where these measurements may be correlated (for the same data point), where the response variable is affected by intrinsic scatter in addition to measurement error, and where the prior distribution of covariates is modeled by a flexible mixture of Gaussians rather than assumed to be uniform. Here I extend the K07 algorithm in two ways. First, the procedure is generalized to the case of multiple response variables. Second, I describe how to model the prior distribution of covariates using a Dirichlet process, which can be thought of as a Gaussian mixture where the number of mixture components is learned from the data. I present an example of multivariate regression using the extended algorithm, namely fitting scaling relations of the gas mass, temperature, and luminosity of dynamically relaxed galaxy clusters as a function of their mass and redshift. An implementation of the Gibbs sampler in the R language, called LRGS, is provided.

For questions, comments, requests, problems, etc. use the GitHub issues.


LRGS for Python is currently in alpha. It has not been vetted for all possible combinations of univariate/multivariate covariates and responses. Some features of the R version are not implemented, in particular the Dirichlet process prior.

A submodule, lrgs.trunc, has been added to facilitate modeling of truncated data sets (see 1901.10522). This submodule depends on the external package LMC. It has no analog in the R version of LRGS.




Install from PyPI by running pip install lrgs. Note that PyPI may not have the latest version.


Download lrgs/ and put it somewhere on your PYTHONPATH. You will need to have the numpy and scipy packages installed.

Usage and Help

Documentation is sparse at this point, but an example notebook can be found here.

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

lrgs-0.1.1.tar.gz (12.1 kB view hashes)

Uploaded source

Built Distribution

lrgs-0.1.1-py3-none-any.whl (10.6 kB view hashes)

Uploaded py3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page