Provides routines for Bayesian Model Averaging (BMA). BMA searches a model space (e.g. linear regression models) for promising models and computes the posterior probability distribution over that space. Coefficients are then estimated from a weighted average over the model space.

Running BMA is as simple as fitting a regression model. Estimates will be close to the ones you would obtain from fitting the "true" nested model, and no knowledge of that model is required.

The following scripts are relevant for end users:

• linear_regression.py contains routines for Bayesian linear regression.
• linear_averaging.py contains routines for linear BMA.
• sim.py demonstrates basic usage of linear BMA.

The following scripts are useful if you wish to adapt BMA to other model spaces:

• core.py contains routines for generic BMA.
• mcmc.py contains generic MCMC routines.

The specific Bayesian regression model I use expects 2 hyperparameters:

• g is a parameter that penalizes model size. I recommend setting it to max(n_obs, n_dim^2).
• p is your prior expectation of how many relevant variables your dataset contains. If you expected 10% of the variables in X to be relevant, you would set it to 1/10.

Basic usage is demonstrated in sim.py. Given regressors X and response y You can fit the model by executing

mod = linear_averaging.LinearMC3(X, y, g, p)

mod.select()

mod.estimate()

The first step computes the posterior model distribution, the second computes the posterior distributions over the model parameters.

Please consult the docstrings for further documentation.

All scripts were written with Python 3 in mind and require the usual set of scientific Python libraries. They can be converted to Python 2.7 with minimal changes. It is crucial to enable true division by adding the following line to all scripts:

from __future__ import division

• Kass and Wassermann (1995) and Kass and Raftery (1995) for Bayesian model averaging and MC3.
• Liang et al. (2008) for the Bayesian Linear Regression model.
• Hastings (1970) for details on the Metropolis-Hastings algorithm.
• Sokal (1997) for MCMC diagnostics.