文件列表:

LICENSE (18047, 2015-07-16)
bayesvarsel_notes.pdf (331215, 2015-07-16)
core.py (9843, 2015-07-16)
linear_averaging.py (8293, 2015-07-16)
linear_regression.py (7466, 2015-07-16)
mcmc.py (6934, 2015-07-16)
sim.py (1800, 2015-07-16)

Bayesian Model Averaging ======================== 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. TOC --- 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. Usage ----- 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 ```python 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. Dependencies ------------- 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: ```python from __future__ import division ``` References ---------- - 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.

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