A python module implementing some generic MCMC routines

## Project description

A python module implementing some generic MCMC routines
=======================================================

The main purpose of this module is to serve as a simple MCMC framework for
generic models. Probably the most useful contribution at the moment, is that
it can be used to train Gaussian process (GP) models implemented in the
[GPy package](http://sheffieldml.github.io/GPy/).

Features
--------
The code features the following things at the moment:
+ Fully object oriented. The models can be of any type as soon as they offer
the right interface.
+ Random walk proposals.
+ The MCMC chains are stored in fast [HDF5](http://www.hdfgroup.org/HDF5/)
format using [PyTables](http://www.pytables.org/moin).
+ A mean function can be added to the (GP) models of the
[GPy package](http://sheffieldml.github.io/GPy/).

Installation
------------
Clone the package, get into its directory and do a:

python setup.py install


Related Packages
----------------
Probably, the most related package to what I am offering is the excellent
[PyMC](https://github.com/pymc-devs/pymc) code. The reason I have departed from
it is two-fold:
+ In the old versions (e.g.
[PyMC 2.3](http://pymc-devs.github.io/pymc/index.html)), could not find an easy
way to implement Metropolis Adjusted Langevin Dynamics. This was unfortunate
because it is one of the most powerful sampling methods when derivatives are
available.
+ In the new version (e.g.
[PyMC 3](http://nbviewer.ipython.org/github/pymc-devs/pymc/blob/master/pymc/examples/tutorial.ipynb),
which is based on [Theano](http://www.deeplearning.net/software/theano/)
schemes with derivatives can be easily implemented but there are several issues
when one tries to deal with existing models. In particular, it is not possible
at the moment to deal in an easy way with a model that is not directly implemented
using Theano (e.g. if it calls an external library or runs a complicated program).
This is a tremendous limitation when it comes to solving realistic inverse
problems. In addition, it is not easy to exploit the Gaussian process
functionality of GPy in order to train these models with MCMC.

Therefore, the purpose of this package is to fill the gap between PyMC 2.3
and PyMC 3. When the programers of PyMC 3 fix the afforementioned problem, then
the MCMC part of this code will become obsolete.

--------------------------
I have written some other packages that are useful in combination with py-mcmc:
+ [Py-ORTHPOL](https://github.com/ebilionis/py-orthpol): Construct orthogonal
polynomials with respect to arbitrary weight functions. These can be useful
as mean functions for the Gaussian processes discussed here. They can be used
directly.
+ [Py-Design](https://github.com/ebilionis/py-design): Design of experiments for
Python. This is extremely useful if you are trying to learn the output of a
computer code and you want to a good design of points to evaluate it.

Demos
-----
I provide various demos demonstrating how the code can be used:
+ [demos/demo1.py](demos/demo1.py): Demonstrates how to train GPy model using MCMC.
+ [demos/demo2.py](demos/demo2.py): Demonstrates how a GP with a mean can be trained.
This model is equivalent to Bayesian linear regression.
+ [demos/demo3.py](demos/demo3.py): Demonstrates how a GP with a mean using
automatic relevance determination for the basis functions can be used. This is
equivalent to a Relevance Vector Machine model.
+ [demos/demo4.py](demos/demo4.py): Demonstrates how a GP with a mean can be
combined with a normal covariance kernel.

Ilias Bilionis,
December, 2014
PredictiveScience Laboratory,
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN, USA