Package: py-mcmc
A python module implementing some generic MCMC routines=======================================================The main purpose of this module is to serve as a simple MCMC framework forgeneric models. Probably the most useful contribution at the moment, is thatit 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 offerthe right interface.+ Random walk proposals.+ Metropolis Adjusted Langevin Dynamics.+ 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 fromit is two-fold:+ In the old versions (e.g.[PyMC 2.3](http://pymc-devs.github.io/pymc/index.html)), could not find an easyway to implement Metropolis Adjusted Langevin Dynamics. This was unfortunatebecause it is one of the most powerful sampling methods when derivatives areavailable.+ 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 issueswhen one tries to deal with existing models. In particular, it is not possibleat the moment to deal in an easy way with a model that is not directly implementedusing 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 inverseproblems. In addition, it is not easy to exploit the Gaussian processfunctionality of GPy in order to train these models with MCMC.Therefore, the purpose of this package is to fill the gap between PyMC 2.3and PyMC 3. When the programers of PyMC 3 fix the afforementioned problem, thenthe MCMC part of this code will become obsolete.Additional Useful Packages--------------------------I have written some other packages that are useful in combination with py-mcmc:+ [Py-ORTHPOL](https://github.com/ebilionis/py-orthpol): Construct orthogonalpolynomials with respect to arbitrary weight functions. These can be usefulas mean functions for the Gaussian processes discussed here. They can be useddirectly.+ [Py-Design](https://github.com/ebilionis/py-design): Design of experiments forPython. This is extremely useful if you are trying to learn the output of acomputer 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 usingautomatic relevance determination for the basis functions can be used. This isequivalent to a Relevance Vector Machine model.+ [demos/demo4.py](demos/demo4.py): Demonstrates how a GP with a mean can becombined with a normal covariance kernel.Ilias Bilionis,December, 2014PredictiveScience Laboratory,School of Mechanical Engineering,Purdue University,West Lafayette, IN, USA