About

Bayesian Inference for PYthon using Markov Chain Monte Carlo (BiPyMc).

BiPyMc contains implementations of common Markov chain Monte Carlo routines.

This package also contains Bayesian optimization routines for 1) finding optimal parameter values when the objective function is too costly for MCMC to be feasible and 2) generating initial parameter guesses for MCMC if the objective function is inexpensive.

Implemented MCMC Methods

• Metropolis-Hastings
• Adaptive Metropolis (AM)
• Differential Evolution Metropolis (DE-MC) (Parallel implementation)
• Differential Evolution Adaptive Metropolis (DREAM) (Parallel implementation)
• Delayed Rejection Metropolis
• Delayed Rejection Adaptive Metropolis (DRAM)

Included Tests:

• tests/test_100dgauss.py: 100 Dimensional normal distribution test. Shows improved performance of DREAM in high dimensions.
• tests/test_banana.py: Ensures all MCMC methods obtain correct samples from non-linear, distorted-gaussian distribution.
• tests/test_dblgauss.py: Ensures DREAM and DE-MC samplers handle multi-modal distributions. Demonstrates DRAM and AM limitations.

Sample Bimodal Gaussian Distribution with DREAM

Implemented Bayesian Optimization Methods

• Gaussian Process with Thompson sampling (Parallel implementation)

References

J. Vurgt and C. Braak. Adaptive Markov Chain Monte Carlo simulation algorithm to solve discrete, noncontinuous, and combinatorial posterior parameter estimation problems

J. Vrugt., C. Braak, et al. Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling

Braak, C.J.F.T. Statistics and Computing (2006) 16: 239. https://doi.org/10.1007/s11222-006-8769-1

rXiv:1710.09486 https://arxiv.org/pdf/1710.09486.pdf

M. Trias, A. Vecchio, J. Veitch. Delayed rejection schemes for efficient Markov-Chain Monte-Carlo sampling of multimodal distributions. https://arxiv.org/abs/0904.2207

Quickstart

Install depends:

pip install corner mpi4py numpy scipy h5py matplotlib pytest

Or if using conda:

conda install -c astropy corner
conda install mpi4py numpy scipy h5py matplotlib pytest

Install and run examples:

git clone https://github.com/wgurecky/bipymc.git
cd bipymc
python setup.py develop --user
python examples/ex_line_fit.py

Optional parallel example:

mpirun -np 4 python examples/ex_para_fit.py

Basic Use Example:

    from mpi4py import MPI
    from bipymc.dream import DreamMpi

    # Define the log liklihood function
    # Has signature ln_p <- ln_like_fn(theta, **kwargs)
    # where theta is a 1d array
    # and returns a float, ln_p.
    def ln_like_fn(theta, **kwargs):
        # extract optional keyword arguments
        opt_model_param1 = kwargs.get('param1', 42)
        # ... compute ln_p
        return ln_p
    
    n_chain, n_burn, n_samples = 10, 20000, 100000
    theta_0 = #... initial parameter guess
    my_mcmc = DreamMpi(ln_like_fn, theta_0, n_chains=n_chains, mpi_comm=MPI.COMM_WORLD,
                       n_cr_gen=50, burnin_gen=int(n_burn / n_chain), ln_kwargs={'param1': 42})
    my_mcmc.run_mcmc(n_samples)

Depends

• python3.2+
• numpy
• scipy
• h5py
• pytest (optional for tests)
• mpi4py (optional for parallel DE-MC)
• matplotlib (optional for plotting)
• corner (optional for plotting)

License

BSD3 Clause:

Copyright © 2018 William Gurecky All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of the organization nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY William Gurecky ''AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL William Gurecky BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.