reddemcee 0.9.0

Adaptive Parallel Tempering MCMC Ensemble Sampler

reddemcee

Adaptive Parallel Tempering MCMC Ensemble Sampler, made for the exoplanet finder algorithm EMPEROR. This sampler works as a stand-alone program, so the community might find it useful.

Overview

reddemcee is an Adaptive Parallel Tempering MCMC implementation based on the excellent emcee code, and a modified version of the Vousden et al. implementation.

It's coded in such a way that minimal differences in input are required compared to emcee (v. 3.1.3). Make sure to check reddemcee's documentation !

Dependencies

This code makes use of:

• numpy
• tqdm
• emcee
• scipy

tqdm is used to display progress bars on the terminal. emcee is used for calculating the autocorrelation times.

Installation

In the console simply type:

pip install reddemcee

Usage

For a complete tutorial please refer to the documentation's tutorial or the test file in the tests folder.

import numpy as np
import reddemcee

def log_like(x, ivar):
    return -0.5 * np.sum(ivar * x ** 2)

def log_prior(x):
    return 0.0

ndim = 2
ntemps, nwalkers, nsweeps, nsteps = 5, 50, 100, 2

ivar = 1. / np.random.rand(ndim)
p0 = np.random.randn(10, nwalkers, ndim)
sampler = reddemcee.PTSampler(nwalkers,
                             ndim,
                             log_like,
                             log_prior,
                             ntemps=ntemps,
                             loglargs=[ivar],
                             )
                             
sampler.run_mcmc(p0, nsweeps, nsteps)  # starting coords, nsweeps, nsteps

Configuring the Sampler

When setting up PTSampler, you can use the arguments:

Arg	Type	Description
ntemps	int	The number of temperatures. If None, determined from betas.
betas	list	The inverse temperatures of the parallel chains.
pool	Pool	A pool object for parallel processing.
loglargs	list	Positional arguments for the log-likelihood function.
loglkwargs	list	Keyword arguments for the log-likelihood function.
logpargs	list	Positional arguments for the log-prior function.
logpkwargs	list	Keyword arguments for the log-prior function.
backend	Backend	A backend object for storing the chain.
smd_history	bool	Whether to store swap mean distance history.
tsw_history	bool	Whether to store temperature swap history.
adapt_tau	float	Halflife of adaptation hyper-parameter.
adapt_nu	float	Rate of adaptation hyper-paramter.
adapt_mode	0-4	Mode of adaptation.

The adaptation modes try to equalise the following quantity:

Mode	Description
0	Temperature Swap Rate
1	Swap Mean Distance
2	Specific Heat
3	dE/sig
4	Thermodynamic Length

Additional Functions

Additional functions on the sampler include:

Function	Description
thermodynamic_integration_classic	Calculates evidence using trapezoidal rule.
thermodynamic_integration	Interpolates, uses Monte-Carlo integration.
stepping_stones	Stepping Stones method
hybrid_evidence	Hybrid method
get_autocorr_time	Auto-correlation time.
get_betas	Returns beta history
get_chain	Returns chain
get_logprob	Returns log posteriors

All these functions accept as arguments:

Arg	Description
flat	Flatten the walkers.
thin	Take one every thin samples.
discard	Drop the first discard steps in samples.

For example, the previous chain would have shape (5, 200, 50, 2), for 5 temperatures, 200 steps (nsweeps*nsteps), 50 walkers, and 2 dimensions.

sampler.get_chain(discard=100)

Would return the samples with shape (5, 100, 50, 2). Dropping the first 100 for every walker.

sampler.get_chain(discard=100, flat=True)

Would return the samples with shape (5, 5000, 2), 'linearising' the walkers.