batty 0.0.7

BAT to Python

BAT to Python (batty)

A small python interface to the Bayesian Analysis Toolkit (BAT.jl) https://github.com/bat/BAT.jl

Quick Start

Installation

There are two parts to an installation, one concerning the python side, and one the julia side:

• Python: pip install batty

• Julia: import Pkg; Pkg.add.(["PyJulia", "DensityInterface", "Distributions", "ValueShapes", "TypedTables", "ArraysOfArrays", "BAT"])

Minimal Example

The code below is showing a minimal example:

• using a gaussian likelihood and a uniform prior
• generating samples via Metropolis-Hastings
• plotting the resulting sampes
• estimating the integral value via BridgeSampling

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
from batty import BAT_sampler, BAT, Distributions

/mnt/c/Users/peller/work/batty/batty.py:6: UserWarning: Not able to use compiled modules, resulting in (very) slow import
 See https://pyjulia.readthedocs.io/en/latest/troubleshooting.html
  warnings.warn("Not able to use compiled modules, resulting in (very) slow import\n See https://pyjulia.readthedocs.io/en/latest/troubleshooting.html")

sampler = BAT_sampler(llh=lambda x : -0.5 * x**2, prior_specs=Distributions.Uniform(-3, 3))
sampler.sample();
sampler.corner();

sampler.integrate()

0.4165591088238079+/-0.00020607405882794568

Usage

Using Different Algotihms

There are a range of algorihtms available within BAT, and those can be further customized via arguments. Here are just a few examples:

Integration:

• AHMI:

sampler.integrate(strategy=BAT.AHMIntegration())

0.41993468380372745+/-0.0015153686310618321

• Bridge Sampling:

sampler.integrate(strategy=BAT.BridgeSampling())

0.4166724726365416+/-0.0002060289597245534

MCMC Sampling:

results = {}

• Metropolis-Hastings:

results['Metropolis-Hastings'] = sampler.sample(strategy=BAT.MCMCSampling(nsteps=10_000, nchains=2))

• Metropolis-Hastings with Accept-Reject weighting:

results['Accept-Reject Weighting'] = sampler.sample(strategy=BAT.MCMCSampling(mcalg=BAT.MetropolisHastings(weighting=BAT.ARPWeighting()), nsteps=10_000, nchains=2))

• Prior Importance Sampling:

results['Prior Importance Sampling'] = sampler.sample(strategy=BAT.PriorImportanceSampler(nsamples=10_000))

• Sobol Sampler:

results['Sobol Quasi Random Numbers'] = sampler.sample(strategy=BAT.SobolSampler(nsamples=10_000))

• Grid Sampler:

results['Grid Points'] = sampler.sample(strategy=BAT.GridSampler(ppa=1000))

Plotting the different results:

fig = plt.figure(figsize=(9,6))
bins=np.linspace(-3, 3, 100)
for key, item in results.items():
    plt.hist(item.v, weights=item.weight, bins=bins, density=True, histtype="step", label=key);
plt.legend()

<matplotlib.legend.Legend at 0x7f05724e28e0>

Specifying Priors and Likelihoods

Priors are specified via Julia Distributions, multiple Dimensions can be defined via a dict, where the key is the dimension name and the value the distribution

s = np.array([[0.25, 0.4], [0.9, 0.75]])
prior_specs = {'a' : Distributions.Uniform(-3,3), 'b' : Distributions.MvNormal([1,1], s@s.T)}

The log-likelihood (llh) can be any python callable, that returns the log-likelihood values. The first argument to the function is the object with paramneter values, here x. If the prior is simple (i.e. like in the example in the beginning, x is directly the parameter value). If the prior is specified via a dict, then x contains a field per parameter with the value. Any additional args to the llh can be given in the sampler, such as here d for data:

def llh(x, d):
    return -0.5 * ((x.b[0] - d[0])**2 + (x.b[1] - d[1])**2/4) - x.a

d = [-1, 1]

sampler = BAT_sampler(llh, prior_specs, llh_args=(d,), progress_bar=True)

Let us generate a few samples:

sampler.sample(strategy=BAT.MCMCSampling(nsteps=10_000, nchains=2));

llh at   -11.0996: : 35132it [01:46, 377.76it/s]     

Some interface to plotting tools are available

• The Great Triangular Confusion (GTC) plot:

sampler.gtc(figureSize=8, customLabelFont={'size':14}, customTickFont={'size':10});

findfont: Font family ['Arial'] not found. Falling back to DejaVu Sans.
findfont: Font family ['Arial'] not found. Falling back to DejaVu Sans.

• The corner plot:

sampler.corner(color='green');

# does not work
#sampler.sample(strategy=BAT.MCMCSampling(nsteps=1000, nchains=2, mcalg=BAT.HamiltonianMC()));

#takes way too long, something wrong
#sampler.sample(strategy=BAT.PartitionedSampling(npartitions=2, sampler=BAT.MCMCSampling(nchains=2, nsteps=100, strict=False), exploration_sampler=BAT.MCMCSampling(nchains=2, nsteps=100, strict=False)))