Skip to main content

BAT to Python

Project description

batty

BAT to Python (batty)

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

  • Please check out the minimal example to get started below
  • To understand how to define a prior + likelihood, please read this
  • For experimental support of gradients, see this

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", "ChainRulesCore", "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
%load_ext autoreload
%autoreload 2
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
from batty import BAT_sampler, BAT, Distributions, jl
sampler = BAT_sampler(llh=lambda x : -0.5 * x**2, prior_specs=Distributions.Uniform(-3, 3))
sampler.sample();
sampler.corner();

png

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:

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 0x7f069fcd5ee0>

png

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, or as a list in case flat vectors with paraeter names are used.

Below the example with parameter names

s = np.array([[0.25, 0.4], [0.9, 0.75]])
prior_specs = {'a' : Distributions.Uniform(-3,3), 'b' : Distributions.MvNormal(np.array([1.,1.]), jl.Array(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

Or alternatively without parameter names (this will result in a flat vector):

# prior_specs = [Distributions.Uniform(-3,3), Distributions.MvNormal(np.array([1.,1.]), jl.Array(s@s.T))]
# def llh(x, d):
#     return -0.5 * ((x[1] - d[0])**2 + (x[2] - d[1])**2/4) - x[0]
d = [-1, 1]
sampler = BAT_sampler(llh=llh, prior_specs=prior_specs, llh_args=(d,))

Let us generate a few samples:

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

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.

png

  • The corner plot:
sampler.corner(color='green');

png

HMC with Gradients

This at the moment only works with preiors defined as flat vectors!

llh = lambda x : -0.5 * np.dot(x, x)
grad = lambda x : -x
sampler = BAT_sampler(llh=llh, prior_specs=[Distributions.Uniform(-3, 3),], grad=grad, )

# Or alternatively:
# llh_and_grad = lambda x: (-0.5 * np.dot(x, x), -x)
# sampler = BAT_sampler(llh=llh, prior_specs=[Distributions.Uniform(-3, 3),], llh_and_grad=llh_and_grad)

sampler.sample(strategy=BAT.MCMCSampling(mcalg=BAT.HamiltonianMC()));
sampler.corner();

png



          

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

batty-0.1.0.tar.gz (7.8 kB view details)

Uploaded Source

File details

Details for the file batty-0.1.0.tar.gz.

File metadata

  • Download URL: batty-0.1.0.tar.gz
  • Upload date:
  • Size: 7.8 kB
  • Tags: Source
  • Uploaded using Trusted Publishing? No
  • Uploaded via: twine/3.4.1 importlib_metadata/3.10.0 pkginfo/1.7.1 requests/2.26.0 requests-toolbelt/0.9.1 tqdm/4.61.2 CPython/3.8.2

File hashes

Hashes for batty-0.1.0.tar.gz
Algorithm Hash digest
SHA256 dfd811faaff41b8de3fb6462c61bb507b46938327280d757d382629d4a3d3672
MD5 75f86d8624d6f46abfba7c8e16b09b56
BLAKE2b-256 65d1180abf1889f4b2f77cd9fbbe9ce83db733f66646588317d218e52f609371

See more details on using hashes here.

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page