samsam documentation#

The samsam package provides two samplers:

samsam.sam : a Scaled Adaptive Metropolis algorithm (see [1], [2], [3]), to robustly obtain samples from a target distribution,
samsam.covis : a COVariance Importance Sampling algorithm, to efficiently compute the model evidence (or other integrals).

It additionally includes tools (samsam.acf) to assess the convergence of the sam sampler (ACF, IAT), and a few commonly used prior distributions (samsam.logprior).

Installation#

Using conda#

The samsam package can be installed using conda with the following command:

conda install -c conda-forge samsam

Using pip#

It can also be installed using pip with:

pip install samsam

Example#

Let us first define a simple log-probability function:

In [1]: import numpy as np
   ...: import matplotlib.pyplot as plt
   ...: from samsam import sam, covis, acf
   ...: from corner import corner
   ...: np.random.seed(0)
   ...: 
   ...: def logprob(x):
   ...:     return(-0.5*(np.sum(x**2) + x.size*np.log(2*np.pi)))
   ...: 

Then we run sam to sample this distribution:

In [2]: ndim = 10
   ...: nsamples = 100000
   ...: x0 = np.random.normal(0, 100, ndim)
   ...: 
   ...: samples, sam_diagnos = sam(x0, logprob, nsamples=nsamples, print_level=0)
   ...: samples = samples[nsamples//4:]
   ...: 

Let us check that sam converged correctly using the ACF/IAT:

In [3]: R = acf.acf(samples)
   ...: tau = np.arange(samples.shape[0])
   ...: 
   ...: plt.figure()
   ...: plt.plot(tau[1:], R[1:])
   ...: plt.xscale('log')
   ...: plt.xlim(1, samples.shape[0])
   ...: plt.xlabel('lag')
   ...: plt.ylabel('ACF')
   ...: 
   ...: iat = acf.iat(R=R)
   ...: print('IAT:', iat.max())
   ...: print('Effective number of samples:', samples.shape[0]/iat.max())
   ...: 
IAT: 40.59274361034297
Effective number of samples: 1847.6454984158759

Now we plot the corner plot of the parameter samples:

In [4]: corner(samples);

Finally we run covis to compute the log-evidence of the model:

In [5]: _, _, covis_diagnos = covis(sam_diagnos['mu'], sam_diagnos['cov'], logprob, nsamples=1000, print_level=0)
   ...: # Should be close to 0 since the logprob is correctly normalized
   ...: print('Log-evidence:', covis_diagnos['logevidence'])
   ...: 
Log-evidence: -0.002628219768561202

API Reference#

`samsam`
`samsam.acf`
`samsam.logprior`