Check the entropy calculator
============================

Many of the probability distributions in scipy.stats include a method
to compute the entropy of the distribution.  We can use these to test
the values from bumps against known good values.

::

    from math import log
    from scipy.stats import distributions
    from bumps.names import *
    
Create the distribution using the name and parameters from the command line.
Provide some handy help if the no distribution is given.

::

    USAGE = """
    Usage: bumps check_entropy.py dist p1 p2 ...
    
    where dist is one of the distributions in scipy.stats.distributions and
    p1, p2, ... are the arguments for the distribution in the order that they
    appear. For example, for the normal distribution, x ~ N(3, 0.8), use:
    
        bumps --fit=dream --entropy  --store=/tmp/T1 check_entropy.py norm 3 0.2
    """
    if len(sys.argv) > 1:
        D_class = getattr(distributions, sys.argv[1])
        args = [float(v) for v in sys.argv[2:]]
        D = D_class(*args)
    else:
        print(USAGE)
        sys.exit()
    
Set the fitting problem using the direct PDF method.  In this case, bumps
is not being used to fit data, but instead to explore the probability
distribution directly through the negative log likelihood function.  The
only argument to this function is the parameter value x, which becomes the
fitting parameter.  This model file will not work for multivariate
distributions.

::

    def D_nllf(x):
        return -D.logpdf(x)
    M = PDF(D_nllf, x=0.9)
    M.x.range(-inf, inf)
    
    problem = FitProblem(M)
    
Before fitting, print the expected entropy from the fit.

::

    print("*** Expected entropy: %.4f"%(D.entropy()/log(2)))
    
To exercise the entropy calculator, try fitting some non-normal
distributions:

.. parsed-literal::

      t 84            # close to normal
      t 4             # high kurtosis
      uniform -5 100  # high entropy
      cauchy 0 1      # undefined variance
      expon 0.1 0.2   # asymmetric, narrow
      beta 0.5 0.5    # 'antimodal' u-shaped pdf
      beta 2 5        # skewed

Ideally, the entropy estimated by bumps will match the predicted entropy
when using *--fit=dream*.  This is not the case for *beta 0.5 0.5*.  For
the other distributions, the estimated entropy is within uncertainty of
actual value, but the uncertainty is a bit high.

The other fitters, which use the curvature at the peak to estimate
the entropy, do not work reliably when the fit is not normal.  Try
the same distributions with *--fit=amoeba* to see this.



.. only:: html

   Download: :download:`check_entropy.py <check_entropy.py>`.
