Bayesian Experimental Design
============================

Perform a tradeoff comparison between point density and counting time when
measuring a peak in a poisson process.

Usage:

.. parsed-literal::

   bumps peak.py N --entropy --store=/tmp/T1 --fit=dream

The parameter N is the number of data points to use within the range.


::

    from bumps.names import *
    from numpy import exp, sqrt, pi, inf
    
    
    # Define the peak shape as a gaussian plus background
    def peak(x, scale, center, width, background):
        return scale * exp(-0.5 * (x - center) ** 2 / width**2) / sqrt(2 * pi * width**2) + background
    
    
    # Get the number of points from the command line
    if len(sys.argv) == 2:
        npoints = int(sys.argv[1])
    else:
        raise ValueError("Expected number of points n in the fit")
    
    # set a constant number of counts, equally divided between points
    x = np.linspace(5, 20, npoints)
    scale = 10000 / npoints
    
    # Build the model, along with the valid fitting range. there is no data yet,
    # so y is None
    M = PoissonCurve(peak, x, y=None, scale=scale, center=15, width=1.5, background=1)
    M.scale.range(0, inf)
    dx = max(x) - min(x)
    M.center.range(min(x) - 0.2 * dx, max(x) + 0.2 * dx)
    M.width.range(0, 0.7 * dx)
    M.background.range(0, inf)
    
    # Make a fake dataset from the give x spacing
    M.simulate_data()
    
    problem = FitProblem(M)
    
    
Running this problem for a few values of the number of points is showing
that adding points and reducing counting time per point is better able
to recover the peak parameters.


.. only:: html

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