# Bumps 0.9.1 documentation

## Bayesian Experimental Design

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

Usage:

    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.

Download: `peak.py`.