Anticorrelation demo
====================

Model with strong correlations between the fitted parameters.

We use a*x = y + N(0,1) made complicated by defining a=p1+p2.

The expected distribution for p1 and p2 will be uniform, with p2 = a-p1 in
each sample.  Because this distribution is inherently unbounded, artificial
bounds are required on a least one of the parameters for finite duration
simulations.

The expected distribution for p1+p2 can be determined from the linear model
y = a*x.  This is reported along with the values estimated from MCMC.

::

    from bumps.names import *
    
Anticorrelated function

::

    def fn(x, a, b): return (a+b)*x
    
Fake data

::

    sigma = 1
    x = np.linspace(-1., 1, 40)
    dy = sigma*np.ones_like(x)
    y = fn(x,5,5) + np.random.randn(*x.shape)*dy
    
Wrap it in a curve fitter

::

    M = Curve(fn, x, y, dy, a=(-20,20), b=(-20,20))
    
Alternative representation, fitting a and S=a+b, and setting b=S-a.

::

    S = Parameter((-20,20), name="sum")
    M.b = S-M.a

::

    problem = FitProblem(M)


.. only:: html

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