# Bumps 0.7.14 documentation

## 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)

Download: `anticor.py`.