C-ness and number of degrees of freedom

Assume a fit of a straight line through 10 points, each point with an error. Then we say that the line has 2 free parameters and the number of degrees of freedom is 10 – 2 = 8.

For a kinematic fit we would say that there are 10 measured variables (the 10 y values), 10 fitted variables (the 10 y values along the line at the same 10 x positions), and 2 unknown variables (the slope and y-intercept of the line). For each fitted variable there is a constraint: that the fitted value lies along the line, i. e., that y_fit,i = ax_i + b. So there are 10 constraints. We say that we have an 8-C fit since the number of constraints minus the number of unknown variables is 10 – 2 = 8.

So the C-ness of the kinematic fit corresponds to the number of degrees of freedom in the chi-squared fit.

 

outline for kinematic fitter API specification

  1. Introduction
    1. general purpose
    2. follows Frodeson et al.
    3. see E787 note
  2. Features
    1. user creates input objects
    2. user creates constraint object
    3. flexibility in how to parametrize problem
    4. reduces algebra that needs to be done
    5. allows errors to be used in their natural form
    6. can be used for mass constraints
    7. can be used for conservation of energy and momentum
  3. Input and Output Classes
    1. input classes
    2. constraint class
      1. “abstract class”
    3. output parameters
  4. Examples
    1. pi0 mass constraint
    2. lambda to pi p
  5. Summary