Fitting data with Python

Fitting models to data is one of the key steps in scientific work:

• fitting some spectrum/spectral line
• fitting 2D light distribution of a galaxy
• fitting orbits of exoplanets
• estimating the stellar IMF from a set of observed masses
• estimating the galaxy luminosity function from data
• ...

Numpy and Scipy provide readily usable tools to fit models to data.

Moreover, Python is an excellent environment to develop your own fitting routines for more advanced problems.

Goals of this session

• This is a Python tutorial but some statistics are inevitable!
• How to use implemented routines: leastsq, curve_fit and Simplex.
• Astrophysical example: Salpeter mass function.
• Metropolis-Hastings MCMC.
• Hamiltonian Monte-Carlo.

At the end of this session, participants will have code fragments that can be readily used or easily adopted for their own scientific work.

Agenda

• Introduction
• Least-squares fitting in Python
• Simplex algorithm
• Additional material: Gradient methods
• Example: Salpeter stellar mass function
• Additional material: Monte-Carlo sampling from Salpeter SMF
• Metropolis-Hastings algorithm
• Hamiltonian Monte-Carlo
• Additional material: Convexity of the Salpeter problem
• Summary

Authors:Rene Andrae Copyright:2012, Rene Andrae