7/26/2019 Using MCMC for Fitting Models to Data

http://slidepdf.com/reader/full/using-mcmc-for-fitting-models-to-data 1/4

Using MCMC for ttinmodels to data

I have used Python for developing the tting cod

7/26/2019 Using MCMC for Fitting Models to Data

http://slidepdf.com/reader/full/using-mcmc-for-fitting-models-to-data 2/4

Why Python? Easy to learn and use

Vast collection of libraries for mathematicalcomputation

Poerful plotting libraries are also available

!anguage of choice for many modern scientic rese

7/26/2019 Using MCMC for Fitting Models to Data

http://slidepdf.com/reader/full/using-mcmc-for-fitting-models-to-data 3/4

"itting a straight line

#oal$ I ant to t a straight line to a sample datase•   I need an estimate of slope and intercept

• Estimate uncertainty associated ith them

  %ataset has &% uncertainty in both ' and y

Problem$ (tandard practice of Ma'imi)ing li*elihoodfunction or eighted least s+uare can only incorpory uncertainty, -o to introduce ' uncertainty in ttimodel as ell?

7/26/2019 Using MCMC for Fitting Models to Data

http://slidepdf.com/reader/full/using-mcmc-for-fitting-models-to-data 4/4

(ome basics ofProbability .heory

!i*elihood function$ Probability of getting a particuldataset given the Model parameters / li*e slope anintercept 0 and a prior *noledge / li*e about ' anduncertainty or everything else I can safely state

beforehand about the problem 0 Posterior probability$ Probability of getting a particu

value of Model parameters given my dataset

Prior Probability$ 1 probability distribution of the Moparameters hat represents all *noledge e'cept th

data yi for all I running over entire dataset3