Bayesian Fits
In this section, we discuss how to run a bayesian fit in Colibri.
In bayesian statistics, the parameters \(\theta\) that describe the theory are treated as random variables. They have a prior probability density (or prior), \(P(\theta)\), which encodes what is known or assumed about the parameters prior to experimental observation.
The posterior probability distribution, i.e. the outcome of the fit, is determined from Bayes’ theorem:
where \(P(\mathrm{data} \mid \theta)\) is the likelihood function.
In a bayesian fit, the posterior distribution of the PDF model parameters is sampled using a sampling method. Colibri currently supports bayesian sampling with the following packages:
Following the links above will take you to a tutorial on how to run a bayesian fit with the respective package.