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Abstract
We describe the development of a new toolkit for data analysis. The analysis package is based on Bayes' Theorem, and is realized with the use of Markov Chain Monte Carlo. This gives access to the full posterior probability distribution. Parameter estimation, limit setting and uncertainty propagation are implemented in a straightforward manner.
Highlights
The goal of data analysis is to compare model predictions with data, and draw conclusions either on the validity of the model as a representation of the data, or on the possible values for parameters within the context of a model
We have described the development of a general purpose analysis tool based on a Bayesian learning algorithm, the BAT package
BAT is based on the Markov Chain Monte Carlo technique, and provides all the standard quantities such as best fit parameters, goodness-of-fit, upper limits, etc
Summary
The goal of data analysis is to compare model predictions with data, and draw conclusions either on the validity of the model as a representation of the data, or on the possible values for parameters within the context of a model. We usually just write Pi = P0, and this quantity is called the prior It contains all information we may have on the model and parameter values before the experiment is performed. The denominator in Eq (12) is the probability to get the data, D, assuming the models M and the description of the experimental conditions describe all possible outcomes, and can be written as P (D). Using this notation, we recover the classic equation due to Bayes:. The precision and accuracy of the results will depend primarily on the quality of the inputs Given that these functions are well-defined, the BAT program will be useful as a tool for model testing and parameter estimation. We give examples of parameter estimation and model testing to make the ideas more concrete
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