## Bayesian Analysis of Data

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# Bayesian Analysis of Data

Bayesian analysis offers an intuitive way to extract the maximum amount information of data. Apart from more philosophical considerations, the main difference between the classical approach to data fitting (normally called "frequentist"), and the Bayesian approach is the way results are presented. The results of the fits using the frequentist approach are expressed as a series parameters with an associated error. The Bayesian approach presents all results as probability distribution functions. If you want to have an idea about Bayesian Analysis applied to the fit of experimental data here, or you can have a more general view reading the excellent monography of D. Sivia (Data Analysis: A Bayesian Tutorial).

## Fitting Algorithm for Bayesian Analysis of DAta (FABADA)

 FABADA is a software developed in order to perform Bayesian Data Analysis in a simple and as general as possible, way. In a few words the programs simply varies randomly the parameters of you fitting model, and accepts those that are compatible with your data and experimantal error. In this way the probability distributions of the model parameters are obtained. In order to perform model selection, the program also calculated the probability distribution functions associated both to the likelihood and the classical chi-square figure of merit. You can find more information in the following slides: FABADA slides Eating a fabada in "Llagu Ercina"

The program is written in plain fortran77, is an open code so that you can add any function you want, and works both for linux and windows systems. The grahics are simply displayed using gnuplot (FABADA simply calls this program every time you want to see a graph). If you find this software interesting and you use it for your own research please cite this paper [L.C. Pardo et al. Phys. Rev. E. 84, 046711 (2011)], and write me an e.mail with the reference. I would be glad to know that it was not wasted time ;-).

### Papers explaining how it works and the Bayesian theory behind the scenes:

• L.C. Pardo et al. Phys. Rev. E. 84, 046711 (2011)
• L.C Pardo et al. J. Phys.: Conf. Ser. 325, 012006 (2011)
• L. C. Pardo et al. arXiv:0907.3711v3 [physics.data-an]

### Paper in which FABADA is used:

#### QENS

• M. Rovira-Esteva et al. Phys. Rev. B   81(9) 092202 (2010)
• S. Busch et al. J. Am. Chem. Soc. 132(10) 3232 (2010)

#### Diffraction

• M. Rovira-Esteva et al. Phys. Rev. B    84, 064202 (2011)

#### Dielectric spectroscopy

• J. C. Martínez et al. J. Phys. Chem. B 114  6099 (2010)

#### Astrophysics

• G. Sala et al. The Astrophysical Journal  (2012) 