BAT.jl: A Julia-Based Tool for Bayesian Inference

We describe the development of a multi-purpose software for Bayesian statistical inference, BAT.jl, written in the Julia language. The major design considerations and implemented algorithms are summarized here, together with a test suite that ensures the proper functioning of the algorithms. We also give an extended example from the realm of physics that demonstrates the functionalities of BAT.jl.

[1]  M. Ciuchini,et al.  Electroweak precision observables, new physics and the nature of a 126 GeV Higgs boson , 2013, 1306.4644.

[2]  Zoubin Ghahramani,et al.  Turing: A Language for Flexible Probabilistic Inference , 2018 .

[3]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[4]  Martin Odersky,et al.  Independently Extensible Solutions to the Expression Problem , 2004 .

[5]  A. W. Kemp,et al.  Kendall's Advanced Theory of Statistics. , 1994 .

[6]  Patrick Kofod Mogensen,et al.  Optim: A mathematical optimization package for Julia , 2018, J. Open Source Softw..

[7]  D. Ghosh,et al.  Extending the analysis of electroweak precision constraints in composite Higgs models , 2015, 1511.08235.

[8]  A. Merle,et al.  Global Bayesian analysis of neutrino mass data , 2017, 1705.01945.

[9]  John Skilling,et al.  Data analysis : a Bayesian tutorial , 1996 .

[10]  M. Pierini,et al.  Global Bayesian Analysis of the Higgs-boson Couplings , 2014, 1410.4204.

[11]  Alan Edelman,et al.  Julia: A Fresh Approach to Numerical Computing , 2014, SIAM Rev..

[12]  M. Agostini,et al.  Discovery probability of next-generation neutrinoless double- β decay experiments , 2017, 1705.02996.

[14]  Thomas Hahn,et al.  Cuba - a library for multidimensional numerical integration , 2004, Comput. Phys. Commun..

[15]  Tim Besard,et al.  Effective Extensible Programming: Unleashing Julia on GPUs , 2017, IEEE Transactions on Parallel and Distributed Systems.

[16]  Allen Caldwell,et al.  Target Density Normalization for Markov Chain Monte Carlo Algorithms , 2014, 1410.7149.

[17]  P. Ullio,et al.  A critical reassessment of particle Dark Matter limits from dwarf satellites , 2016, 1603.07721.

[18]  S. Duane,et al.  Hybrid Monte Carlo , 1987 .

[19]  J. Erdmann,et al.  A likelihood-based reconstruction algorithm for top-quark pairs and the KLFitter framework , 2013, 1312.5595.

[20]  O. Luongo,et al.  Cosmological degeneracy versus cosmography: a cosmographic dark energy model , 2015, 1512.07076.

[21]  J. Erdmann,et al.  Constraining top-quark couplings combining top-quark and B decay observables , 2020 .

[22]  F. Beaujean A Bayesian analysis of rare B decays with advanced Monte Carlo methods , 2012 .

[24]  Kevin Kröninger,et al.  BAT - The Bayesian Analysis Toolkit , 2008, Comput. Phys. Commun..

[25]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

[26]  N. Kurz,et al.  Hypernuclear production cross section in the reaction of 6 Li + 12 C at 2 A GeV , 2015 .

[27]  Giulio D'Agostini,et al.  BAYESIAN REASONING IN DATA ANALYSIS: A CRITICAL INTRODUCTION , 2003 .

[28]  M. Pierini,et al.  Update of the electroweak precision fit, interplay with Higgs-boson signal strengths and model-independent constraints on new physics☆ , 2014, 1410.6940.

[29]  Radford M. Neal MCMC Using Hamiltonian Dynamics , 2011, 1206.1901.

[30]  Miles Lubin,et al.  Forward-Mode Automatic Differentiation in Julia , 2016, ArXiv.

[31]  Steffen Schumann,et al.  MC3 - A Multi-Channel Markov Chain Monte Carlo algorithm for phase-space sampling , 2014, Comput. Phys. Commun..

[32]  Jiqiang Guo,et al.  Stan: A Probabilistic Programming Language. , 2017, Journal of statistical software.

[33]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[34]  E. Jaynes Probability theory : the logic of science , 2003 .

[36]  Mark A. Moraes,et al.  Parallel random numbers: As easy as 1, 2, 3 , 2011, 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC).

[37]  Andrew Gelman,et al.  Inference from Simulations and Monitoring Convergence , 2011 .

[38]  John Salvatier,et al.  Probabilistic programming in Python using PyMC3 , 2016, PeerJ Comput. Sci..

[39]  D. Lindley Bayes theory , 1984 .

[40]  Michael Innes,et al.  Don't Unroll Adjoint: Differentiating SSA-Form Programs , 2018, ArXiv.

[41]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[42]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[43]  M. Pierini,et al.  The UTfit collaboration average of D meson mixing data: Winter 2014 , 2014, 1402.1664.

[44]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[45]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[46]  Andrew Gelman,et al.  The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo , 2011, J. Mach. Learn. Res..

[47]  Alan D. Martin,et al.  Review of Particle Physics , 2010 .

[48]  A. Sokal,et al.  The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk , 1988 .

[49]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[50]  A. Gelman,et al.  Weak convergence and optimal scaling of random walk Metropolis algorithms , 1997 .

[51]  A. Nozik,et al.  Prototype of a segmented scintillator detector for particle flux measurements on spacecraft , 2020, Journal of Instrumentation.

[52]  Michael Betancourt,et al.  A Conceptual Introduction to Hamiltonian Monte Carlo , 2017, 1701.02434.

[53]  P. Eller,et al.  Integration with an adaptive harmonic mean algorithm , 2018, International Journal of Modern Physics A.