Preprint / Version 1

Bayesian Data Analysis for Sport Science

##article.authors##

  • Jorge del Rosario Fernández Santos University of Cadiz
  • Jesus Gustavo Ponce Gonzalez University of Cadiz
  • Jose Castro Piñero University of Cadiz
  • Jose Luis Gonzalez Montesinos University of Cadiz

DOI:

https://doi.org/10.51224/SRXIV.116

Keywords:

Bayesian data analysis, statistical modeling, sport science

Abstract

Bayesian data analysis (BDA) is method of statistical inference that make use of the probability for quantify uncertainty in inferences based on statistical data analysis. Along the manuscript different concepts are addressed to those sport scientists that want to start to use BDA: the Bayes ‘rule, hierarchical modeling, Markov Chain Monte Carlo techniques, predictive modeling, hypothesis testing and Bayesian workflow. Finally, an applied example is performed to help to apply of the previous concepts form a practical point of view and to report results.

Metrics

Metrics Loading ...

References

Lee, M.D.; Wagenmakers, E.-J. Bayesian Cognitive Modeling: A Practical Course; Cambridge University Press: Cambridge, 2014; ISBN 978-1-107-01845-7.

Kery, M. Introduction to WinBUGS for Ecologists: Bayesian Approach to Regression, ANOVA, Mixed Models and Related Analyses; Academic Press, Inc., 2010; ISBN 0-12-378605-3.

Greenberg, E. Introduction to Bayesian Econometrics; 2nd ed.; Cambridge University Press: Cambridge, 2012; ISBN 978-1-107-01531-9.

Lesaffre, E.; Lawson, A.B. Bayesian Biostatistics; John Wiley & Sons, 2012;

Gelman, A.; Carlin, J.B.; Stern, H.S.; Dunson, D.B.; Vehtari, A.; Rubin, D.B. Bayesian Data Analysis; CRC press, 2013;

Wagenmakers, E.-J.; Marsman, M.; Jamil, T.; Ly, A.; Verhagen, J.; Love, J.; Selker, R.; Gronau, Q.F.; Šmíra, M.; Epskamp, S.; et al. Bayesian Inference for Psychology. Part I: Theoretical Advantages and Practical Ramifications. Psychon. Bull. Rev. 2018, 25, 35–57, doi:10.3758/s13423-017-1343-3.

Kruschke, J.K.; Liddell, T.M. Bayesian Data Analysis for Newcomers. Psychon. Bull. Rev. 2018, 25, 155–177, doi:10.3758/s13423-017-1272-1.

Dienes, Z.; Mclatchie, N. Four Reasons to Prefer Bayesian Analyses over Significance Testing. Psychon. Bull. Rev. 2018, 25, 207–218, doi:10.3758/s13423-017-1266-z.

Santos-Fernandez, E.; Wu, P.; Mengersen, K.L. Bayesian Statistics Meets Sports: A Comprehensive Review. J. Quant. Anal. Sports 2019, 15, 289–312, doi:10.1515/jqas-2018-0106.

Bernards, J.R.; Sato, K.; Haff, G.G.; Bazyler, C.D. Current Research and Statistical Practices in Sport Science and a Need for Change. Sports Basel Switz. 2017, 5, doi:10.3390/sports5040087.

Mengersen, K.L.; Drovandi, C.C.; Robert, C.P.; Pyne, D.B.; Gore, C.J. Bayesian Estimation of Small Effects in Exercise and Sports Science. PloS One 2016, 11, e0147311, doi:10.1371/journal.pone.0147311.

Mai, Y.; Zhang, Z. Software Packages for Bayesian Multilevel Modeling. Struct. Equ. Model. Multidiscip. J. 2018, 25, 650–658, doi:10.1080/10705511.2018.1431545.

Bürkner, P.-C. Brms: An R Package for Bayesian Multilevel Models Using Stan. J. Stat. Softw. Vol 1 Issue 1 2017.

Bürkner, P.-C. Advanced Bayesian Multilevel Modeling with the R Package Brms. R J. 2018, 10, 395–411, doi:10.32614/RJ-2018-017.

Lunn, D.; Jackson, C.; Best, N.; Thomas, A.; Spiegelhalter, D. The BUGS Book: A Practical Introduction to Bayesian Analysis; CRC press, 2012;

Gelman, A.; Simpson, D.; Betancourt, M. The Prior Can Often Only Be Understood in the Context of the Likelihood. Entropy 2017, 19, doi:10.3390/e19100555.

Zondervan-Zwijnenburg, M.; Peeters, M.; Depaoli, S.; Van de Schoot, R. Where Do Priors Come From? Applying Guidelines to Construct Informative Priors in Small Sample Research. Res. Hum. Dev. 2017, 14, 305–320, doi:10.1080/15427609.2017.1370966.

McElreath, R. Statistical Rethinking: A Bayesian Course with Examples in R and Stan; CRC press, 2020;

Gill, J. Bayesian Methods: A Social and Behavioral Sciences Approach; CRC press, 2014; Vol. 20;.

Carpenter, B.; Gelman, A.; Hoffman, M.D.; Lee, D.; Goodrich, B.; Betancourt, M.; Brubaker, M.; Guo, J.; Li, P.; Riddell, A. Stan: A Probabilistic Programming Language. J. Stat. Softw. Vol 1 Issue 1 2017.

Hoffman, M.D.; Gelman, A. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 2014, 15, 1593–1623.

Monnahan, C.C.; Thorson, J.T.; Branch, T.A. Faster Estimation of Bayesian Models in Ecology Using Hamiltonian Monte Carlo. Methods Ecol. Evol. 2017, 8, 339–348, doi:10.1111/2041-210X.12681.

Kruschke, J. Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan. 2014.

Vehtari, A.; Gelman, A.; Simpson, D.; Carpenter, B.; Burkner, P.-C. Rank-Normalization, Folding, and Localization: An Improved $widehat{R}$ for Assessing Convergence of MCMC. Bayesian Anal 2021, doi:10.1214/20-BA1221.

Vehtari, A.; Gelman, A.; Gabry, J. Practical Bayesian Model Evaluation Using Leave-One-out Cross-Validation and WAIC. Stat. Comput. 2017, 27, 1413–1432, doi:10.1007/s11222-016-9696-4.

Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. J Mach Learn Res 2010, 11, 3571–3594.

Wasserstein, R.L.; Lazar, N.A. The ASA Statement on P-Values: Context, Process, and Purpose. Am. Stat. 2016, 70, 129–133, doi:10.1080/00031305.2016.1154108.

Greenland, S.; Senn, S.J.; Rothman, K.J.; Carlin, J.B.; Poole, C.; Goodman, S.N.; Altman, D.G. Statistical Tests, P Values, Confidence Intervals, and Power: A Guide to Misinterpretations. Eur. J. Epidemiol. 2016, 31, 337–350, doi:10.1007/s10654-016-0149-3.

Amrhein, V.; Greenland, S.; McShane, B. Scientists Rise up against Statistical Significance; Nature Publishing Group, 2019;

Wasserstein, R.L.; Schirm, A.L.; Lazar, N.A. Moving to a World Beyond “p < 0.05.” Am. Stat. 2019, 73, 1–19, doi:10.1080/00031305.2019.1583913.

Rouder, J.N.; Haaf, J.M.; Vandekerckhove, J. Bayesian Inference for Psychology, Part IV: Parameter Estimation and Bayes Factors. Psychon. Bull. Rev. 2018, 25, 102–113, doi:10.3758/s13423-017-1420-7.

Kruschke, J.K. Rejecting or Accepting Parameter Values in Bayesian Estimation. Adv. Methods Pract. Psychol. Sci. 2018, 1, 270–280, doi:10.1177/2515245918771304.

Kruschke, J.K.; Liddell, T.M. The Bayesian New Statistics: Hypothesis Testing, Estimation, Meta-Analysis, and Power Analysis from a Bayesian Perspective. Psychon. Bull. Rev. 2018, 25, 178–206, doi:10.3758/s13423-016-1221-4.

Gelman, A.; Vehtari, A.; Simpson, D.; Margossian, C.C.; Carpenter, B.; Yao, Y.; Kennedy, L.; Gabry, J.; Bürkner, P.-C.; Modrák, M. Bayesian Workflow; 2020;

Muth, C.; Oravecz, Z.; Gabry, J. User-Friendly Bayesian Regression Modeling: A Tutorial with Rstanarm and Shinystan. Quant. Methods Psychol. 2018, 14, 99–119, doi:10.20982/tqmp.14.2.p099.

Vasishth, S.; Nicenboim, B.; Beckman, M.E.; Li, F.; Kong, E.J. Bayesian Data Analysis in the Phonetic Sciences: A Tutorial Introduction. J. Phon. 2018, 71, 147–161, doi:10.1016/j.wocn.2018.07.008.

Bautista, J.R.; Pavlakis, A.; Rajagopal, A. Bayesian Analysis of Randomized Controlled Trials. Int. J. Eat. Disord. 2018, 51, 637–646, doi:10.1002/eat.22928.

Schad, D.J.; Betancourt, M.; Vasishth, S. Toward a Principled Bayesian Workflow in Cognitive Science; 2020;

Zuur, A.F.; Ieno, E.N. A Protocol for Conducting and Presenting Results of Regression-Type Analyses. Methods Ecol. Evol. 2016, 7, 636–645, doi:10.1111/2041-210X.12577.

Gabry, J.; Simpson, D.; Vehtari, A.; Betancourt, M.; Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 2019, 182, 389–402, doi:10.1111/rssa.12378.

Humberstone-Gough, C.E.; Saunders, P.U.; Bonetti, D.L.; Stephens, S.; Bullock, N.; Anson, J.M.; Gore, C.J. Comparison of Live High: Train Low Altitude and Intermittent Hypoxic Exposure. J. Sports Sci. Med. 2013, 12, 394.

Gore, C.J.; Sharpe, K.; Garvican-Lewis, L.A.; Saunders, P.U.; Humberstone, C.E.; Robertson, E.Y.; Wachsmuth, N.B.; Clark, S.A.; McLean, B.D.; Friedmann-Bette, B.; et al. Altitude Training and Haemoglobin Mass from the Optimised Carbon Monoxide Rebreathing Method Determined by a Meta-Analysis. Br. J. Sports Med. 2013, 47, i31, doi:10.1136/bjsports-2013-092840.

Wickham, H.; Averick, M.; Bryan, J.; Chang, W.; McGowan, L.D.; François, R.; Grolemund, G.; Hayes, A.; Henry, L.; Hester, J.; et al. Welcome to the Tidyverse. J. Open Source Softw. 2019, 4, 1686, doi:10.21105/joss.01686.

Kassambara, A. Ggpubr: “ggplot2” Based Publication Ready Plots; 2020;

Makowski, D.; Ben-Shachar, M.S.; Lüdecke, D. BayestestR: Describing Effects and Their Uncertainty, Existence and Significance within the Bayesian Framework. J. Open Source Softw. 2019, 4, 1541, doi:10.21105/joss.01541.

Gabry J, Mahr T Bayesplot: Plotting for Bayesian Models;

Vethari, A.; Gabry, J.; Magnusson, M.; Yao, Y.; Bürkner, P.; Paananen, T.; Gelman, A. Loo: Efficient Leave-One-out Cross-Validation and WAIC for Bayesian Models.; 2020;

Downloads

Posted

2022-01-28