Bayesçi ANOVA(BANOVA): Ankara’da Hava Kirliliği Üzerine Bir Uygulama

Yıl 2021, , 8 - 22, 30.06.2021

Serpil Aktaş

https://doi.org/10.52693/jsas.940764

Cited By: 1

Öz

Bayesçi yaklaşım, klasik istatistik yaklaşımının aksine önsel dağılım bilgisi yardımı ile sonsal dağılımı tahmin eden bir yöntemdir. BANOVA gibi yöntemlerde p-değeri yerine farklı Bayesçi kriterlere göre yokluk hipotezi için karar verilir. BANOVA modelinde sadece genel ortalama terimin mi yer alacağı ya da deneme etkisinin yer aldığı model mi geçerlidir araştırmasında, Bayesçi faktör (BF)’e bakılarak yokluk hipotezi ile seçenek hipotezi karşılaştırılarak hangisi için daha güçlü bir kanıt varsa ona göre karar verilir. BF ile verilen bu karar aşaması deneme etkisinin anlamlı olup olmadığına dair elimizde ne kadar güçlü bir kanıt olup olmadığını ortaya koyan ANOVA’dan daha detaylı bir çıkarsamadır. Bu çalışmada Çevre ve Şehircilik Bakanlığı Ulusal Hava Kalitesi İzleme Sisteminden alınan Ocak-Aralık 2018 dönemine ait Ankara iline ait sekiz istasyondan alınmış PM10, PM2,5 ve SO2 değerlerine göre istasyonlar arası farklılık BANOVA ile analiz edilmiş ve sonuçlar yorumlanmıştır.

Anahtar Kelimeler

BANOVA, Bayes Faktörü, ANOVA, Hava Kirliliği

Bayesian ANOVA(BANOVA): An Application on Air Pollution in Ankara

Öz

Bayesian approach is a posterior prediction method via a priori distribution knowledge on the contrary to classical methods. In the methods like BANOVA, Bayesian criteria are employed for the null hypothesis instead of the p-value. The question of whether only the overall mean term will represent the ANOVA model or whether the treatment effect will be added is answered with the Bayesian (BF). According to the BF, the null hypothesis is compared to the alternative hypothesis, and which model has stronger evidence is given accordingly. This decision step with the BF, which reveals how strong evidence we have about whether the treatment effect is significant or not, is a more detailed inference than classical ANOVA. In this study, the BANOVA method is applied to PM10, PM2,5, and SO2 data from eight stations of the province of Ankara for the period January-December 2018, taken from the National Air Quality Monitoring System of the Ministry of Environment and Urbanization. Whether there is any difference between stations is analyzed and conclusions are made.

Anahtar Kelimeler

BANOVA, ANOVA, Bayes Factor, Air Pollution

Kaynakça

• Ankara İli Temiz Hava Eylem Plani, 2020-2024.
• Amrhein, V., Greenland, S., & McShane, B. (2019). “Scientists rise up against statistical significance”. Nature, 567 , pp.305-307.
• Bayarri, M. J., and Garc´ıa-Donato, G. (2007), “Extending Conventional Priors for Testing General Hypotheses in Linear Models,” Biometrika, 94, pp.135–152.
• Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer Series in Statistics (Second ed.). Springer-Verlag
• Box, G. E. P. and Tiao, G. C. (1992). Bayesian Inference in Statistical Analysis, John Wiley and Sons, Inc.
• Carlin, B.P. and Louis, T.A. (2000). Bayes and Empirical Bayes Methods for Data Analysis. 2nd Edition, Chapman and Hall/CRC, New York.
• Ellison, A. M., 2004. “Bayesian inference in ecology”. Ecology Letters, 7(6), pp.509–520.
• König, C. and Van de Schoot, R. (2017). Bayesian statistics in educational research: a look at the current state of affairs, Educational Review, 70(4), 486-509.
• Cohen, J. (1994). The earth is round (p < :05). American Psychologist, 49, pp.997-1003.
• Dienes, Z. (2016).” How Bayes factors change scientific practice”. Journal of Mathematical Psychology, 72, 78-89.
• Gelman, A. (2005). “Analysis of variance why it is more important than ever”. Annals of Statistics, 33, pp.1–53.
• Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis (2nded.). London: Chapman and Hall.
• Kass, R. E. and Raftery, A. E. (1995). Bayes Factors. Journal of the American Statistical Association, 90(430),pp.773–795.
• Jeffreys, H.(1961). Theory of Probability, Third Edition.Clarendon Press:Oxford.
• Kaplan, D. (2014). Bayesian Statistics for the Social Sciences. London: Guilford.
• Kirk, R. E. (2003). “The Importance of Effect Magnitude.” In Handbook of Research Methods in Experimental Psychology, edited by Stephen F. Davis, 83–105. Malden, MA: Blackwell.
• Kruschke, J. (2010), “Doing Bayesian Data Analysis”, Wiley interdisciplinary reviews. Cognitive Science 1(5),pp.658 – 676.
• JASP Team (2020). JASP (Version 0.14.1)[Computer software].
• Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16(2), pp.225–237.
• Schmidt, F. L. (1996). “Statistical Significance Testing and Cumulative Knowledge in Psychology:Implications for Training of Researchers.” Psychological Methods, 1, pp.115–129.
• Wagenmakers, Eric-Jan & Marsman, Maarten & Jamil, Tahira & Ly, Alexander & Verhagen, A J & Love, Jonathon & Selker, Ravi & Gronau, Quentin & Šmíra, Martin & Epskamp, Sacha & Matzke, Dora & Rouder, Jeffrey & Morey, Richard. (2017). Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications. Psychonomic Bulletin & Review. 25(1),pp.35-57.
• Morey, R. D. (2018). Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications. Psychonomic Bulletin & Review, 25, pp.35–57.
• Morey, R. D., & Rouder, J. N. (2011). Bayes factor approaches for testing interval null hypotheses. Psychological Methods, 16, pp.406–419.
• Nel, A., 2005. “Air Pollution-Related Illness: Effects of Particles”. Science, 308, pp.804-806. Van den Bergh, D., van Doorn, J., Marsman, M., Draws, T., van Kesteren, E.-J., Derks, K., Dablander, F., Gronau, Q. F., Kucharsky, S., Komarlu Narendra Gupta, A. R., Sarafoglou, A., Voelkel, J. G., Stefan, A., Ly, A., Hinne, M., Matzke, D., & Wagenmakers, E.-J . “A tutorial on conducting and interpreting a Bayesian ANOVA in JASP”. Dans L’Année psychologique 2020/1 (Vol. 120), pp.73-96
• Plummer, M. 2016. “Rjags: Bayesian Graphical Models Using MCMC. R Package Version 4-6.” https:// CRAN.R-project.org/package=rjags.
• Schönbrodt, F. D., & Wagenmakers, E.-J. (2018). Bayes factor design analysis: Planning for compelling evidence. Psychonomic Bulletin & Review, 25(1), pp.128–142.
• Morey, R. D., & Rouder, J. N. (2015). BayesFactor 0.9.12-4.2. Comprehensive R Archive Network. Retrieved from https://CRAN.R-project.org/
• Wetzels, R., Grasman, R. P. P. P. , Wagenmakers E., (2012) “A Default Bayesian Hypothesis Test For Anova Designs”. The American Statistician, 66(2), pp.104-111.