THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING
Key aspects of Markov Chain Monte Carlo simulations in Bayesian statistical analysis
- 1 Faculty of Computer Science and Engineering, University Ss Cyril and Methodius Skopje, Republic of North Macedonia
Abstract
This paper focuses on the simulation aspects of Bayesian hypothesis testing applied on ophthalmic data. Bayesian statistical analysis often relies on Markov Chain Monte Carlo (MCMC) methods for estimation, when analytical solutions are not possible. We highlight the key aspects of MCMC including model specification, details on the simulation, MCMC diagnostics as well as its limitations and advantages. The simulations are done using R and JAGS.
Keywords
References
- Kruschke, J. K. Bayesian estimation supersedes the t test. Journal of Experimental Psychology: General, 142(2), 2013, 573-603
- J.K. Kruschke, Bayesian Analysis Reporting Guidelines. Nature Human Behavior 5, (2021), 1282–1291
- G. Dimitrova, A. Ljubic, B. Tojtovska, K. Tagasovska, U. Tomasevic. Pressure Related Ocular Parameters in Caucasian Patients with Primary Open-Angle Glaucoma. Journal of Ocular Diseases and Therapeutics. 9, (June 2021), 10–14
- Gelman, A. Bayesian Data Analysis. Boca Raton, CRC press, 2013
- A. Gabrio, Faculty of Health medicine and life sciences, Maastricht University, Blog post on Comparing two populations in Jags
- Plummer, M. JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), Vienna, Austria, 2003
- Brooks, S., Gelman, A., Jones, G. L., & Meng, X. L. (Eds.). Handbook of Markov chain Monte Carlo. Boca Raton, CRC press, 2011
- M.C. Leske, Ocular perfusion pressure and glaucoma: clinical trial and epidemiologic findings. Current opinion in ophthalmology. (March 2009) 20(2):73-8
- K.E. Kim, S. Oh, S.U. Baek, et al. Ocular Perfusion Pressure and the Risk of Open-Angle Glaucoma: Systematic Review and Metaanalysis. Science Reports, 10, 10056 (2020)
- B. Tojtovska, P. Ribarski, G. Dimitrova, A. Ljubic, Bayesian vs frequentist inference – an ophthalmic study on ocular perfusion pressure, Conference “Mathmodel 2024”, Borovets, Bulgaria, 2024