Bayesian Analysis of Agricultural Experiments Using PROC MCM

Year 2021, Volume: 4 Issue: 3, 88 - 96, 01.07.2021

Mehmet Ziya Fırat

https://doi.org/10.47115/bsagriculture.874580

Abstract

The purpose of this study is to present the general concept of Bayesian analysis and the Markov chain Monte Carlo (MCMC) algorithm and to make some numerical comparisons with frequentist analyses. A factorial randomized complete-block (RCB) experiment is used to analyze the cowpea data set that has four separate single-column replicates, each containing 9 combinations of 3 varieties and 3 spacings. Response is the yield of cowpea hay. Point estimates of variance components obtained in the Bayesian analysis under the priors presented some differences with the Restricted Maximum Likelihood (REML) estimate. The Bayesian method overestimates the variance component compared with the REML estimate. Bayesian method to agricultural experiments is a very rich and useful tool. It provides in depth study of different features of the data which are otherwise hidden and cannot be explored using other techniques. Moreover, SAS software has a power and efficiency to deal with the numerical as well as graphical features of data sets from agricultural experiments.

Keywords

Bayesian analysis, Agricultural experiments, Markov Chain Monte Carlo, PROC MCMC

References

• Besag J, Green PJ, Higdon DM, Mengersen, KL. 1995 Bayesian computation and stochastic systems. Stat Sci, 10: 3-66.
• Besag J, Higdon DM. 1993. Bayesian inference for agricultural field experiments. Bull Int Statist IIIst, 55: 121-136.
• Besag J, Higdon, DM. 1999. Bayesian analysis of agricultural field experiments. J Royal Stat Society B, 61: 691–746.
• Cemal I, Karaman E, Firat MZ, Yilmaz O, Ata N, Karaca O. 2016. Bayesian inference of genetic parameters for ultrasound scanning traits of Kivircik lambs. Animal, 11(3): 375-381.
• Firat M.Z, Karaman E, Kaya Basar E, Narinc D. 2016. Bayesian analysis for the comparison of nonlinear regression model parameters: an Application to the growth of Japanese quail. Brazilian J Poultry Sci, 18: 19-26.
• Firat MZ, Theobald CM, Thompson R. 1997a. Univariate analysis of test day milk yields of British Holstein Friesian heifers using Gibbs sampling. Acta Agri Scand Section A, Animal Science, 47: 213-220.
• Firat MZ, Theobald CM, Thompson R. 1997b. Multivariate analysis of test day milk yields of British Holstein Friesian heifers using Gibbs sampling. Acta Agri Scanda Section A, Animal Science, 47: 221-229.
• Firat MZ. 2001. Bayesian analysis of test day milk yields in an unbalanced mixed model assuming random herd-year-montheffects. Turk J Vet Anim Sci, 25: 327-333
• Karaman E, Firat MZ, Narinc D. 2014. Single-Trait Bayesian analysis of some growth traits in Japanese. Brazilian J Poultry Sci, 16: 51-56.
• SAS Institute, 2004. SAS version 9.1.3. SAS Institute Inc., Cary, NC, USA.
• Smith RL, Naylor JC. 1987. A Comparison of Maximum Likelihood and Bayesian Estimators for the three-parameter Weibull Distribution. J Royal Stat Society Series C, 36: 358-369.
• Snedecor GW, Cochran WG. 1989. Statistical methods. Iowa State University Press, Ames, USA, 8th ed., pp 308.