Bayesian Analysis of Agricultural Experiments Using PROC MCM

Mehmet Ziya Firat

doi: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.

Highlights

A main objective of most of agricultural experiments is to determine the effect of different treatments on a particular crop variety
Faster computers and increasing popularity of Markov chain Monte Carlo (MCMC) methods have allowed Bayesian methods to become widely used in complex data analysis problems, the Bayesian approach has yet to provide a completely satisfactory answer in the analysis of agricultural experiments, since there has been a lack of application in this area
We have presented the general concept of Bayesian methodology and the MCMC algorithm for the analysis of agricultural field experiments, a subject that has received not much previous attention despite an enormous number of frequentist literatures, in a way that can be understood by agricultural practitioners

Summary

Introduction

A main objective of most of agricultural experiments is to determine the effect of different treatments on a particular crop variety. Faster computers and increasing popularity of MCMC methods have allowed Bayesian methods to become widely used in complex data analysis problems, the Bayesian approach has yet to provide a completely satisfactory answer in the analysis of agricultural experiments, since there has been a lack of application in this area. Besag and Higdon (1993, 1999) and Besag et al (1995) discussed Bayesian approaches for analyzing agricultural field experiments They proposed complex formulations for situations when spatial effects were considered, while our approach is for the standard additive mixed model.

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