Bayesian sequential procedure to estimate the viability of seeds Coffea arabica L. in tetrazolium test

Abstract

Tetrazolium tests use conventional sampling techniques in which a sample has a o Zootecnia, Av. Visconde do Rio Preto, s/n — 36301-360 — fixed size. These tests may be improved by sequential sampling, which does not work with fixed- s São João Del-Rei, MG — Brasil. size samples. When data obtained from an experiment are analyzed sequentially the analysis can OM 2Universidade Federal de Lavras -— Depto. de Estatística, C.P. be terminated when a particular decision has been made, and thus, there is no need to pre-es- "O 3037 - 37200-000 - Lavras, MG - Brasil. tablish the number of seeds to assess. Bayesian statistics can also help, if we have sufficient = Embrapa Café, PqEB, s/n - 70770-901 - Brasília, DF — knowledge about coffee production in the area to construct a prior distribution. Therefore, we Brasil. used the Bayesian sequential approach to estimate the percentage of viable coffee seeds sub- os “Universidade Federal de Lavras — Depto. de Agricultura. mitted to tetrazolium testing, and we incorporated priors with information from other analyses — *Corresponding author <carlabrighentiQufs).edu.br> of crops from previous years. We used the Beta prior distribution and, using data obtained from Ss sample lots of Coffea arabica, determined its hyperparameters with a histogram and O'Hagan's O Edited by: Marcin Kozak methods. To estimate the lowest risk, we computed the Bayes risks, which provided us with a = basis for deciding whether or not we should continue the sampling process. The results confirm e Received April 13, 2017 that the Bayesian sequential estimation can indeed be used for the tetrazolium test: the average Fi; Accepted January 06, 2018 percentage of viability obtained with the conventional frequentist method was 88 %, whereas that v obtained with the Bayesian method with both priors was 89 %. However, the Bayesian method E required, on average, only 89 samples to reach this value while the traditional estimation method O needed as many as 200 samples.