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Genebank managers conduct viability tests on stored seeds so they can replace lots that have viability near a critical threshold, such as 50 or 85 % germination. Currently, these tests are typically scheduled at uniform intervals; testing every 5 years is common. A manager needs to balance the cost of an additional test against the possibility of losing a seed lot due to late retesting. We developed a data-informed method to schedule viability tests for a collection of 2,833 maize seed lots with 3 to 7 completed viability tests per lot. Given these historical data reporting on seed viability at arbitrary times, we fit a hierarchical Bayesian seed-viability model with random seed lot specific coefficients. The posterior distribution of the predicted time to cross below a critical threshold was estimated for each seed lot. We recommend a predicted quantile as a retest time, chosen to balance the importance of catching quickly decaying lots against the cost of premature tests. The method can be used with any seed-viability model; we focused on two, the Avrami viability curve and a quadratic curve that accounts for seed after-ripening. After fitting both models, we found that the quadratic curve gave more plausible predictions than did the Avrami curve. Also, a receiver operating characteristic (ROC) curve analysis and a follow-up test demonstrated that a 0.05 quantile yields reasonable predictions. RightsWorks produced by employees of the U.S. Government as part of their official duties are not copyrighted within the U.S. The content of this document is not copyrighted. Genebank managers conduct viability tests on stored seeds so they can replace lots that have viability near a critical threshold, such as 50 or 85 % germination. Currently, these tests are typically scheduled at uniform intervals; testing every 5 years is common. A manager needs to balance the cost of an additional test against the possibility of losing a seed lot due to late retesting. We developed a data-informed method to schedule viability tests for a collection of 2,833 maize seed lots with 3 to 7 completed viability tests per lot. Given these historical data reporting on seed viability at arbitrary times, we fit a hierarchical Bayesian seed-viability model with random seed lot specific coefficients. The posterior distribution of the predicted time to cross below a critical threshold was estimated for each seed lot. We recommend a predicted quantile as a retest time, chosen to balance the importance of catching quickly decaying lots against the cost of premature tests. The method can be used with any seed-viability model; we focused on two, the Avrami viability curve and a quadratic curve that accounts for seed after-ripening. After fitting both models, we found that the quadratic curve gave more plausible predictions than did the Avrami curve. Also, a receiver operating characteristic (ROC) curve analysis and a follow-up test demonstrated that a 0.05 quantile yields reasonable predictions.

P. Widrlechner. You have made me a better writer with your amazing word smithing and awesome editing skills. And to the rest of my committee, you have taught me so much. Thank you! 1 CHAPTER 1. INTRODUCTIONThe genesis of this dissertation comes from responses to two questions tied to risk. The first question regards the testing of seed viability, the ability of a seed to germinate. A seed is a living organism and over time it dies. The United States government has assembled a vast collection of seed lots in long-term storage facilities for many decades. The goal of storing these lots is to preserve genetic information that may be useful in the future. Genebank managers maintain these stores of seeds and must periodically test the lots to ensure they are still viable. In the event that less than 50% [85% or some other critical value] of seeds germinate in a viability test, the manager regenerates the lot. Genebank managers use their subjective discretion when scheduling viability tests. In a perfect world, they schedule every test at the right moment. In such a world, every lot has exactly one test, and the proportion of viable seeds is very near the critical germination proportion that determines the regeneration of a lot. Genebank managers do not want to risk losing a seed lot because a test is too late, and a large portion, if not all, of the seeds are dead. They do not want to waste resources because the test is too early, and a large portion, if not all, of the seeds are viable. Five years ago, Mark Widrlechner and David Kovach asked Philip Dixon and me if a statistically based, seed-viability testing schedule was possible. Chapter 2 is the result of our collaboration.The creation of a viability-test schedule requires the use of a bevy of statistical methods and procedures. From a collection of historical seed-viability test data on long-term stored maize seed lots, we fit a random-coefficients regression model where the coefficients describe a quadratic curve of seed age versus germination percentage (Laird and Ware (1982)). A seed lot's individuality is not lost with this model's form. This is important because we desire a testing schedule that has unique testing ages for each seed lot. Given a critical germination level like 50%, we back-solve predicted age for each seed lot's quadratic curve. To deduce the