Bayesian A-optimal two-phase designs with a single blocking factor in each phase

Abstract

Two-phase experiments are widely used in many areas of science (e.g., agriculture, industrial engineering, food processing, etc.). For example, consider a two-phase experiment in plant breeding. Often, the first phase of this experiment is run in a field involving several blocks. The samples obtained from the first phase are then analyzed in several machines (or days, etc.) in a laboratory in the second phase. There might be field-block-to-field-block and machine-to-machine (or day-to-day, etc.) variation. Thus, it is practical to consider these sources of variation as blocking factors. Clearly, there are two possible strategies to analyze this kind of two-phase experiment, i.e., blocks are treated as fixed or random. While there are a few studies regarding fixed block effects, there are still a limited number of studies with random block effects and when information of block effects is uncertain. Hence, it is beneficial to consider a Bayesian approach to design for such an experiment, which is the main goal of this work. In this paper, we construct a design for a two-phase experiment that has a single treatment factor, a single blocking factor in each phase, and a response that can only be observed in the second phase.