Abstract: We take a Bayesian approach to choosing among fractional factorials. Experimental observations are thought of as realizations of a stationary Gaussian process operating on the design space. Pre-experimental knowledge is formally incorporated in the distribution of . Rather than demanding a precise prior distribution for , we seek designs that are optimal for families of priors, making the results robust. We examine Bayesian D-, A-, G-, E-, and -optimality, paying closest attention to D-optimality. Within a family of processes, we characterize D-optimal designs for nearly-independent and nearly-dependent priors. Often the maximum resolution-minimum aberration design is found optimal in all cases. However, for some and , a second design turns out to be optimal for certain subfamilies of processes.
Key words and phrases: Asymptotic D-optimality, Bayesian prediction, fractional factorials, Gaussian processes, maximin distance designs, resolution, stationary processes, two-level factors, word length pattern.