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Statistica Sinica 11(2001), 605-630


M. Kathleen Kerr

The Jackson Laboratory

Abstract: We take a Bayesian approach to choosing among $2^{k-p}$ fractional factorials. Experimental observations are thought of as realizations of a stationary Gaussian process $X$ operating on the design space. Pre-experimental knowledge is formally incorporated in the distribution of $X$. Rather than demanding a precise prior distribution for $X$, we seek designs that are optimal for families of priors, making the results robust. We examine Bayesian D-, A-, G-, E-, and $\bc$-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 $k$ and $p$, 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.

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