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Abstract:
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Historically, design an analysis of computer experiments focuses on deterministic solvers from the physical sciences. But nowadays computer modeling is common in the social and biological sciences, where stochastic simulations abound. As the simulations become noisier the experiments need to be bigger, in order to isolate signal from noise. Replication offers a pure look at noise, not obfuscated by signal, but ultimately it is the signal which is of primary interest. So how much replication should be performed in the context of simulation experiments? We develop a sequential design scheme that can determine if new runs should be at new input locations, or rather should instead be replications (at existing input locations). Our heteroskedastic Gaussian process (hetGP) model learns the signal-to-noise ratio throughout the input space, in a way that is computationally favorable when replication is present. Based on those estimates, het GP can dynamically determine the balance of replicates in the design, differentially throughout the input space. We show designs so-developed for two challenging real-data simulation experiments, from inventory management and epidemiology.
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