4/23/2024 0 Comments Latin hypercube sampling in excelMaximin designs are more deterministic, even if many solvers for such designs deploy stochastic search. LHSs are random, so they disperse in a probabilistic sense, targeting a certain uniformity property. Both are based on geometric criteria but offer optimal spread in different senses. Our development will focus on variations between, and combinations of, two of the most popular space-filling schemes: Latin hypercube sampling (LHS), and maximin distance designs. A spread of training examples, the thinking goes, will ultimately yield fitted models which smooth/interpolate/extrapolate best, leading to more accurate predictions at out-of-sample testing locations. Here we seek so-called space-filling designs, ones which spread out points with the aim of encouraging a diversity of data once responses are observed. Later in Chapter 6 we’ll develop model-specific analogs and find striking similarity, and in some sense inferiority – a bizarre result considering their optimality – compared to these model-free analogs. Designs here are model-free, meaning that we don’t need to know anything about the (Gaussian process) models we intend to use with them, except in the loose sense that those are highly flexible models which impose limited structure on the underlying data they’re trained on. One of the goals here is pragmatic from an organizational perspective: to have some simple, good designs for illustrations and comparisons in later chapters. Nonparametric spatial regression, emphasizing Gaussian processes in Chapter 5, benefits from a more agnostic approach to design compared to classical, linear modeling-based, response surface methods. This segment puts the cart before the horse a little.
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