Signal aliasing in Gaussian random fields for experiments with qualitative factors
| Autor: | Ching-Shui Cheng, Ming-Chung Chang, Shao-Wei Cheng |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Random field Covariance function fractional factorial computer experiment Gaussian eigen-decomposition kriging model Linear model Fractional factorial design Random effects model Bayesian design 01 natural sciences fixed-effect model Gaussian random field 010104 statistics & probability symbols.namesake 62K15 symbols 0101 mathematics Statistics Probability and Uncertainty Aliasing (computing) Algorithm random-effect model Mathematics |
| Zdroj: | Ann. Statist. 47, no. 2 (2019), 909-935 |
| Popis: | Signal aliasing is an inevitable consequence of using fractional factorial designs. Unlike linear models with fixed factorial effects, for Gaussian random field models advocated in some Bayesian design and computer experiment literature, the issue of signal aliasing has not received comparable attention. In the present article, this issue is tackled for experiments with qualitative factors. The signals in a Gaussian random field can be characterized by the random effects identified from the covariance function. The aliasing severity of the signals is determined by two key elements: (i) the aliasing pattern, which depends only on the chosen design, and (ii) the effect priority, which is related to the variances of the random effects and depends on the model parameters. We first apply this framework to study the signal-aliasing problem for regular fractional factorial designs. For general factorial designs including nonregular ones, we propose an aliasing severity index to quantify the severity of signal aliasing. We also observe that the aliasing severity index is highly correlated with the prediction variance. |
| Databáze: | OpenAIRE |
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