Parallel partial Gaussian process emulation for computer models with massive output

Gu, Mengyang; Berger, James O.

doi:10.1214/16-aoas934

Cited by 99 publications

(122 citation statements)

References 42 publications

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“…We will then fit a GP to our scalar output—the max height data, h , at each location on the map (e.g., the discretized locations indexed k =1,…, M max height output is reported). It is worth noting that, once the training runs of TITAN2D are complete, these M emulators can be fit in parallel (the approach we take here), or the so‐called partial‐parallel emulation can be applied (Gu & Berger, ). Considering one location, we will let y S =[ h 1 ,…, h N ] T be a vector of simulated output corresponding to each of N TITAN2D runs at scenarios in the design

X_{D}

.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Probabilistic Hazard Mapping in the Long Valley Volcanic Region CA: Integrating Vent Opening Maps and Statistical Surrogates of Physical Models of Pyroclastic Density Currents

et al. 2019

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Ideally, probabilistic hazard assessments combine available knowledge about physical mechanisms of the hazard, data on past hazards, and any precursor information. Systematically assessing the probability of rare, yet catastrophic hazards adds a layer of difficulty due to limited observation data. Via computer models, one can exercise potentially dangerous scenarios that may not have happened in the past but are probabilistically consistent with the aleatoric nature of previous volcanic behavior in the record. Traditional Monte Carlo‐based methods to calculate such hazard probabilities suffer from two issues: they are computationally expensive, and they are static. In light of new information, newly available data, signs of unrest, and new probabilistic analysis describing uncertainty about scenarios the Monte Carlo calculation would need to be redone under the same computational constraints. Here we present an alternative approach utilizing statistical emulators that provide an efficient way to overcome the computational bottleneck of typical Monte Carlo approaches. Moreover, this approach is independent of an aleatoric scenario model and yet can be applied rapidly to any scenario model making it dynamic. We present and apply this emulator‐based approach to create multiple probabilistic hazard maps for inundation of pyroclastic density currents in the Long Valley Volcanic Region. Further, we illustrate how this approach enables an exploration of the impact of epistemic uncertainties on these probabilistic hazard forecasts. Particularly, we focus on the uncertainty of vent opening models and how that uncertainty both aleatoric and epistemic impacts the resulting probabilistic hazard maps of pyroclastic density current inundation.

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X_{D}

.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Probabilistic Hazard Mapping in the Long Valley Volcanic Region CA: Integrating Vent Opening Maps and Statistical Surrogates of Physical Models of Pyroclastic Density Currents

et al. 2019

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“…For spatial fields, the most common approach to emulation and calibration involves projecting the model output onto a low-dimensional basis, Γ, and emulating the coefficients, so that fewer emulators are required (Bayarri et al, 2007;Higdon et al, 2008;Wilkinson, 2010;Sexton et al, 2011) (although alternatives, such as emulating every grid box individually, have been applied, e.g. by Gu et al (2016)).…”

Section: Calibration With Spatial Outputmentioning

confidence: 99%

Uncertainty Quantification for Computer Models With Spatial Output Using Calibration-Optimal Bases

Salter

Williamson

Scinocca³

et al. 2019

Journal of the American Statistical Association

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The calibration of complex computer codes using uncertainty quantification (UQ) methods is a rich area of statistical methodological development. When applying these techniques to simulators with spatial output, it is now standard to use principal component decomposition to reduce the dimensions of the outputs in order to allow Gaussian process emulators to predict the output for calibration. We introduce the 'terminal case', in which the model cannot reproduce observations to within model discrepancy, and for which standard calibration methods in UQ fail to give sensible results. We show that even when there is no such issue with the model, the standard decomposition on the outputs can and usually does lead to a terminal case analysis. We present a simple test to allow a practitioner to establish whether their experiment will result in a terminal case analysis, and a methodology for defining calibration-optimal bases that avoid this whenever it is not inevitable. We present the optimal rotation algorithm for doing this, and demonstrate its efficacy for an idealised example for which the usual principal component methods fail. We apply these ideas to the CanAM4 model to demonstrate the terminal case issue arising for climate models. We discuss climate model tuning and the estimation of model discrepancy within this context, and show how the optimal rotation algorithm can be used in developing practical climate model tuning tools. * The authors gratefully acknowledge support from EPSRC fellowship No. EP/K019112/1 and support from the NSERC funded Canadian Network for Regional Climate and Weather Processes (CNRCWP). We would also like to thank Yanjun Jiao for managing our ensembles of CanAM4.

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“…Define the nugget variance ratio parameter η = σ 2 0 /σ 2 . The reference prior π R (γ, η) has been derived for the GaSP model with a noise (Ren et al (2012); Kazianka and Pilz (2012); Gu and Berger (2016)). The advantages of using the reference prior with a nugget are similar to our previous discussion and are thus omitted here.…”

Section: )mentioning

confidence: 99%

Jointly Robust Prior for Gaussian Stochastic Process in Emulation, Calibration and Variable Selection

Gu¹

2019

Bayesian Anal.

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Gaussian stochastic process (GaSP) has been widely used in two fundamental problems in uncertainty quantification, namely the emulation and calibration of mathematical models. Some objective priors, such as the reference prior, are studied in the context of emulating (approximating) computationally expensive mathematical models. In this work, we introduce a new class of priors, called the jointly robust prior, for both the emulation and calibration. This prior is designed to maintain various advantages from the reference prior. In emulation, the jointly robust prior has an appropriate tail decay rate as the reference prior, and is computationally simpler than the reference prior in parameter estimation. Moreover, the marginal posterior mode estimation with the jointly robust prior can separate the influential and inert inputs in mathematical models, while the reference prior does not have this property. We establish the posterior propriety for a large class of priors in calibration, including the reference prior and jointly robust prior in general scenarios, but the jointly robust prior is preferred because the calibrated mathematical model typically predicts the reality well. The jointly robust prior is used as the default prior in two new R packages, called "RobustGaSP" and "RobustCalibration", available on CRAN for emulation and calibration, respectively.

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Parallel partial Gaussian process emulation for computer models with massive output

Cited by 99 publications

References 42 publications

Dynamic Probabilistic Hazard Mapping in the Long Valley Volcanic Region CA: Integrating Vent Opening Maps and Statistical Surrogates of Physical Models of Pyroclastic Density Currents

Dynamic Probabilistic Hazard Mapping in the Long Valley Volcanic Region CA: Integrating Vent Opening Maps and Statistical Surrogates of Physical Models of Pyroclastic Density Currents

Uncertainty Quantification for Computer Models With Spatial Output Using Calibration-Optimal Bases

Jointly Robust Prior for Gaussian Stochastic Process in Emulation, Calibration and Variable Selection

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