Assessing First-Order Emulator Inference for Physical Parameters in Nonlinear Mechanistic Models

Hooten, Mevin B.; Leeds, William B.; Fiechter, Jérôme; Wikle, Christopher K.

doi:10.1007/s13253-011-0073-7

Cited by 52 publications

(54 citation statements)

References 29 publications

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“…Harmon and Challenor, 1997), while characteristic (2) can be resolved using truncated error distributions (e.g. Hooten et al, 2011). All three characteristics together can be captured by gamma distributions (Dowd, 2007) or power-normal distributions whereby normality is assumed on a power-transformed scale (Freeman and Modarres, 2006).…”

Section: Uncertainty In Observationsmentioning

confidence: 99%

“…Increasing the dimension of the model introduces additional difficulties. One suggestion on how to reduce the dimension of a complex model output is given by Hooten et al (2011). The authors decomposed modelled surface Chl a concentrations of a suite of training runs into singular vectors and predicted the leading modes in dependence of a suite of biological and physical model parameters.…”

Section: Statistical Emulatorsmentioning

confidence: 99%

“…During a subsequent parameter optimization with respect to satellite chlorophyll, they identified zooplankton grazing rate and the light response of phytoplankton to be the most influential parameters. In contrast to most other approaches, where variances are estimated based on Bayesian techniques, Hooten et al (2011) used a Bayesian approach to estimate the mean values. The study of Leeds et al (2014) applied a similar technique for DA.…”

Section: Statistical Emulatorsmentioning

confidence: 99%

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Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

et al. 2017

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Abstract. To describe the underlying processes involved in oceanic plankton dynamics is crucial for the determination of energy and mass flux through an ecosystem and for the estimation of biogeochemical element cycling. Many planktonic ecosystem models were developed to resolve major processes so that flux estimates can be derived from numerical simulations. These results depend on the type and number of parameterizations incorporated as model equations. Furthermore, the values assigned to respective parameters specify a model's solution. Representative model results are those that can explain data; therefore, data assimilation methods are utilized to yield optimal estimates of parameter values while fitting model results to match data. Central difficulties are (1) planktonic ecosystem models are imperfect and (2) data are often too sparse to constrain all model parameters. In this review we explore how problems in parameter identification are approached in marine planktonic ecosystem modelling.We provide background information about model uncertainties and estimation methods, and how these are considered for assessing misfits between observations and model results. We explain differences in evaluating uncertainties in parameter estimation, thereby also discussing issues of parameter identifiability. Aspects of model complexity are addressed and we describe how results from cross-validation studies provide much insight in this respect. Moreover, approaches are discussed that consider time-and spacedependent parameter values. We further discuss the use of dynamical/statistical emulator approaches, and we elucidate issues of parameter identification in global biogeochemical models. Our review discloses many facets of parameter identification, as we found many commonalities between the objectives of different approaches, but scientific insight differed between studies. To learn more from results of planktonic ecosystem models we recommend finding a good balance in the level of sophistication between mechanistic modelling and statistical data assimilation treatment for parameter estimation.

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Section: Uncertainty In Observationsmentioning

confidence: 99%

Section: Statistical Emulatorsmentioning

confidence: 99%

Section: Statistical Emulatorsmentioning

confidence: 99%

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Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

et al. 2017

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“…An additional scenario for which this package can be useful is when the numerical method is not a finite difference method; e.g., a FEM. To this end, we will attempt to utilize Bayesian numerical analysis (Owhadi and Scovel, 2017) and emulator inference (Hooten et al, 2011); this will be crucial to ensure that 15 the methodology scales well computationally, since each posterior sample requires a forward PDE solve. Finally, and perhaps most importantly, future work will involve the application of the modeling and methodologies developed within this paper to real data collected by the IES-UI, which includes bedrock elevation and mass balance measurements.…”

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confidence: 99%

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

Gopalan¹,

Hrafnkelsson²,

Ađalgeirsdóttir³

et al. 2018

Preprint

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Abstract. Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). 5A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation 10 of numerical errors between the dome, interior, and margin of a glacier.

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“…We illustrate our methodology from Section 3 with a first-order emulator model as presented by Hooten et al (2011). Let x = {x i , i = 1, .…”

Section: Power Law Emulatormentioning

confidence: 99%

A Monte Carlo approach to quantifying model error in Bayesian parameter estimation

White

Herbei

2015

Computational Statistics & Data Analysis

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Assessing First-Order Emulator Inference for Physical Parameters in Nonlinear Mechanistic Models

Cited by 52 publications

References 29 publications

Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

A Monte Carlo approach to quantifying model error in Bayesian parameter estimation

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