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Calibration under Uncertainty Using Bayesian Emulation and History Matching: Methods and Illustration on a Building Energy Model (2024)
Journal Article
Domingo, D., Royapoor, M., Du, H., Boranian, A., Walker, S., & Goldstein, M. (2024). Calibration under Uncertainty Using Bayesian Emulation and History Matching: Methods and Illustration on a Building Energy Model. Energies, 17(16), Article 4014. https://doi.org/10.3390/en17164014

Energy models require accurate calibration to deliver reliable predictions. This study offers statistical guidance for a systematic treatment of uncertainty before and during model calibration. Statistical emulation and history matching are introduce... Read More about Calibration under Uncertainty Using Bayesian Emulation and History Matching: Methods and Illustration on a Building Energy Model.

Emulation and History Matching using the hmer Package (2024)
Journal Article
Iskauskas, A., Vernon, I., Goldstein, M., Scarponi, D., McKinley, T. J., White, R. G., & McCreesh, N. (2024). Emulation and History Matching using the hmer Package. Journal of Statistical Software, 109(10), 1–48. https://doi.org/10.18637/jss.v109.i10

Modeling complex real-world situations such as infectious diseases, geological phenomena, and biological processes can present a dilemma: the computer model (referred to as a simulator) needs to be complex enough to capture the dynamics of the system... Read More about Emulation and History Matching using the hmer Package.

Demonstrating multi-country calibration of a tuberculosis model using new history matching and emulation package - hmer (2023)
Journal Article
Scarponi, D., Iskauskas, A., Clark, R. A., Vernon, I., McKinley, T. J., Goldstein, M., Mukandavire, C., Deol, A., Weerasuriya, C., Bakker, R., White, R. G., & McCreesh, N. (2023). Demonstrating multi-country calibration of a tuberculosis model using new history matching and emulation package - hmer. Epidemics, 43, Article 100678. https://doi.org/10.1016/j.epidem.2023.100678

Infectious disease models are widely used by epidemiologists to improve the understanding of transmission dynamics and disease natural history, and to predict the possible effects of interventions. As the complexity of such models increases, however,... Read More about Demonstrating multi-country calibration of a tuberculosis model using new history matching and emulation package - hmer.

Foundations for temporal reasoning using lower previsions without a possibility space (2022)
Book Chapter
Troffaes, M. C., & Goldstein, M. (2022). Foundations for temporal reasoning using lower previsions without a possibility space. In T. Augustin, F. Gagliardi Cozman, & G. Wheeler (Eds.), Reflections on the Foundations of Probability and Statistics: Essays in Honor of Teddy Seidenfeld (69-96). (1). Springer Verlag. https://doi.org/10.1007/978-3-031-15436-2_4

We introduce a new formal mathematical framework for probability theory, taking random quantities to be the fundamental objects of interest, without reference to a possibility space, in spirit of de Finetti’s treatment of probability, Goldstein’s Bay... Read More about Foundations for temporal reasoning using lower previsions without a possibility space.

Complex model calibration through emulation, a worked example for a stochastic epidemic model (2022)
Journal Article
Dunne, M., Mohammadi, H., Challenor, P., Borgo, R., Porphyre, T., Vernon, I., Firat, E. E., Turkay, C., Torsney-Weir, T., Goldstein, M., Reeve, R., Fang, H., & Swallow, B. (2022). Complex model calibration through emulation, a worked example for a stochastic epidemic model. Epidemics, 39, Article 100574. https://doi.org/10.1016/j.epidem.2022.100574

Uncertainty quantification is a formal paradigm of statistical estimation that aims to account for all uncertainties inherent in the modelling process of real-world complex systems. The methods are directly applicable to stochastic models in epidemio... Read More about Complex model calibration through emulation, a worked example for a stochastic epidemic model.

Varying Coefficient Models and Design Choice for Bayes Linear Emulation of Complex Computer Models with Limited Model Evaluations (2022)
Journal Article
Wilson, A. L., Goldstein, M., & Dent, C. J. (2022). Varying Coefficient Models and Design Choice for Bayes Linear Emulation of Complex Computer Models with Limited Model Evaluations. SIAM/ASA Journal on Uncertainty Quantification, 10(1), 350-378. https://doi.org/10.1137/20m1318560

Computer models are widely used to help make decisions about real-world systems. As computer models of large and complex systems can have long run-times and high-dimensional input spaces, it is often necessary to use emulation to assess uncertainties... Read More about Varying Coefficient Models and Design Choice for Bayes Linear Emulation of Complex Computer Models with Limited Model Evaluations.

Intermediate Variable Emulation: using internal processes in simulators to build more informative emulators (2022)
Journal Article
Oughton, R., Goldstein, M., & Hemmings, J. (2022). Intermediate Variable Emulation: using internal processes in simulators to build more informative emulators. SIAM/ASA Journal on Uncertainty Quantification, 10(1), 268-293. https://doi.org/10.1137/20m1370902

Complex systems are often modelled by intricate and intensive computer simulators. This makes their behaviour difficult to study, and so a statistical representation of the simulator is often used, known as an emulator, to enable users to explore the... Read More about Intermediate Variable Emulation: using internal processes in simulators to build more informative emulators.

Challenges in estimation, uncertainty quantification and elicitation for pandemic modelling (2022)
Journal Article
Swallow, B., Birrell, P., Blake, J., Burgman, M., Challenor, P., Coffeng, L. E., Dawid, P., De Angelis, D., Goldstein, M., Hemming, V., Marion, G., McKinley, T. J., Overton, C. E., Panovska-Griffiths, J., Pellis, L., Probert, W., Shea, K., Villela, D., & Vernon, I. (2022). Challenges in estimation, uncertainty quantification and elicitation for pandemic modelling. Epidemics, 38, https://doi.org/10.1016/j.epidem.2022.100547

The estimation of parameters and model structure for informing infectious disease response has become a focal point of the recent pandemic. However, it has also highlighted a plethora of challenges remaining in the fast and robust extraction of infor... Read More about Challenges in estimation, uncertainty quantification and elicitation for pandemic modelling.

Optimization via Statistical Emulation and Uncertainty Quantification: Hosting Capacity Analysis of Distribution Networks (2021)
Journal Article
Du, H., Sun, W., Goldstein, M., & Harrison, G. (2021). Optimization via Statistical Emulation and Uncertainty Quantification: Hosting Capacity Analysis of Distribution Networks. IEEE Access, 9, 118472-118483. https://doi.org/10.1109/access.2021.3105935

In power systems modelling, optimization methods based on certain objective function(s) are widely used to provide solutions for decision makers. For complex high-dimensional problems, such as network hosting capacity evaluation of intermittent renew... Read More about Optimization via Statistical Emulation and Uncertainty Quantification: Hosting Capacity Analysis of Distribution Networks.

Bayes linear analysis for ordinary differential equations (2021)
Journal Article
Jones, M., Goldstein, M., Randell, D., & Jonathan, P. (2021). Bayes linear analysis for ordinary differential equations. Computational Statistics & Data Analysis, 161, Article 107228. https://doi.org/10.1016/j.csda.2021.107228

Differential equation models are used in a wide variety of scientific fields to describe the behaviour of physical systems. Commonly, solutions to given systems of differential equations are not available in closed-form; in such situations, the solut... Read More about Bayes linear analysis for ordinary differential equations.

Accounting for Model Discrepancy in Uncertainty Analysis by Combining Numerical Simulation and Bayesian Emulation Techniques (2020)
Presentation / Conference Contribution
Formentin, H. N., Vernon, I., Goldstein, M., Caiado, C., Avansi, G., & Schiozer, D. (2020, September). Accounting for Model Discrepancy in Uncertainty Analysis by Combining Numerical Simulation and Bayesian Emulation Techniques. Presented at ECMOR XVII

Model discrepancy specifies unavoidable differences between a physical system and its corresponding computer model. Incomplete information, simplifications and lack of knowledge about the physical state originate model discrepancy. Misevaluation of m... Read More about Accounting for Model Discrepancy in Uncertainty Analysis by Combining Numerical Simulation and Bayesian Emulation Techniques.

Efficient Selection of Reservoir Model Outputs within an Emulation-Based Bayesian History Matching Uncertainty Analysis (2020)
Journal Article
Ferreira, C., Vernon, I., Caiado, C., Formentin, H., Avansi, G., Goldstein, M., & Schiozer, D. (2020). Efficient Selection of Reservoir Model Outputs within an Emulation-Based Bayesian History Matching Uncertainty Analysis. SPE Journal, 25(4), 2119-2142. https://doi.org/10.4043/29801-ms

When performing classic uncertainty reduction based on dynamic data, a large number of reservoir simulations need to be evaluated at high computational cost. As an alternative, we construct Bayesian emulators that mimic the dominant behaviour of the... Read More about Efficient Selection of Reservoir Model Outputs within an Emulation-Based Bayesian History Matching Uncertainty Analysis.

Gaining more understanding about reservoir behavior through assimilation of breakthrough time and productivity deviation in the history matching process (2019)
Journal Article
Formentin, H. N., Almeida, F. L. R., Avansi, G. D., Maschio, C., Schiozer, D. J., Caiado, C., Vernon, I., & Goldstein, M. (2019). Gaining more understanding about reservoir behavior through assimilation of breakthrough time and productivity deviation in the history matching process. Journal of Petroleum Science and Engineering, 173, 1080-1096. https://doi.org/10.1016/j.petrol.2018.10.045

History matching (HM) is an inverse problem where uncertainties in attributes are reduced by comparison with observed dynamic data. Typically, normalized misfit summarizes dissimilarities between observed and simulation data. Especially for long-time... Read More about Gaining more understanding about reservoir behavior through assimilation of breakthrough time and productivity deviation in the history matching process.

Bayes linear analysis of risks in sequential optimal design problems (2018)
Journal Article
Jones, M., Goldstein, M., Jonathan, P., & Randell, D. (2018). Bayes linear analysis of risks in sequential optimal design problems. Electronic Journal of Statistics, 12(2), 4002-4031. https://doi.org/10.1214/18-ejs1496

In a statistical or physical model, it is often the case that a set of design inputs must be selected in order to perform an experiment to collect data with which to update beliefs about a set of model parameters; frequently, the model also depends o... Read More about Bayes linear analysis of risks in sequential optimal design problems.

Evaluation of Regions of Influence for Dimensionality Reduction in Emulation of Production Data (2018)
Presentation / Conference Contribution
Ferreira, C., Avansi, G., Vernon, I., Schiozer, D., & Goldstein, M. (2018, September). Evaluation of Regions of Influence for Dimensionality Reduction in Emulation of Production Data. Presented at ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery, Barcenola, Spain

Oil and gas companies use reservoir simulation models for production forecasting and for business and technical decisions at the various stages of field management. The size and complexity of the reservoirs often requires reservoir models with a high... Read More about Evaluation of Regions of Influence for Dimensionality Reduction in Emulation of Production Data.

Emulation of reservoir production forecast considering variation in petrophysical properties (2018)
Journal Article
Moreno, R., Avansi, G., Schiozer, D., Vernon, I., Goldstein, M., & Caiado, C. (2018). Emulation of reservoir production forecast considering variation in petrophysical properties. Journal of Petroleum Science and Engineering, 165, 711-725. https://doi.org/10.1016/j.petrol.2018.02.056

Implementation of proxy models, such as emulators might reduce the computational time required in a variety of reservoir simulation studies. By definition, an emulator uses reservoir properties as input parameters in a statistical model constructed f... Read More about Emulation of reservoir production forecast considering variation in petrophysical properties.

Multi-level emulation of a volcanic ash transport and dispersion model to quantify sensitivity to uncertain parameters (2018)
Journal Article
Harvey, N. J., Huntley, N., Dacre, H. F., Goldstein, M., Thomson, D., & Webster, H. (2018). Multi-level emulation of a volcanic ash transport and dispersion model to quantify sensitivity to uncertain parameters. Natural Hazards and Earth System Sciences, 18(1), 41-63. https://doi.org/10.5194/nhess-18-41-2018

Following the disruption to European airspace caused by the eruption of Eyjafjallajökull in 2010 there has been a move towards producing quantitative predictions of volcanic ash concentration using volcanic ash transport and dispersion simulators. Ho... Read More about Multi-level emulation of a volcanic ash transport and dispersion model to quantify sensitivity to uncertain parameters.

Quantifying uncertainty in wholesale electricity price projections using Bayesian emulation of a generation investment model (2017)
Journal Article
Wilson, A., Dent, C., & Goldstein, M. (2018). Quantifying uncertainty in wholesale electricity price projections using Bayesian emulation of a generation investment model. Sustainable Energy, Grids and Networks, 13, 42-55. https://doi.org/10.1016/j.segan.2017.11.003

Policy-makers need to be confident that decisions based on the outputs of energy system models will be robust in the real-world. To make robust decisions it is critical that the consequences of uncertainty in model outputs are assessed. This paper pr... Read More about Quantifying uncertainty in wholesale electricity price projections using Bayesian emulation of a generation investment model.

History matching of a complex epidemiological model of human immunodeficiency virus transmission by using variance emulation (2016)
Journal Article
Andrianakis, I., Vernon, I., McCreesh, N., McKinley, T., Oakley, J., Nsubuga, R., …White, R. (2017). History matching of a complex epidemiological model of human immunodeficiency virus transmission by using variance emulation. Journal of the Royal Statistical Society: Series C, 66(4), 717-740. https://doi.org/10.1111/rssc.12198

Complex stochastic models are commonplace in epidemiology, but their utility depends on their calibration to empirical data. History matching is a (pre)calibration method that has been applied successfully to complex deterministic models. In this wor... Read More about History matching of a complex epidemiological model of human immunodeficiency virus transmission by using variance emulation.

Bayesian Framework for Power Network Planning Under Uncertainty (2016)
Journal Article
Lawson, A., Goldstein, M., & Dent, C. (2016). Bayesian Framework for Power Network Planning Under Uncertainty. Sustainable Energy, Grids and Networks, 7, 47-57. https://doi.org/10.1016/j.segan.2016.05.003

Effective transmission expansion planning is necessary to ensure a power system can satisfy all demand both reliably and economically. However, at the time reinforcement decisions are made many elements of the future system background are uncertain,... Read More about Bayesian Framework for Power Network Planning Under Uncertainty.