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Bayesian calibration of mathematical models: Optimization of model structure and examination of the role of process error covariance

Maryam Ramin, George B. Arhonditsis
2013 Ecological Informatics  
In this study, we address two important questions related to the ramifications of the statistical assumptions typically made about the model structural error and the prospect of Bayesian calibration to  ...  of the process error terms.  ...  Acknowledgments This project has received funding support from the Natural Sciences and Engineering Research Council of Canada through a Doctoral Scholarship awarded to Maryam Ramin and a Discovery Grant  ... 
doi:10.1016/j.ecoinf.2013.07.001 fatcat:rcbc3joqcfhcpopn7dtxo6zely

A Bayesian hierarchical framework for calibrating aquatic biogeochemical models

Weitao Zhang, George B. Arhonditsis
2009 Ecological Modelling  
between model structure and the natural system dynamics (e.g., missing key ecological processes, erroneous formulations, misspecified forcing functions).  ...  , and model structure imperfection.  ...  The rest parameters of the calibration vector can be classified into two groups: (i) parameters that depending on the scenario examined can play an active role during the model training process, e.g.,  ... 
doi:10.1016/j.ecolmodel.2009.05.023 fatcat:jtsg6qphcjg7jptbpnsfwyk3yy

Population Pharmacokinetics/PD Modelling: a Systematic Review

Mary Hexy, Subha Hency Jose
2022 International Journal of Computers  
This paper examines the various methods for developing pharmacokinetic and pharmacodynamic models.  ...  There are a variety of ways that can be used to build population modelling: Nonlinear Mixed-effects Modeling, Bayesian population pharmacokinetic (PBPK) models, Physiological covariate modeling, Visual  ...  Mathematical modelling, simulation, and optimization of the therapy process may help doctors make better decisions, which could lead to fewer severe side effects and longer remissions. [57] .  ... 
doi:10.46300/9108.2022.16.13 fatcat:7o2xn5axynep3liqemn2evulji

New challenges in integrated water quality modelling

Michael Rode, George Arhonditsis, Daniela Balin, Tesfaye Kebede, Valentina Krysanova, Ann van Griensven, Sjoerd E. A. T. M. van der Zee
2010 Hydrological Processes  
In this regard, we recommend the use of Bayesian calibration frameworks that explicitly accommodate measurement errors, parameter uncertainties, and model structure errors.  ...  The Bayesian inference can be used to quantify the information the data contain about model inputs, to offer insights into the covariance structure among parameter estimates, to obtain predictions along  ...  We recommend the use of Bayesian calibration frameworks that explicitly accommodate the measurement errors, parameter uncertainties, and model structure errors.  ... 
doi:10.1002/hyp.7766 fatcat:bbvknur3mfahvdlnkbcajoycam

Ab initio models of atomic nuclei: challenges and new ideas [article]

Andreas Ekström
2019 arXiv   pre-print
The importance of careful model calibration and uncertainty quantification of theoretical predictions is highlighted.  ...  The focus is on statistical computing and methods for analyzing the link between bulk properties of atomic nuclei, such as radii and binding energies, and the underlying microscopic description of the  ...  A complete Bayesian parameter estimation including model discrepancy will hopefully reveal more details about the structure of the chiral EFT error.  ... 
arXiv:1912.02227v1 fatcat:ru4eics7svetnfkucm2msuiwqi

An empirical Bayesian approach for model-based inference of cellular signaling networks

David J Klinke
2009 BMC Bioinformatics  
The posterior distributions of the parameters exhibited complicated structure, including significant covariance between specific parameters and a broad range of variance among the parameters.  ...  The model predictions, in contrast, were narrowly distributed and were used to identify areas of agreement among a collection of experimental studies.  ...  The content is solely the responsibility of the author and does not necessarily represent the official views of the National Cancer Institute, the National Institute of Allergy and Infectious Diseases,  ... 
doi:10.1186/1471-2105-10-371 pmid:19900289 pmcid:PMC2781012 fatcat:l2qfyxw3onf5xhusbib65ebmfy

Considering discrepancy when calibrating a mechanistic electrophysiology model

Chon Lok Lei, Sanmitra Ghosh, Dominic G. Whittaker, Yasser Aboelkassem, Kylie A. Beattie, Chris D. Cantwell, Tammo Delhaas, Charles Houston, Gustavo Montes Novaes, Alexander V. Panfilov, Pras Pathmanathan, Marina Riabiz (+5 others)
2020 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales.  ...  Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average  ...  The authors thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the 'Fickle Heart' programme.  ... 
doi:10.1098/rsta.2019.0349 pmid:32448065 pmcid:PMC7287333 fatcat:nczx3d3zbjanllgkmvm6o2afw4

Data fusion modeling for groundwater systems

David W. Porter, Bruce P. Gibbs, Walter F. Jones, Peter S. Huyakorn, L.Larry Hamm, Gregory P. Flach
2000 Journal of Contaminant Hydrology  
Field-scale application of DFM at the DOE Savannah River Site is presented and compared with manual calibration.  ...  DFM calibration runs converge in less than 1 h on a Pentium Pro PC for a 3D model with more than 15,000 nodes. Run time is approximately linear with the number of nodes.  ...  Acknowledgements This work was performed for the Department of Energy. We are deeply appreciative of the support that we received from Caroline Purdy at DOE Headquarters, without  ... 
doi:10.1016/s0169-7722(99)00081-9 fatcat:hvge2d75tjhphcxu4ylu3syt3e

Leveraging Bayesian Analysis To Improve Accuracy of Approximate Models [article]

Balasubramanya T. Nadiga, Chiyu Jiang, Daniel Livescu
2019 arXiv   pre-print
In effect parametric dependencies found from the Bayesian analysis are used to improve structural aspects of the model.  ...  We start by considering various methods of calibrating and analyzing such a model given a few well-resolved simulations.  ...  Acknowledgements We thank the referees for their extensive comments and suggestions. The presentation of this article has benefitted greatly from them.  ... 
arXiv:1905.08227v1 fatcat:7wonsybohnd6lgqhvdkmxkebqy

Eutrophication risk assessment using Bayesian calibration of process-based models: Application to a mesotrophic lake

George B. Arhonditsis, Song S. Qian, Craig A. Stow, E. Conrad Lamon, Kenneth H. Reckhow
2007 Ecological Modelling  
Environmental management Risk assessment Adaptive management implementation Plankton dynamics Eutrophication tion of uncertainty in model predictions, optimization of the sampling design of monitoring  ...  programs using value of information concepts from decision theory, alignment with the policy practice of adaptive management, and expression of model outputs as probability distributions, that are perfectly  ...  Acknowledgments Funding for this study was provided by the National Sciences and Engineering Research Council of Canada (NSERC, Discovery Grants), the Connaught Committee (University of Toronto, Matching  ... 
doi:10.1016/j.ecolmodel.2007.05.020 fatcat:cxabezobnjhxvctbr4bjunpvoi

Subset selection for linear mixed models [article]

Daniel R. Kowal
2022 arXiv   pre-print
More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal  ...  Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy  ...  The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office  ... 
arXiv:2107.12890v2 fatcat:qxpueupigfhvvoscnuibchrmoa

Quantification of Model Uncertainty in RANS Simulations: A Review [article]

Heng Xiao, Paola Cinnella
2018 arXiv   pre-print
However, model uncertainties are still a major obstacle for the predictive capability of RANS simulations. This review examines both the parametric and structural uncertainties in turbulence models.  ...  Moreover, the fundamentals of uncertainty propagation and Bayesian inference are introduced in the context of RANS model uncertainty quantification.  ...  Their results showed the choice of spatial correlation structure for the modeling inadequacy played an important role in the Bayesian model selection.  ... 
arXiv:1806.10434v2 fatcat:4a4l63lrr5d3jjqk4lacrzlp7q

Functional Gaussian processes for regression with linear PDE models [article]

Ngoc-Cuong Nguyen, Jaime Peraire
2014 arXiv   pre-print
We augment the linear PDE with a functional that accounts for the uncertainty in the mathematical model and is modeled as a Gaussian process.  ...  We develop a functional Gaussian process regression method to determine the posterior mean and covariance of the Gaussian functional, thereby solving the stochastic PDE to obtain the posterior distribution  ...  Freund of Sloan School of Management at MIT for fruitful discussions. This work was supported by AFOSR Grant No. FA9550-11-1-0141, AFOSR Grant No. FA9550-12-0357, and the Singapore-MIT Alliance.  ... 
arXiv:1405.7569v1 fatcat:tgw262hr45awzmk3kjilu5z7ya

MODEL CALIBRATION IN WATERSHED HYDROLOGY [chapter]

Koray K. Yilmaz, Jasper A. Vrugt, Hoshin V. Gupta, Soroosh Sorooshian
2010 Advances in Data-Based Approaches for Hydrologic Modeling and Forecasting  
During this process, known as model calibration, the parameters are adjusted so that the behavior of the model approximates, as closely and consistently as possible, the observed response of the hydrologic  ...  Hydrologic models use relatively simple mathematical equations to conceptualize and aggregate the complex, spatially distributed, and highly interrelated water, energy, and vegetation processes in a watershed  ...  Partial support for the first and third authors was provided by SAHRA, the Science and Technology Center for Sustainability of semi-Arid Hydrology and Riparian Areas under NSF-STC grant EAR-9876800 and  ... 
doi:10.1142/9789814307987_0003 fatcat:ctvg77gehff35ibmxak4t77mmm

Considering discrepancy when calibrating a mechanistic electrophysiology model [article]

Chon Lok Lei, Sanmitra Ghosh, Dominic G. Whittaker, Yasser Aboelkassem, Kylie A. Beattie, Chris D. Cantwell, Tammo Delhaas, Charles Houston, Gustavo Montes Novaes, Alexander V. Panfilov, Pras Pathmanathan, Marina Riabiz (+5 others)
2020 arXiv   pre-print
Here we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales.  ...  Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes (GPs) and  ...  Acknowledgements We would like to thank all the participants at the Isaac Newton Institute 'Fickle Heart' programme for helpful discussions which informed this manuscript.  ... 
arXiv:2001.04230v2 fatcat:6ztxzr2g3bbg7o5qjbc4lr6dzu
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