Process Interactions Can Change Process Ranking in a Coupled Complex System Under Process Model and Parametric Uncertainty

Low-cost adaptive square-root cubature Kalman filter for systems with process model uncertainty

Event Abstract Back to Event Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis Olivia Eriksson1, 2*, Alexandra Jauhiainen1, 3, Sara Maad Sasane4, Anu G Nair5, Carolina Sartorius4 and Jeanette Hellgren Kotaleski2, 5, 6 1 Contributed equally to this work, Sweden 2 Stockholm University, Department of Numerical Analysis and Computer Science, Sweden 3 AstraZeneca AB R&D, Early Clinical Biometrics, Sweden 4 Lund University, Centre for Mathematical Sciences, Sweden 5 KTH Royal Institute of Technology, School of Computer Science and Communication, Sweden 6 Karolinska Institute, Department of Neuroscience, Sweden Computational dynamical models describing intracellular signaling pathways of nerve cells are increasing in size and complexity as more information is obtained from experiments. Models describing protein interactions within neurons can contain over hundred protein reactions [1, 2]. These models are built from knowledge about the interaction topology, inferred from e.g. gene knock-out experiments, as well as from experimental quantitative data describing the input-output relationship of the observed system. The quantitative data are often sparse as compared to the size of the system, and translating the experimental information into dynamical models often results in large uncertainties in the parameter (e.g reaction rates) values. This uncertainty is partly due to the sparseness in experimental time series data (practical unidentifiability), but it is also an intrinsic feature of the modeled system (structural unidentifiability) and could reflect the possibility for biological variation [3]; in many biological systems the same function can be achieved in partly different ways due to degeneracy and redundancy. Here we investigate the extent of this parameter uncertainty, in a model describing calcium (Ca)-dependent activation of Calmodulin (CaM), Protein phosphatase 2B (PP2B) and Ca/CaM-dependent protein kinase II (CamKII) [4], which is an intracellular pathway of importance to synaptic plasticity. We presume that the structure of the model is correct and then characterize the uncertainty in the parameters based on data. This is done by sampling the subspace of parameter values which has an equally good fit to data (corresponding to the “viable space” in [5]), through a statistical approach known as Approximate Bayesian Computation (ABC) with Markov Chain Monte Carlo (MCMC) [6]. ABC has been proposed for parameter estimation in system biology models previously, albeit in slightly different settings, e.g. [7, 8], and can be applied to a wide range of problems. In order to characterize the viable space efficiently with several experimental datasets, we employ multivariate probability distributions called copulas as a part of the ABC sampling. The result is a multivariate posterior distribution for the parameters, which represents how much they are constrained by the data (i.e. the uncertainty) as illustrated in Figure 1 (pairwise plots of viable space for four parameters indicating constraints and dependencies before and after calibration to data). The next step is to look into how the parameter uncertainty is translated to uncertainty of the predictions made from the model. We also investigate the role and importance of different parameters, with respect to different model outputs including the predictions, by means of global sensitivity analysis [9]. Figure 2 illustrates the sensitivity of one of the outputs calculated by a method based on the decomposition of the variance [10, 11, 12], showing different types of sensitivity measures. Finally, we explore how the sensitivity of different subsets of parameters change as different parts of the viable space are investigated, which is shown in Figure 3, where sensitivity profiles are clustered into groups with different sensitivity characteristics. Figure 1 Figure 2 Figure 3 Acknowledgements This research was supported by funding from the Swedish e-Science Research Centre and the Human Brain Project References [1] Gutierrez-Arenas O, Eriksson O, Hellgren Kotaleski J (2014) Segregation and Crosstalk of D1 Receptor-Mediated Activation of ERK in Striatal Medium Spiny Neurons upon Acute Administration of Psychostimulants. PLoS Comput Biol 10, e1003445. [2] Nair AG, Gutierrez-Arenas O, Eriksson O, Vincent P, and Hellgren Kotaleski J (2015) Sensing Positive versus Negative Reward Signals through Adenylyl Cyclase-Coupled GPCRs in Direct and Indirect Pathway Striatal Medium Spiny Neurons. J. Neuroscience 35, 14017-14030. [3] Marder E, Goeritz ML, Otopalik AG (2015) Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms. Curr Opin Neurobiol 31, 156-163. [4] Nair AG, Gutierrez-Arenas O, Eriksson O, Jauhiainen A, Blackwell KT and Kotaleski, JH (2014). Modeling intracellular signaling underlying striatal function in health and disease. Progress in molecular biology and translational science, 123, 277 [5] Zamora-Sillero E, Hafner M, Ibig A, Stelling J, and Wagner, A. (2011). Efficient characterization of high-dimensional parameter spaces for systems biology. BMC systems biology 5, 142. [6] Marjoram P, Molitor J, Plagnol V, and Tavare S (2003) Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U.S.A. 100, 15324–15328. [7] Toni T, Welch D, Strelkowa N, Ipsen A, and Stumpf MP. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J R Soc Interface, 6, 187–202. [8] Liepe J, Kirk P, Filippi S, Toni T, Barnes CP, and Stumpf MP. A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat Protoc, 9, 439–456. [9] Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S Global sensitivity analysis: the primer. In Wiley 2008 New York, NY:Wiley. [10] Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul. 55, 271–280. [11] Saltelli A (2002) Making best use of model evaluations to compute sensitivity indices. Comp Phys Comm 145, 280 – 297. [12] Halnes G, Ulfhielm E Ljunggren EE, Kotaleski JH and Rospars JP (2009) Modelling and sensitivity analysis of the reactions involving receptor, G-protein and effector in vertebrate olfactory receptor neurons. Journal of computational neuroscience 27, 471-491. Keywords: sensitivity analysis, Approximate Bayesian Computation, copulas, intracellular signalling, Dynamical Modeling, global sensitivity analysis, Markov chain Monte Carlo, variance decomposition Conference: Neuroinformatics 2016, Reading, United Kingdom, 3 Sep - 4 Sep, 2016. Presentation Type: Investigator presentations Topic: Computational neuroscience Citation: Eriksson O, Jauhiainen A, Maad Sasane S, Nair A, Sartorius C and Hellgren Kotaleski J (2016). Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis. Front. Neuroinform. Conference Abstract: Neuroinformatics 2016. doi: 10.3389/conf.fninf.2016.20.00014 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 31 May 2016; Published Online: 18 Jul 2016. * Correspondence: PhD. Olivia Eriksson, Contributed equally to this work, Stockholm, Sweden, olivia@kth.se Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Scholar Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski PubMed Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Hydrologic and water quality models (HWQMs) are increasingly used to support decisions on various environmental issues and policy directions for present and future scenarios, at scales varying from watershed to continental levels. Uncertainty associated with such models may affect the ability of the models to accurately evaluate the response of complex systems, leading to misguided assessments and risk management decisions. Current well-known HWQMs contain numerous input parameters, many of which are not known with certainty, and in other cases model users can hardly recognize the genesis of uncertainty. Uncertainty in data, model structure, and model parameters can propagate throughout model runs, causing the model output to substantially deviate from the expected response of the natural system. Various uncertainty assessment methods have been used with different HWQMs, creating concerns about an adequate approach for handling uncertainty in these models and how such an approach can be implemented across various discretization complexities and scales. In this article, our primary intention is to review uncertainty in the currently used HWQMs and to provide guidance and useful information for researchers and investigators. In this regard, we explore the genesis of uncertainty in hydrologic and water quality modeling (i.e., spatiotemporal scales, model representation, model discretization, model parameterization) and provide strategies for assessing uncertainty in hydrologic and water quality modeling on local and global scales when interpreting the model output.

Bayesian methods for model uncertainty analysis with application to future sea level rise.

The need for more accurate asteroid models is perhaps secondary to the need to measure their quality. The uncertainties of models' parameters propagate to quantities like volume or density -- the most important and informative properties of asteroids -- affecting conclusions about their physical nature. Our knowledge on shapes and spins of small solar system bodies comes mostly from visual, disk-integrated photometry. In this work we present a method for asteroid model uncertainty assessment based on visual photometry (lightcurves and sparse-in-time absolute measurements) allowing the determination of realistic volume uncertainty, as well as spin axis orientation, rotational period and local surface features. The sensitivity analysis is conducted by creating clones of the nominal model and accepting the ones that fit the observations within a confidence level. The uncertainties of model parameters are extracted from the extreme values found in the accepted clone population. Creation of such population of clones enables the conversion of a deterministic asteroid model into stochastic one, and can be utilized to create observation predictions with error bars. The method was used to assess the uncertainties of fictitious test models and real targets, i.e. (21) Lutetia, (89) Julia, (243) Ida, (433) Eros and (162173) Ryugu. We conclude that volumes, and subsequently, densities of asteroids derived from lightcurve-based models likely have vastly understated uncertainties, the biggest source of which is the inability to establish the extent of the model along its spin axis.

Abstract. Sensitivity analysis of atmospheric models is necessary to identify the processes that lead to uncertainty in model predictions, to help understand model diversity through comparison of driving processes, and to prioritise research. Assessing the effect of parameter uncertainty in complex models is challenging and often limited by CPU constraints. Here we present a cost-effective application of variance-based sensitivity analysis to quantify the sensitivity of a 3-D global aerosol model to uncertain parameters. A Gaussian process emulator is used to estimate the model output across multi-dimensional parameter space, using information from a small number of model runs at points chosen using a Latin hypercube space-filling design. Gaussian process emulation is a Bayesian approach that uses information from the model runs along with some prior assumptions about the model behaviour to predict model output everywhere in the uncertainty space. We use the Gaussian process emulator to calculate the percentage of expected output variance explained by uncertainty in global aerosol model parameters and their interactions. To demonstrate the technique, we show examples of cloud condensation nuclei (CCN) sensitivity to 8 model parameters in polluted and remote marine environments as a function of altitude. In the polluted environment 95 % of the variance of CCN concentration is described by uncertainty in the 8 parameters (excluding their interaction effects) and is dominated by the uncertainty in the sulphur emissions, which explains 80 % of the variance. However, in the remote region parameter interaction effects become important, accounting for up to 40 % of the total variance. Some parameters are shown to have a negligible individual effect but a substantial interaction effect. Such sensitivities would not be detected in the commonly used single parameter perturbation experiments, which would therefore underpredict total uncertainty. Gaussian process emulation is shown to be an efficient and useful technique for quantifying parameter sensitivity in complex global atmospheric models.

In this study, a factorial multimodel Bayesian copula (FMBC) method is proposed to investigate various uncertainties in the copula-based multivariate risk models and further track the major contributors to the imprecise predictions for different risk indices. In FMBC, the copula models with different marginals and dependence structures will be firstly established with the parameter uncertainties being quantified by the adaptive Metropolis algorithm. A multilevel factorial analysis approach is then adopted to characterize the individual and interactive effects of marginals, copula functions and the associated parameter uncertainties on different risk indices. Moreover, a copula-based dependent sampling algorithm is proposed in the factorial analysis process to generate parameter samples under consideration of their correlation. The applicability of the FMBC approach is demonstrated through the multivariate flood risk analysis at two gauging stations in Wei River basin. The results indicate that extensive fluctuation exists in the inferences of multivariate return periods resulting from different marginal and dependence structures as well as the associated parameter uncertainties. For risk indices of the failure probabilities in AND and Kendall, their predictive variability can be mainly attributed to the uncertainties in model parameters and copula structure, with their total contribution more than 75%. In comparison, the failure probability in OR would be mainly influenced by the parameter uncertainty and also marginal structures, with their total contribution more than 80%. The copula structure would not have a visible effect on the failure probability in OR, with its contribution less than 5% for most scenarios. The obtained results can provide scientific support for reliable hydrological risk inferences within a multivariate context.

Land surface processes and their coupling to the atmosphere over the Tibetan Plateau (TP) play an important role in modulating the regional and global climate. Therefore, identifying and quantifying uncertainty in these land surface model (LSM) processes are essential for improving climate models. The specifications of land cover and soil texture types, intertwined with the uncertainties in associated vegetation and soil parameters in LSMs, are significant sources of uncertainty due to the lack of detailed land survey in the TP. To differentiate the effects of land cover or soil texture specifications in the Noah with Multiple Parameterizations (Noah‐MP) LSM from the effects of uncertainties in the model parameters, this study first identified the most sensitive vegetation and soil parameters through global sensitivity analysis and then conducted parametric ensemble simulations using two land cover data sets and two soil texture data sets over the central TP to estimate their corresponding impacts on the overall model responses. The distinction level and the Kolmogorov‐Smirnov test were then applied to assess the differences between the results from parametric ensemble simulations using different land cover or soil texture data sets. The results show that the simulated energy and water fluxes over the central TP are dominated by soil parameters. The canopy height is the most sensitive vegetation parameter, and the Clapp‐Hornberger b parameter (the exponent in the function that relates soil water potential and water content) is the most sensitive soil parameter. Relative to the background parametric uncertainties, the Noah‐MP LSM could not sufficiently distinguish the effects of changes between forested types or soil texture types, which highlight the need for further quantifying and reducing the parametric uncertainties in LSMs. Further analysis shows significant sensitivities of the distinction level and changes in model response to annual precipitation and vegetation fraction. This work provides a scientific reference for assessing the impacts of land cover or soil texture changes on Noah‐MP simulations under future climate change conditions.

Summary Active control is an alternative method to suppress the civil structural vibration, which is more effective than the passive control or strengthening the structural components. The performance of active control is dependent on the control strategy and the accuracy of the structural model. However, there always exist some uncertainties in the model, such as mass, damping and stiffness uncertainties. This paper presents a robust H∞ controller design for civil structures with consideration of the parametric uncertainties. The formulation to extract the parametric uncertainties from the structural model matrices is proposed through the linear fractional transformations approach. The robust H∞ controller design for the civil structures with the parametric uncertainties is achieved through the D-K iteration method. The linear matrix inequality is then used in the H∞ optimization procedure of the D-K iteration. The robustness of the controller is first numerically validated by a four-story building example and then experimentally corroborated by a shaking table test of a two-story frame with one active mass damper. The results show that the robust H∞ controller can consider the parametric uncertainties in the civil structural model and achieve the robust performance. Copyright © 2015 John Wiley & Sons, Ltd.

Parameter uncertainty in hydrologic modeling is commonly evaluated, but assessing the impact of spatial input data uncertainty in spatially descriptive ‘distributed’ models is not common. This study compares the significance of uncertainty in spatial input data and model parameters on the output uncertainty of a distributed hydrology and sediment transport model, HYdrology Simulation using Time-ARea method (HYSTAR). The Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm was used to quantify parameter uncertainty of the model. Errors in elevation and land cover layers were simulated using the Sequential Gaussian/Indicator Simulation (SGS/SIS) techniques and then incorporated into the model to evaluate their impact on the outputs relative to those of the parameter uncertainty. This study demonstrated that parameter uncertainty had a greater impact on model output than did errors in the spatial input data. In addition, errors in elevation data had a greater impact on model output than did errors in land cover data. Thus, for the HYSTAR distributed hydrologic model, accuracy and reliability can be improved more effectively by refining parameters rather than further improving the accuracy of spatial input data and by emphasizing the topographic data over the land cover data.

SummaryThis paper presents a modified strong tracking unscented Kalman filter (MSTUKF) to address the performance degradation and divergence of the unscented Kalman filter because of process model uncertainty. The MSTUKF adopts the hypothesis testing method to identify process model uncertainty and further introduces a defined suboptimal fading factor into the prediction covariance to decrease the weight of the prior knowledge on filtering solution. The MSTUKF not only corrects the state estimation in the occurrence of process model uncertainty but also avoids the loss of precision for the state estimation in the absence of process model uncertainty. Further, it does not require the cumbersome evaluation of Jacobian matrix involved in the calculation of the suboptimal fading factor. Experimental results and comparison analysis demonstrate the effectiveness of the proposed MSTUKF. Copyright © 2015 John Wiley & Sons, Ltd.

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model

This report presents guidelines for evaluating uncertainty in mathematical equations and computer models applied to assess human health and environmental risk. Uncertainty analyses involve the propagation of uncertainty in model parameters and model structure to obtain confidence statements for the estimate of risk and identify the model components of dominant importance. Uncertainty analyses are required when there is no a priori knowledge about uncertainty in the risk estimate and when there is a chance that the failure to assess uncertainty may affect the selection of wrong options for risk reduction. Uncertainty analyses are effective when they are conducted in an iterative mode. When the uncertainty in the risk estimate is intolerable for decision-making, additional data are acquired for the dominant model components that contribute most to uncertainty. This process is repeated until the level of residual uncertainty can be tolerated. A analytical and numerical methods for error propagation are presented along with methods for identifying the most important contributors to uncertainty. Monte Carlo simulation with either Simple Random Sampling (SRS) or Latin Hypercube Sampling (LHS) is proposed as the most robust method for propagating uncertainty through either simple or complex models. A distinction is made between simulating a stochastically varying assessment endpoint (i.e., the distribution of individual risks in an exposed population) and quantifying uncertainty due to lack of knowledge about a fixed but unknown quantity (e.g., a specific individual, the maximally exposed individual, or the mean, median, or 95%-tile of the distribution of exposed individuals). Emphasis is placed on the need for subjective judgement to quantify uncertainty when relevant data are absent or incomplete.

Performance and robustness trade-offs in PID control

Uncertainty in structural dynamics: Experimental validation of a Wishart random matrix model