scholarly journals Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

2015 ◽  
Vol 12 (108) ◽  
pp. 20150233 ◽  
Author(s):  
Shuohao Liao ◽  
Tomáš Vejchodský ◽  
Radek Erban
Keyword(s):  
Parameter Estimation ◽  
Stochastic Models ◽  
Regulatory Networks ◽  
Stochastic Modelling ◽  
Qualitative Change ◽  
Biochemical Networks ◽  
Model Parameters ◽  
Cellular Functions ◽  
Indispensable Tool ◽  
Parameter Values

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org .

scholarly journals Parameter estimation for functional–structural plant models when data are scarce: using multiple patterns for rejecting unsuitable parameter sets

2020 ◽  
Vol 126 (4) ◽  
pp. 559-570 ◽  
Author(s):  
Ming Wang ◽  
Neil White ◽  
Jim Hanan ◽  
Di He ◽  
Enli Wang ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Predictive Power ◽  
Model Performance ◽  
Persea Americana ◽  
Strong Interactions ◽  
Model Parameters ◽  
Timely Manner ◽  
Complex Interactions ◽  
Output Uncertainty ◽  
Parameter Values

Abstract Background and Aims Functional–structural plant (FSP) models provide insights into the complex interactions between plant architecture and underlying developmental mechanisms. However, parameter estimation of FSP models remains challenging. We therefore used pattern-oriented modelling (POM) to test whether parameterization of FSP models can be made more efficient, systematic and powerful. With POM, a set of weak patterns is used to determine uncertain parameter values, instead of measuring them in experiments or observations, which often is infeasible. Methods We used an existing FSP model of avocado (Persea americana ‘Hass’) and tested whether POM parameterization would converge to an existing manual parameterization. The model was run for 10 000 parameter sets and model outputs were compared with verification patterns. Each verification pattern served as a filter for rejecting unrealistic parameter sets. The model was then validated by running it with the surviving parameter sets that passed all filters and then comparing their pooled model outputs with additional validation patterns that were not used for parameterization. Key Results POM calibration led to 22 surviving parameter sets. Within these sets, most individual parameters varied over a large range. One of the resulting sets was similar to the manually parameterized set. Using the entire suite of surviving parameter sets, the model successfully predicted all validation patterns. However, two of the surviving parameter sets could not make the model predict all validation patterns. Conclusions Our findings suggest strong interactions among model parameters and their corresponding processes, respectively. Using all surviving parameter sets takes these interactions into account fully, thereby improving model performance regarding validation and model output uncertainty. We conclude that POM calibration allows FSP models to be developed in a timely manner without having to rely on field or laboratory experiments, or on cumbersome manual parameterization. POM also increases the predictive power of FSP models.

scholarly journals Parameter variations in prediction skill optimization at ECMWF

2013 ◽  
Vol 20 (6) ◽  
pp. 1001-1010 ◽  
Author(s):  
P. Ollinaho ◽  
P. Bechtold ◽  
M. Leutbecher ◽  
M. Laine ◽  
A. Solonen ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Weather Prediction ◽  
Prediction Skill ◽  
Convective Precipitation ◽  
Ensemble Prediction ◽  
Model Parameters ◽  
Ongoing Research ◽  
Medium Range ◽  
Parameter Values ◽  
Very High

Abstract. Algorithmic numerical weather prediction (NWP) skill optimization has been tested using the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). We report the results of initial experimentation using importance sampling based on model parameter estimation methodology targeted for ensemble prediction systems, called the ensemble prediction and parameter estimation system (EPPES). The same methodology was earlier proven to be a viable concept in low-order ordinary differential equation systems, and in large-scale atmospheric general circulation models (ECHAM5). Here we show that prediction skill optimization is possible even in the context of a system that is (i) of very high dimensionality, and (ii) carefully tuned to very high skill. We concentrate on four closure parameters related to the parameterizations of sub-grid scale physical processes of convection and formation of convective precipitation. We launch standard ensembles of medium-range predictions such that each member uses different values of the four parameters, and make sequential statistical inferences about the parameter values. Our target criterion is the squared forecast error of the 500 hPa geopotential height at day three and day ten. The EPPES methodology is able to converge towards closure parameter values that optimize the target criterion. Therefore, we conclude that estimation and cost function-based tuning of low-dimensional static model parameters is possible despite the very high dimensional state space, as well as the presence of stochastic noise due to initial state and physical tendency perturbations. The remaining question before EPPES can be considered as a generally applicable tool in model development is the correct formulation of the target criterion. The one used here is, in our view, very selective. Considering the multi-faceted question of improving forecast model performance, a more general target criterion should be developed. This is a topic of ongoing research.

Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation

2008 ◽  
Vol 136 (12) ◽  
pp. 5062-5076 ◽  
Author(s):  
Dmitri Kondrashov ◽  
Chaojiao Sun ◽  
Michael Ghil
Keyword(s):  
Parameter Estimation ◽  
State Estimation ◽  
Tropical Pacific ◽  
The State ◽  
Vector Model ◽  
Model Parameters ◽  
Ocean Atmosphere ◽  
Augmented State ◽  
Parameter Values ◽  
The Tropical Pacific

Abstract The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upper-ocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identical-twin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Model-generated oceanic datasets are assimilated to produce a time-continuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30-yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean variables, such as zonal currents, are improved when model parameters are estimated. A key advantage of using this augmented-state approach is that the incremental cost of applying the EKF to joint state and parameter estimation is small relative to the cost of state estimation alone. A similar approach generalizes various reduced-state approximations of the EKF and could improve simulations and forecasts using large, realistic models.

scholarly journals Continualization of Probabilistic Programs With Correction

2020 ◽  
pp. 366-393 ◽  
Author(s):  
Jacob Laurel ◽  
Sasa Misailovic
Keyword(s):  
Parameter Estimation ◽  
Real World ◽  
Stochastic Models ◽  
Original Model ◽  
Continuous Approximation ◽  
Continuous Distributions ◽  
True Parameter ◽  
Inference Algorithms ◽  
Parameter Values ◽  
Probabilistic Programs

AbstractProbabilistic Programming offers a concise way to represent stochastic models and perform automated statistical inference. However, many real-world models have discrete or hybrid discrete-continuous distributions, for which existing tools may suffer non-trivial limitations. Inference and parameter estimation can be exceedingly slow for these models because many inference algorithms compute results faster (or exclusively) when the distributions being inferred are continuous. To address this discrepancy, this paper presents Leios. Leios is the first approach for systematically approximating arbitrary probabilistic programs that have discrete, or hybrid discrete-continuous random variables. The approximate programs have all their variables fully continualized. We show that once we have the fully continuous approximate program, we can perform inference and parameter estimation faster by exploiting the existing support that many languages offer for continuous distributions. Furthermore, we show that the estimates obtained when performing inference and parameter estimation on the continuous approximation are still comparably close to both the true parameter values and the estimates obtained when performing inference on the original model.

scholarly journals Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

2017 ◽  
Vol 14 (6) ◽  
pp. 1647-1701 ◽  
Author(s):  
Markus Schartau ◽  
Philip Wallhead ◽  
John Hemmings ◽  
Ulrike Löptien ◽  
Iris Kriest ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Parameter Identification ◽  
Estimation Methods ◽  
Model Parameters ◽  
Ecosystem Modelling ◽  
Ecosystem Models ◽  
Element Cycling ◽  
Biogeochemical Models ◽  
Parameter Values

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 space-dependent 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.

Global estimation of rainfall-runoff model parameters: an empirical experiment

2021 ◽  
Author(s):  
Léonard Santos ◽  
Jafet C. M. Andersson ◽  
Berit Arheimer
Keyword(s):  
Land Use ◽  
Parameter Estimation ◽  
World Wide ◽  
Global Scale ◽  
Second Step ◽  
Model Parameters ◽  
Earth System ◽  
Climate Classification ◽  
Soil Map ◽  
Parameter Values

<p>When setting up global scale hydrological models, parameter estimation is a crucial step. Some modellers assign pre-defined parameter values to physical characteristics (such as soil, land cover, etc.) while others estimate parameter values based on observed hydrological data. In both cases, the regionalisation of parameters is a major challenge since both literature values and observed data are often lacking and assumptions are needed. This work aims at identifying suitable parameter regions to perform a regional calibration of the global model World-Wide HYPE (Arheimer et al., 2020) through empirical tests.<br>The work is organised in two steps. First we compare different ways of taking soil into account when creating hydrological response units. The soil is either considered uniform, indexed to land use or to a simplified soil map. The best soil representation is selected based on the model performance at a global scale. Based on this best representation, the second step aims at evaluating different ways to regionalise the soil parameters of the hydrological model.  Previous classifications of hydrological uniform regions are tested for regionalisation of model parameters: hydrobelts (Meybeck et al., 2013), Köppen climate regions (Kottek et al., 2006), soil capacity index (Wang-Erlandsson et al., 2016) and hydroclimatic regions (Knoben et al., 2018).<br>For the first step, the results show that the best solution is to represent soil by land use. This counterintuitive result is due to the fact that adding information based on a soil map add another calibration step. To avoid increased equifinality, such an effort increases the need for data, which is often lacking at the global scale.  For the second step, the creation of parameter regions contributed with minor improvement in terms of model performances, probably because the choice of regions was not suitable for the model approach. Also, the improvement has shown to be higher when available discharge data for calibration were better distributed over the different regions. This work shows that, when calibrating a model at very large scale, a balance should be found between available data and parameter regions resolution. </p><p><br><strong>References</strong><br>Arheimer, B., Pimentel, R., Isberg, K., Crochemore, L., Andersson, J. C. M., Hasan, A., and Pineda, L.: Global catchment modelling using World-Wide HYPE (WWH), open data and stepwise parameter estimation, Hydrol. Earth Syst. Sci. 24, 535–559, 2020.<br>Knoben, W. J., Woods, R. A., and Freer, J. E.: A Quantitative Hydrological Climate Classification Evaluated With Independent Streamflow Data. Water Resources Research, 54(7), 5088-5109, 2018.<br>Kottek, M., Grieser, J., Beck, C., Rudolf, B., and Rubel, F.: World map of the Köppen-Geiger climate classification updated. Meteorologische Zeitschrift, 15, 259-263, 2006.<br>Meybeck, M., Kummu, M., and Dürr, H. H.: Global hydrobelts and hydroregions: improved reporting scale for waterrelated issues? Hydrology and Earth System Sciences, 17(3), 1093-1111, 2013.<br>Wang-Erlandsson, L., Bastiaanssen, W. G. M., Gao, H., Jägermeyr, J., Senay, G. B., van Dijk, A. I. J. M., Guerschman, J. P., Keys, P. W., Gordon, L. J., and Savenije, H. H. G.: Global root zone storage capacity from satellite-based evaporation, Hydrology Earth System Sciences, 20, 1459-1481, 2016.</p>

scholarly journals Multi-fidelity approach to Bayesian parameter estimation in subsurface heat and fluid transport models 

2021 ◽  
Author(s):  
Kathrin Menberg ◽  
Asal Bidarmaghz ◽  
Alastair Gregory ◽  
Ruchi Choudhary ◽  
Mark Girolami
Keyword(s):  
Heat Transfer ◽  
Parameter Estimation ◽  
Numerical Model ◽  
Computer Model ◽  
Model Calibration ◽  
Large Scale ◽  
Model Parameters ◽  
Output Data ◽  
Resolution Model ◽  
Parameter Values

<p>The increased use of the urban subsurface for multiple purposes, such as anthropogenic infrastructures and geothermal energy applications, leads to an urgent need for large-scale sophisticated modelling approaches for coupled mass and heat transfer. However, such models are subject to large uncertainties in model parameters, the physical model itself and in available measured data, which is often rare. Thus, the robustness and reliability of the computer model and its outcomes largely depend on successful parameter estimation and model calibration, which are often hampered by the computational burden of large-scale coupled models.</p><p>To tackle this problem, we present a novel Bayesian approach for parameter estimation, which allows to account for different sources of uncertainty, is capable of dealing with sparse field data and makes optimal use of the output data from computationally expensive numerical model runs. This is achieved by combining output data from different models that represent the same physical problem, but at different levels of fidelity, e.g. reflected by different spatial resolution, i.e. different model discretization. Our framework combines information from a few parametric model outputs from a physically accurate, but expensive, high-fidelity computer model, with a larger number of evaluations from a less expensive and less accurate low-fidelity model. This enables us to include accurate information about the model output at sparse points in the parameter space, as well as dense samples across the entire parameter space, albeit with a lower physical accuracy.</p><p>We first apply the multi-fidelity approach to a simple 1D analytical heat transfer model, and secondly on a semi-3D coupled mass and heat transport numerical model, and estimate the unknown model parameters. By using synthetic data generated with known parameter values, we are able to test the reliability of the new method, as well as the improved performance over a single-fidelity approach, under different framework settings. Overall, the results from the analytical and numerical model show that combining 50 runs of the low resolution model with data from only 10 runs of a higher resolution model significantly improves the posterior distribution results, both in terms of agreement with the true parameter values and the confidence interval around this value. The next steps for further testing of the method are employing real data from field measurements and adding statistical formulations for model calibration and prediction based on the inferred posterior distributions of the estimated parameters.</p>

scholarly journals Bayesian inference of distributed time delay in transcriptional and translational regulation

2019 ◽  
Author(s):  
Boseung Choi ◽  
Yu-Yu Cheng ◽  
Selahittin Cinar ◽  
William Ott ◽  
Matthew R. Bennett ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Regulatory Networks ◽  
Stochastic Systems ◽  
Imaging Techniques ◽  
Reaction Rates ◽  
Biochemical Networks ◽  
Mcmc Methods ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Cell Functions

AbstractMotivationAdvances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks.ResultsWe propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth-death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy.

scholarly journals Reviews and syntheses: Parameter identification in marine planktonic ecosystem modelling

2016 ◽  
Author(s):  
Markus Schartau ◽  
Philip Wallhead ◽  
John Hemmings ◽  
Ulrike Löptien ◽  
Iris Kriest ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Parameter Identification ◽  
Estimation Methods ◽  
Model Parameters ◽  
Ecosystem Modelling ◽  
Ecosystem Models ◽  
Element Cycling ◽  
Biogeochemical Models ◽  
Parameter Values

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 parameterisations 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 utilised 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 addressing issues of parameter identifiability. Aspects of model complexity will be covered and we describe how results from cross-validation studies provide much insight in this respect. Moreover, we elucidate inferences made in studies that allowed for variations in space and time of parameter values. The usage of dynamical and statistical emulator approaches will be briefly explained, discussing their advantage for parameter optimisations of large-scale biogeochemical models. Our survey extends to studies that approached parameter identification in global biogeochemical modelling. Parameter estimation results will exemplify some of the advantages and remaining problems in optimising 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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