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Parameter estimation
Published in Karthik Raman, An Introduction to Computational Systems Biology, 2021
Model identification involves identifying the components of the model, the structure or topology (wiring), as well as the kinetics that describe the interactions between the various components. Much of the previous chapter dwelt on these topics. An important aspect of model identification is the study of structural identifiability, which is essential before we go ahead with parameter estimation. A model is structurally identifiable if it is possible to determine the values of its parameters uniquely, by fitting the model to experimental observations [4]. In practice, structural identifiability requires that each parameter has a strong influence on at least one of the variables, and the effects of the parameters on the variables are not correlated with one another. When the parameter effects are correlated, we will have multiple feasible parameter sets, with the variation in one parameter counteracting the variation in another.
Parameter Estimation
Published in Alex Martynenko, Andreas Bück, Intelligent Control in Drying, 2018
To ensure meaningful parameter estimates, a sophisticated identifiability analysis is of significant importance. Identifiability measures if and how good parameters can be estimated based on an assumed model structure (determined with either white-, grey-, or black-box modeling approach) and available experimental data. A model is called structurally identifiable if there is a unique solution of the inverse problem, that is, there is one optimal parameter set enabling the optimal fit between measurement and model data.
Phenomenological modelling of phase transitions with hysteresis in solid/liquid PCM
Published in Journal of Building Performance Simulation, 2019
Tilman Barz, Johannn Emhofer, Klemens Marx, Gabriel Zsembinszki, Luisa F. Cabeza
The quality of the parameter estimates is assessed by an identifiability analysis. It is a local analysis based on the condition of the sensitivity matrix at the solution of the regression problem, for details see López Cárdenas et al. (2015). For heating, the condition number of the sensitivity matrix is 11,669. This value exceeds the maximum threshold of 1000 and diagnoses an ill-conditioned matrix. However, none of the singular values is very close to zero (values between 5.14 and 59,984) and the collinearity index is 0.195 and below its maximum threshold of 15. Therefore the problem can be considered rank-deficient. For cooling, the condition number is 4035 diagnosing ill-conditioning. However, the singular values are well above zero (between 11.9 and 48,050) and the collinearity index is with 0.084 below the critical threshold. Thus, the problem can also be considered rank-deficient. It can be concluded that for both, heating and cooling, the estimated parameter values are not severely affected by the ill-conditioning of the sensitivity matrix.
Tensor Mixed Effects Model With Application to Nanomanufacturing Inspection
Published in Technometrics, 2020
Xiaowei Yue, Jin Gyu Park, Zhiyong Liang, Jianjun Shi
The identifiability of a statistical model is essential because it ensures correct inference on model parameters. For the TME model, the identifiability is extremely complex because it involves three aspects: (i) whether the fixed effects core tensor is identifiable; (ii) the identifiability of the Kronecker covariance structure, because for any c > 0; (iii) and the identifiability of covariance matrices of random effects and residual errors, because and . We will investigate the identifiability for each these aspects, respectively.
Influence of error terms in Bayesian calibration of energy system models
Published in Journal of Building Performance Simulation, 2019
Kathrin Menberg, Yeonsook Heo, Ruchi Choudhary
Previous studies applying similar Bayesian calibration frameworks to computer models have also shown that the model bias can suffer from a lack of identifiability (Arendt, Apley, and Chen 2012; Brynjarsdóttir and O'Hagan 2014). The problem of identifiability in the modelling process deals with the question of whether or not there is a unique solution for the unknown model parameters (Cobelli and DiStefano 1980). In the context of the KOH calibration process, the lack of identifiability in the model bias function often occurs in the form of posterior distributions that simply mirror the corresponding prior information, and/or do not reflect the characteristics of the true physical discrepancy in the computer model (Arendt, Apley, and Chen 2012; Brynjarsdóttir and O'Hagan 2014). In addition, the application of the KOH framework in the context of building simulation has so far been mostly limited to monthly aggregated energy data (Heo, Choudhary, and Augenbroe 2012; Li et al., “Calibration of Dynamic,” 2015; Tian et al. 2016), while BEM outputs often represent point data, such as temperature values. The use of a set of point measurements for calibration, instead of aggregated data, requires additional examination of the potential effect of outliers and larger random noise on the robustness of the obtained calibration results. In Bayesian analysis, results are commonly viewed as robust when the posterior distributions or predictions are not sensitive to the prior assumptions or data inputs (Berger et al. 1994; Lopes and Tobias 2011). Thus, the issues that have not been assessed in relation to Bayesian calibration include the following points: Robustness of hyper-parameters of the GP emulator;Potential of the hyper-parameters associated with error terms to provide useful information about the model;Effect of using a small number of point measurements on the results. To address these research gaps, we apply Bayesian calibration with the KOH framework to a single, yet often used component of an energy supply system model, namely the heat pump, using fluid temperatures as model input data. Previous studies have calibrated models of heat pumps (Fisher et al. 2006; Cacabelos et al. 2015; Niemelä et al. 2016), but not with full consideration of uncertainties.