scholarly journals A methodology for global-sensitivity analysis of time-dependent outputs in systems biology modelling

2012 ◽  
Vol 9 (74) ◽  
pp. 2156-2166 ◽  
Author(s):  
T. Sumner ◽  
E. Shephard ◽  
I. D. L. Bogle
Keyword(s):  
Sensitivity Analysis ◽  
Systems Biology ◽  
Computational Models ◽  
Global Sensitivity Analysis ◽  
Insulin Signalling ◽  
Principal Component ◽  
Functional Principal Component Analysis ◽  
Global Sensitivity ◽  
Insulin Signalling Pathway ◽  
Parameter Values

One of the main challenges in the development of mathematical and computational models of biological systems is the precise estimation of parameter values. Understanding the effects of uncertainties in parameter values on model behaviour is crucial to the successful use of these models. Global sensitivity analysis (SA) can be used to quantify the variability in model predictions resulting from the uncertainty in multiple parameters and to shed light on the biological mechanisms driving system behaviour. We present a new methodology for global SA in systems biology which is computationally efficient and can be used to identify the key parameters and their interactions which drive the dynamic behaviour of a complex biological model. The approach combines functional principal component analysis with established global SA techniques. The methodology is applied to a model of the insulin signalling pathway, defects of which are a major cause of type 2 diabetes and a number of key features of the system are identified.

scholarly journals Global sensitivity analysis of the climate–vegetation system to astronomical forcing: an emulator-based approach

2015 ◽  
Vol 6 (1) ◽  
pp. 205-224 ◽  
Author(s):  
N. Bounceur ◽  
M. Crucifix ◽  
R. D. Wilkinson
Keyword(s):  
Climate Change ◽  
Sensitivity Analysis ◽  
Land Surface ◽  
Global Sensitivity Analysis ◽  
Climate Model ◽  
Principal Component ◽  
Arctic Region ◽  
Global Sensitivity ◽  
Oscillatory Pattern ◽  
Astronomical Forcing

Abstract. A global sensitivity analysis is performed to describe the effects of astronomical forcing on the climate–vegetation system simulated by the model of intermediate complexity LOVECLIM in interglacial conditions. The methodology relies on the estimation of sensitivity measures, using a Gaussian process emulator as a fast surrogate of the climate model, calibrated on a set of well-chosen experiments. The outputs considered are the annual mean temperature and precipitation and the growing degree days (GDD). The experiments were run on two distinct land surface schemes to estimate the importance of vegetation feedbacks on climate variance. This analysis provides a spatial description of the variance due to the factors and their combinations, in the form of "fingerprints" obtained from the covariance indices. The results are broadly consistent with the current under-standing of Earth's climate response to the astronomical forcing. In particular, precession and obliquity are found to contribute in LOVECLIM equally to GDD in the Northern Hemisphere, and the effect of obliquity on the response of Southern Hemisphere temperature dominates precession effects. Precession dominates precipitation changes in subtropical areas. Compared to standard approaches based on a small number of simulations, the methodology presented here allows us to identify more systematically regions susceptible to experiencing rapid climate change in response to the smooth astronomical forcing change. In particular, we find that using interactive vegetation significantly enhances the expected rates of climate change, specifically in the Sahel (up to 50% precipitation change in 1000 years) and in the Canadian Arctic region (up to 3° in 1000 years). None of the tested astronomical configurations were found to induce multiple steady states, but, at low obliquity, we observed the development of an oscillatory pattern that has already been reported in LOVECLIM. Although the mathematics of the analysis are fairly straightforward, the emulation approach still requires considerable care in its implementation. We discuss the effect of the choice of length scales and the type of emulator, and estimate uncertainties associated with specific computational aspects, to conclude that the principal component emulator is a good option for this kind of application.

The AusBeef model for beef production: II. sensitivity analysis

2017 ◽  
Vol 155 (9) ◽  
pp. 1459-1474 ◽  
Author(s):  
H. C. DOUGHERTY ◽  
E. KEBREAB ◽  
M. EVERED ◽  
B. A. LITTLE ◽  
A. B. INGHAM ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Protein Production ◽  
Global Sensitivity Analysis ◽  
Total Order ◽  
Model Parameters ◽  
Microbial Protein ◽  
Beef Production ◽  
Global Sensitivity ◽  
Highly Sensitive ◽  
Parameter Values

SUMMARYThe present study evaluated the behaviour of the AusBeef model for beef production as part of a 2 × 2 study simulating performance on forage-based and concentrate-based diets from Oceania and North America for four methane (CH4)-relevant outputs of interest. Three sensitivity analysis methods, one local and two global, were conducted. Different patterns of sensitivity were observed between forage-based and concentrate-based diets, but patterns were consistent within diet types. For the local analysis, 36, 196, 47 and 8 out of 305 model parameters had normalized sensitivities of 0, >0, >0·01 and >0·1 across all diets and outputs, respectively. No parameters had a normalized local sensitivity >1 across all diets and outputs. However, daily CH4 production had the greatest number of parameters with normalized local sensitivities >1 for each individual diet. Parameters that were highly sensitive for global and local analyses across the range of diets and outputs examined included terms involved in microbial growth, volatile fatty acid (VFA) yields, maximum absorption rates and their inhibition due to pH effects and particle exit rates. Global sensitivity analysis I showed the high sensitivity of forage-based diets to lipid entering the rumen, which may be a result of the use of a feedlot-optimized model to represent high-forage diets and warrants further investigation. Global sensitivity analysis II showed that when all parameter values were simultaneously varied within ±10% of initial value, >96% of output values were within ±20% of the baseline, which decreased to >50% when parameter value boundaries were expanded to ±25% of their original values, giving a range for robustness of model outputs with regards to potential different ‘true’ parameter values. There were output-specific differences in sensitivity, where outputs that had greater maximum local sensitivities displayed greater degrees of non-linear interaction in global sensitivity analysis I and less variance in output values for global sensitivity analysis II. For outputs with less interaction, such as the acetate : propionate ratio and microbial protein production, the single most sensitive term in global sensitivity analysis I contributed more to the overall total-order sensitivity than for outputs with more interaction, with an average of 49, 33, 15 and 14% of total-order sensitivity for microbial protein production, acetate : propionate ratio, CH4 production and energy from absorbed VFAs, respectively. Future studies should include data collection for highly sensitive parameters reported in the present study to improve overall model accuracy.

scholarly journals Implementation of Supervised PCA for Global Sensitivity Analysis of Models with Correlated Inputs

2021 ◽  
Author(s):  
M. A. M. J. Sharbaf ◽  
Mohammad Javad Abedini
Keyword(s):  
Sensitivity Analysis ◽  
Reproducing Kernel ◽  
Global Sensitivity Analysis ◽  
Principal Component ◽  
Coefficient Of Determination ◽  
Ratio Method ◽  
Correlation Ratio ◽  
Total Contribution ◽  
Global Sensitivity ◽  
The Impact

Abstract Global Sensitivity Analysis (GSA) plays a significant role in quantifying the tangible impact of model inputs on the uncertainty of response variable. As GSA results are strongly affected by correlated inputs, several studies considered this issue, but most of them are quite time-consuming, labor-intensive, and difficult to implement. Accordingly, this paper puts forward a novel strategy based on the Supervised Principal Component analysis (Supervised PCA), benefiting from the Reproducing Kernel Hilbert Space (RKHS). Indeed, by conducting one kind of variance-based sensitivity analysis (SA), a renowned method exclusively customized for models with orthogonal inputs, on Supervised PCA (SPCA) regression, the impact of correlation structure of input variables is effectively taken into account. The ability of the suggested technique is evaluated with five test cases as well as two hydrologic and hydraulic models, and the results are compared and contrasted with those obtained from the correlation ratio method taken as a robust benchmark solution. It is found that the proposed method satisfactorily identifies the sensitivity ordering of model inputs. Furthermore, it is proved in this study that the performance of the proposed approach is also supported by the total contribution index in the derived covariance decomposition equation. Moreover, the proposed method compared to the correlation ratio method, is found to be time efficient and easy to implement. Overall, the proposed scheme is appropriate for high dimensional, relatively nonlinear or expensive models with correlated inputs whose coefficient of determination is larger than 0.5.

Global Sensitivity Analysis for Field Response Based on the Manifold of Feature Covariance Matrix

2021 ◽  
Author(s):  
Zhouzhou Song ◽  
Zhao Liu ◽  
Can Xu ◽  
Ping Zhu
Keyword(s):  
Sensitivity Analysis ◽  
Covariance Matrix ◽  
Computational Models ◽  
Global Sensitivity Analysis ◽  
Feature Selection Method ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Field Response ◽  
Input Variables ◽  
The Impact

Abstract In real-world applications, it is commonplace that the computational models have field responses, i.e., the temporal or spatial fields. It has become a critical task to develop global sensitivity analysis (GSA) methods to measure the effect of each input variable on the full-field. In this paper, a new sensitivity analysis method based on the manifold of feature covariance matrix (FCM) is developed for quantifying the impact of input variables on the field response. The method firstly performs feature extraction on the field response to obtain a low-dimensional FCM. An adaptive feature selection method is proposed to avoid the FCM from singularity. Thereby, the field response is represented by a FCM, which lies on a symmetric positive-definite matrix manifold. Then, the GSA technique based on the Cramér-von Mises distance for output valued on the Riemannian manifold is introduced for estimating the sensitivity indices for field response. An example of a temporal field and an example of a 2-D displacement field are introduced to demonstrate the applicability of the proposed method in estimating global sensitivity indices for field solution. Results show that the proposed method can distinguish the important input variables correctly and can yield robust index values. Besides, the proposed method can be implemented for GSA for field responses of different dimensionalities.

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