Estimating Sobol sensitivity indices using correlations

Abstract. Simulation models are commonly used to understand and predict the development of ecological systems, for instance to study the occurrence of tipping points and their possible ecological effects. Sensitivity analysis is a key tool in the study of model responses to changes in conditions. The applicability of available methodologies for sensitivity analysis can be problematic if tipping points are involved. In this paper we demonstrate that not considering these tipping points may result in misleading statistics on model behaviour. In turn, this limits the applicability of simulation models in ecological research. Tipping points are best revealed when asymptotic model behaviour is considered, i.e. by applying bifurcation analysis. Bifurcation analysis, however, is limited to deterministic dynamic models, whereas many ecological simulation models are nondeterministic and can only be analysed using sensitivity analysis methodologies. In this paper we explore the possibilities for applying methodologies of sensitivity analysis to analyse models with tipping points. The Bazykin-Berezovskaya model, a deterministic ecological model of which the structure regarding tipping points is known a priori, is used as case study. We conclude that important clues about the occurrence of tippings points can be revealed from different sensitivity analysis methodologies, if proper statistical and graphical measures are used. The results raise awareness about how tipping points affect temporal model responses in ecological simulation models, and may also be more generally applicable for nondeterministic models that cannot be analysed using bifurcation analysis.

show abstract

“…Alternative estimators for S i,j andS i,j are discussed by [12,26], while alternative methods are evaluated by [26].…”

Section: F Sampling Methods For the Sobol' Indicesmentioning

confidence: 99%

Detecting Tipping points in Ecological Models with Sensitivity Analysis

Broeke

Voorn

Kooi³

et al. 2016

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

show abstract

“…The method is based on variance decomposition [41] and is a global and model-independent sensitivity analysis. The method is superior to traditional local methods that examine sensitive parameters one at a time and the method is robust [42].…”

Section: Sensitivity Analysis Of Acrmmentioning

confidence: 99%

An Extended Fourier Approach to Improve the Retrieved Leaf Area Index (LAI) in a Time Series from an Alpine Wetland

Quan

Wang

et al. 2014

Remote Sensing

View full text Add to dashboard Cite

An extended Fourier approach was presented to improve the retrieved leaf area index (LAIr) of herbaceous vegetation in a time series from an alpine wetland. The retrieval was performed from the Aqua MODIS 8-day composite surface reflectance product (MYD09Q1) from day of year (DOY) 97 to 297 using a look-up table (LUT) based inversion of a two-layer canopy reflectance model (ACRM). To reduce the uncertainty (the ACRM inversion is ill-posed), we used NDVI and NIR images to reduce the influence of the soil background and the priori information to constrain the range of sensitive ACRM parameters determined using the Sobol's method. Even so the uncertainty caused the LAIr versus time curve to oscillate. To further reduce the uncertainty, a Fourier model was fitted using the periodically LAIr results, obtaining LAIF. We note that the level of precision of the LAIF potentially may increase through removing singular points or decrease if the LAIr data were too noisy. To further improve the precision level of the LAIr, the Fourier model was extended by considering the LAIr uncertainty. The LAIr, the LAI simulated using the Fourier model, and the LAI simulated using the extended Fourier approach (LAIeF) were validated through comparisons with the field measured LAI. The R 2 values were 0.68, 0.67 and 0.72, the residual sums of squares (RSS) were 3.47, 3.42 and 3.15, and the root-mean-square errors (RMSE) were 0. 31, 0.30 and 0.29, respectively, on DOY 177 (early July 2011

show abstract

“…Here, J is the number of random samples needed per model iteration. While J is often called "the number of inputs", this is not necessarily the same as the number of modeling input variables, because some models (typically ones with either spatial or temporal variation) may draw multiple samples for the same modeling variable on each iteration (Glen and Isaacs, 2012). According with (Yang, 2011) the Sobol's method has been shown to be robust and it is superior to traditional sensitivity methods (such as local methods that examine parameters one at a time) when considering cases where the assumption of linearity is invalid (Saltelli et al, 2004).…”

Section: Major Headings Sensitive Analysis Methodsmentioning

confidence: 99%

“…Such techniques include Fourier Amplitude Sensitivity Test (FAST), High Dimensional Model Representation (HDMR), random balance designs, and traditional ANOVA methods (Glen and Isaacs, 2012). In variance decomposition, the model output variance is represented as a sum of (2J-1) partial variances.…”

Section: Major Headings Sensitive Analysis Methodsmentioning

confidence: 99%

Multivalued Fuzzy Logics: A Sensitive Analysis

Ortega¹,

Andrade²,

Gómez³

2013

Procedings of the Fourth International Workshop on Knowledge Discovery, Knowledge Management and Decision Support

View full text Add to dashboard Cite

The main goal of this research is develop a sensitive analysis (SA) among some fuzzy operators, to ask the question: which is the most robustness fuzzy operators? The fuzzy operators consider in this study are: Zadeh operators, Probabilistic operators and finally the compensatory fuzzy logic operators: Geometric mean and Arithmetic mean. The Sobol model and the Monte Carlo simulations was been used to develop the SA. According with the main result of the study the compensatory fuzzy logic operators are the most robust.

show abstract

Estimating Sobol sensitivity indices using correlations

Cited by 126 publications

References 25 publications

Detecting Tipping points in Ecological Models with Sensitivity Analysis

Detecting Tipping points in Ecological Models with Sensitivity Analysis

An Extended Fourier Approach to Improve the Retrieved Leaf Area Index (LAI) in a Time Series from an Alpine Wetland

Multivalued Fuzzy Logics: A Sensitive Analysis

Contact Info

Product

Resources

About