Matieyendou Lamboni

University of French Guiana · Department Of Science & Technology

In this paper, we investigate a statistical model for disaggregating the observations of resources shares, available only at a regional level (large scale), into spatial explicit scales. The model runs at a fine scale and we have as many models as the number of the fine scales within an administrative region (NUTS2). We aggregate the models inside...

Cross-partial derivatives are relevant in modeling such as inverse problems, functional analysis and exploring complex mathematical models. In addition to adjoint-based methods that provide the exact gradients for some POE/PDE-based models, Richardson's extrapolation and its generalization in one hand, and the Monte-Carlo approach in the other h...

Computing cross-partial derivatives using fewer model runs is relevant in modeling, such as stochastic approximation, derivative-based ANOVA, exploring complex models, and active subspaces. This paper introduces surrogates of all the cross-partial derivatives of functions by evaluating such functions at N randomized points and using a set of L cons...

Computing cross-partial derivatives using fewer model runs is relevant in modeling, such as stochastic approximation, derivative-based ANOVA, exploring complex models, and active subspaces. This paper introduces surrogates of all the cross-partial derivatives of functions by evaluating such functions at $N$ randomized points and using a set of $L$...

Gradients of smooth functions with nonindependent variables are relevant for exploring complex models and for the optimization of the functions subjected to constraints. In this paper, we investigate new and simple approximations and computations of such gradients by making use of independent, central, and symmetric variables. Such approximations a...

Gradients of smooth functions with non-independent variables are relevant for exploring complex models and for the optimization of functions subjected to constraints. In this paper, we investigate new and simple approximations and computations of such gradients by making use of independent, central and symmetric variables. Such approximations are w...

ANOVA decomposition of a function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate reproducing kernel Hilbert space regarding their distributions, we propose an efficient statistical test of independe...

ANOVA decomposition of function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate reproducing kernel Hilbert space regarding their distributions, we propose an efficient statistical test of independenc...

A methodology for assessing the inputs-outputs association for time-dependent predictive models subjected to safety objectives is investigated. Firstly, new dependency models for sampling random values of uncertain inputs that comply with the safety objectives are provided by making use of the desirability measures. Secondly, combining predictive r...

Complex models are often used to understand interactions and drivers of human-induced and/or natural phenomena. It is worth identifying the input variables that drive the model output(s) in a given domain and/or govern specific model behaviors such as contextual indicators based on socio-environmental models. Using the theory of multivariate weight...

Stochastic characterizations of functions subject to constraints result in treating them as functions with non-independent variables. By using the distribution function or copula of the input variables that comply with such constraints, we derive two types of partial derivatives of functions with non-independent variables (i.e., actual and dependen...

Human-induced dynamic systems are widely encountered in engineering. Such systems are represented by complex dynamic models, which are used for understanding interactions and drivers that affect predictions of a wide range of problems and issues. Such mathematical representations of physical realities are often non-linear with important interaction...

Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with non-independent variables. Using the distribution function or copula of such variables that comply with such equati...

We are interested in analyzing specific model behaviors such as the model output(s) values within a given cluster using the probability theory. By showing the relevance of the multivariate weighted distribution theory to characterize some behaviors of interest thanks to the weight functions, we derive the distribution function of the model inputs t...

Hoeffding’ decomposition of functions (i.e., ANOVA) is widely used in statistical modeling and uncertainty quantification such as variance-based sensitivity analysis ([1.2]). In this abstract, we extend functional ANOVA to cope with non-independent variables by making use of dependency functions of any non-independent variables (see [3,4]). The pro...

Dependency functions of dependent variables are relevant for (i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and (ii) simulating random dependent variables. In this paper, we mathematically derive practical dependency functions for classical multivariate distribution...

We are interested in identifying the input variables that drive model output(s) in a domain of interest and/or govern specific model behaviors defined via weight functions such as outputs belonging to a given cluster from any classification approach

Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In this paper, we mathematically derive practical dependency functions for classical multivariate distributions...

Functional analysis of variance (FANOVA) is widely used in statistical modeling and sensitivity analysis. Knowing the important role of derivatives in models’ analysis and/or development such as variational formulation of phenomena, we develop new expansions of functions using their weak derivatives, the density and distribution functions of input...

We use to work with models defined through a function and some equations connecting the input variables such as a given function subject to some constraints involving input variables. For such models, it is interesting to better determine the partial derivatives with respect to each input variable that comply with the constrained equations. As the...

In this paper, we propose a novel methodology for better performing uncertainty and sensitivity analysis for complex mathematical models under constraints and/or with dependent input variables, including correlated variables. Our approach allows for assessing the single, overall and interactions effects of any subset of input variables, that accoun...

A new method named cluster-based GSA is proposed to enhance the sensitivity analysis of models with temporal or spatial outputs. It is based on a tight coupling between Global Sensitivity Analysis (GSA) and clustering procedures. Clustering is introduced to characterize the different behaviors of the model outputs by grouping them into clusters. Th...

In this paper, we propose a new methodology for better assessing the single, overall and interactions contributions of dependent and/or correlated variables over the whole model outputs. Our methodology relies on our ability to extract a model that characterizes the dependency structures of any random vector. Such dependency model is then coupled w...

In this paper, we propose a new methodology for better assessing the single, overall and interactions contributions of dependent and/or correlated variables over the whole model outputs. Our methodology relies on our ability to extract a model that characterizes the dependency structures of any random vector. Such dependency model is then coupled w...

Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify th...

Weighted Poincaré-type and related inequalities provide upper bounds of the variance of functions. Their applications in sensitivity analysis allow for quickly identifying the active inputs. Although the efficiency in prioritizing inputs depends on that upper bounds, the latter can take higher values, and therefore useless in practice. In this pape...

Weighted Poincar\'e-type and related inequalities provide upper bounds of the variance of functions. Their application in sensitivity analysis allows for quickly identifying the active inputs. Although the efficiency in prioritizing inputs depends on the upper bounds, the latter can be big, and therefore useless in practice. In this paper, an optim...

Variance-based sensitivity analysis (Vb-SA) [1-3] and Multivariate Sensitivity Analysis (MSA) [4-5] provide the first-order and total sensitivity indices for single and multivariate response models, respectively. In the presence of dependent or correlated input factors, some mathematical methodologies have been developed to deal with that issues fo...

In uncertainty quantification, multivariate sensitivity analysis (MSA), including variance-based sensitivity analysis, and derivative global sensitivity measure (DGSM) are widely used for assessing the effects of input factors on the model outputs. While MSA allows for identifying the order and the strength of interactions among inputs, DGSM provid...

Computer models are developed to simulate physical systems of interest for supporting decision making. The models are often complex so that classical analysis are intractable (model calibration, evaluation, diagnostic). Quantifying the association between the variability of the model outputs (dynamic or multiple) and the inputs allows for better...

In uncertainty quantification, classical multivariate sensitivity analysis (MSA) extends variance-based sensitivity analysis to cope with the multivariate response models, and it aims to apportion the variability of the multivariate response into input factors and their interactions. The first-order and total-effect covariance matrices from MSA, wh...

In uncertainty quantification, multivariate sensitivity analysis (MSA) extends variance-based sensitivity analysis to cope with the multivariate response, and it aims to apportion the variability of the multivariate response into input factors and their interactions. The first-order and total-effect covariance matrices from MSA, which assess the ef...

A deep exploration of mathematical complex models is often made by using model-free methods. Variance-based sensitivity analysis, Derivative-based sensitivity analysis, and multivariate sensitivity analysis (MSA) are ones of them. In one hand, variance-based sensitivity analysis (VbSA) allows for assessing the effects of inputs on the model outputs...

Variance-based sensitivity analysis and multivariate sensitivity analysis aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’s total index, which accounts for the effects of interactions, serves as a practical tool to deal with the curse of dimensionality. In this paper, we address the problem o...

A deep exploration of mathematical models in reliability analysis is often made by using model-free methods. Variance-based sensitivity analysis ([18,17,3]) and multivariate sensitivity analysis ([10,9,2]) are ones of them and aim at apportioning the variability of the model output(s) into input factors and their interactions. Sobol's first-order i...

Variance-based sensitivity analysis [1-2] and multivariate sensitivity analysis [3-5] aim at apportioning the variability of the model output(s) into input factors and their interac- tions. Sobol’s total index, which accounts for the effects of interactions, is often used for selecting the most influential parameters. In this paper, we propose a gene...

Changes of carbon stocks in agricultural soils, emissions of greenhouse gases from agriculture, and the delivery of ecosystem services of agricultural landscapes depend on combinations of land-use, livestock density, farming practices, climate and soil types. Many environmental processes are highly non-linear. If the analysis of the environmental i...

The Land-Use Disaggregation Model (LUDM) aims at predicting the land-use areas within the fine-scale units called Homogenous Spatial Units (HSUs). It is based upon three main steps presented in Figure 1 (see Lamboni et. al, 2016 for more comprehensive details). First, it combines point-based field observations of land-use with the environmental and...

Variance-based sensitivity analysis and multivariate sensitivity analysis aim to apportion the variability of model output(s) into input factors and their interactions. Total sensitivity index (TSI) gives for each input its overall contribution, including the effects of its interactions with all the other inputs, in the variability of the model out...

The spatial data set delineates areas with similar environmental properties regarding soil, terrain morphology, climate and affiliation to the same administrative unit (NUTS3 or comparable units in size) at a minimum pixel size of 1km2. The scope of developing this data set is to provide a link between spatial environmental information (e.g. soil p...

Shares of available resources, such as land resources, at a fine meshed grid of 1km*1km are required as a priori information for i) managing these resources at a local level by disaggregating the resource scenarios to a spatial explicit scale; ii) allowing the development of local environmental indicators, many of which depend on the local combinat...

Process-based models are widely used as an experimental tool for monitoring, managing natural, environment and human-induced hazards. This paper deals with Multivariate Factor Mapping (MFM) for controlling input variables and process parameters in such a way that the model outputs meet a safety objective, fixed by the competent authorities. It give...

Variance-based sensitivity analysis and multivariate sensitivity analysis aim to ap-portion the variability of model output(s) into input factors and their interactions. Total sensitivity index (TSI) gives for each input its overall contribution, includ-ing the eects of its interactions with all the other inputs, in the variability of the model out...

Microbiological food safety is an important economic and health issue in the context of globalization and presents food business operators with new challenges in providing safe foods. The hazard analysis and critical control point approach involve identifying the main steps in food processing and the physical and chemical parameters that have an im...

The agricultural sector contributes to 9.3-10.6% of total greenhouse gas (GHG) emission, and there is a growing interest in modelling environmental impacts of agricultural activities. For the quantification of agri-environmental indicators and the estimation of GHG, the distribution of crop shares over the Homogenous Spatial Units (HSU) is required...

The agricultural sector contributes to 9.3-10.6% of total greenhouse gas (GHG) emission in EU, and there is a growing interest in modelling environmental impacts of agricultural activities. The prediction of the crop shares over the Homogenous Spatial Units (HSU, fine meshed grid of 1km*1km) is required as many indicators depend on the local combin...

Global Sensitivity Analysis (GSA) methods and Multivariate Sensitivity Analysis (MSA) methods, which aim to apportion the variability of model output(s) into input variables and their interactions, are an objective way to evaluate the impact of the uncertainty in input variables on the model output(s). In particular, The Total Sensitivity Index (TS...

The agricultural sector contributes to 9.3 − 10.6% of total greenhouse gas (GHG) emission, excluding LULUCF, in the EU27 (EEA [1]) and there is a growing interest in modelling environmental impacts of agricultural activities. GHG emission heavily depends on a number of different biophysical characteristics, such as soil, landform, and climate (Lambo...

Global Sensitivity Analysis (GSA) methods [1], [2] and Multivariate Sensitivity Analysis (MSA) methods [3], which aim to apportion model output variability into input variables and their interactions, are an objective way to evaluate the impact of the uncertainty in input variables on the model output. In particular, The Total Sensitivity Index (TS...

The estimation of variance-based importance measures (i.e. the sensitivity indices called Sobol’ indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for huge model involving a large number of input variables (typically more than ten). This problem of dimensionality can be...

The estimation of variance-based importance measures (called Sobol' indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a large number of input variables (typically more than ten). Recently, Sobol and Kucherenko have proposed the Deriv...

Nitrous oxide, carbon dioxide and methane are the main biogenic greenhouse gases (GHGs) contributing to net greenhouse gas balance of agro-ecosystems. Evaluating the impact of agriculture on climate thus requires capacity to predict the net exchanges of these gases in a systemic approach, as related to environmental conditions and crop management....

The hazard control in international trade becomes an important economic issue in the context of globalization and new challenges are addressed to food industrials to produce safe ready-to-eat foods. In quantitative HACCP plan (ILSI, 2004), identifying the physico-chemical and process parameters having an impact on the safety of the products is nece...

Hazard control in international trade becomes an important economic issue in the context of globalization and new challenges are addressed to food industrials to produce safe ready-to-eat foods. In quantitative HACCP plan, identifying the physico-chemical and process parameters having an impact on the safety of the products is necessary and setting...

When a model contains a large number of parameters, sensitivity analysis is often used to select the parameters to be estimated among those identified as the most influent. This selection procedure is based on simulated data and is different from the model validation procedure that is based on real data. Nevertheless, these two processes are interr...

Many dynamic models are used for risk assessment and decision support in ecology and crop science. Such models generate time-dependent model predictions, with time either discretised or continuous. Their global sensitivity analysis is usually applied separately on each time output, but Campbell et al. (2006 [1]) advocated global sensitivity analyse...

Sensitivity analysis is frequently used to select the most influent parameters to be estimated from scarce available data. However, the capability of this approach to improve model predictions is not well known, especially for complex environmental models. This paper investigates the relevance of estimating the most influent parameters only and set...

Dynamic models are often used to simulate the impact of agricultural practices and sometimes to test some decision rules. These models include many uncertain parameters and it is sometimes difficult or impossible to estimate all the parameters. A common practice in literature is to select key parameters by using sensitivity index and then to estimate...

Des modèles dynamiques sont souvent utilisés pour simuler l'impact des pratiques agricoles et parfois pour tester des règles de décision. Ces modèles incluent de nombreux paramètres incertains et il est parfois difficile voire impossible de tous les estimer. Une pratique courante dans la littérature consiste à s sélectionner les paramètres clés à l...

Nitrous oxide, carbon dioxide and methane are the main biogenic greenhouse gases (GHG) contributing to the global warming potential (GWP) of agro-ecosystems. Evaluating the impact of agriculture on climate thus requires a capacity to predict the net exchanges of these gases in an systemic approach, as related to environmental conditions and crop ma...

Dynamic crop models are frequently used in ecology, agronomy and environmental sciences for simulating crop and environmental variables at a discrete time step. They often include a large number of parameters whose values are uncertain, and it is often impossible to estimate all these parameters accurately. A common practice consists in selecting a...

In the context of managed herds, epidemiological models usually take into account relatively complex interactions involving a high number of parameters. Some parameters may be uncertain and/or highly variable, especially epidemiological parameters. Their impact on the model outputs must then be assessed by a sensitivity analysis, allowing to identi...

definition of Generalized Sensitivity Indices using covariance

Discrete-time models are frequently used in ecology and agronomy. These models can be used for the management of endangered species, for understanding intraspecific and interspecific competitions, for pest management, or for predicting plant growth. Their outputs can be expressed as time series. It is often impossible to estimate all the parameters...

The development of dynamic models describing complex ecological or soil-crop systems continues to grow in popularity, for both academic research and project management (1). Sensitivity Analysis (SA) is a prerequisite tool for model building and for model-based applications (2). It can be used to identify the model components which may need a more t...

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