1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

Advances in enhanced biological phosphorus removal: from micro to macro scale.

Mathematical simulation models are commonly applied to analyze experimental or environmental data and eventually to acquire predictive capabilities. Typically these models depend on poorly defined, unmeasurable parameters that need to be given a value. Fitting a model to data, so-called inverse modelling, is often the sole way of finding reasonable values for these parameters. There are many challenges involved in inverse model applications, e.g., the existence of non-identifiable parameters, the estimation of parameter uncertainties and the quantification of the implications of these uncertainties on model predictions.

The R package FME is a modeling package designed to confront a mathematical model with data. It includes algorithms for sensitivity and Monte Carlo analysis, parameter identifiability, model fitting and provides a Markov-chain based method to estimate parameter confidence intervals. Although its main focus is on mathematical systems that consist of differential equations, FME can deal with other types of models. In this paper, FME is applied to a model describing the dynamics of the HIV virus.

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Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME

Identification and qualitative comparison of sensitivity analysis methods that have been used across various disciplines, and that merit consideration for application to food-safety risk assessment models, are presented in this article. Sensitivity analysis can help in identifying critical control points, prioritizing additional data collection or research, and verifying and validating a model. Ten sensitivity analysis methods, including four mathematical methods, five statistical methods, and one graphical method, are identified. The selected methods are compared on the basis of their applicability to different types of models, computational issues such as initial data requirement and complexity of their application, representation of the sensitivity, and the specific uses of these methods. Applications of these methods are illustrated with examples from various fields. No one method is clearly best for food-safety risk models. In general, use of two or more methods, preferably with dissimilar theoretical foundations, may be needed to increase confidence in the ranking of key inputs.

Identification and Review of Sensitivity Analysis Methods

Activated sludge systems are designed and operated globally to remove phosphorus microbiologically, a process called enhanced biological phosphorus removal (EBPR). Yet little is still known about the ecology of EBPR processes, the microbes involved, their functions there and the possible reasons why they often perform unreliably. The application of rRNA-based methods to analyze EBPR community structure has changed dramatically our understanding of the microbial populations responsible for EBPR, but many substantial gaps in our knowledge of the population dynamics of EBPR and its underlying mechanisms remain. This review critically examines what we once thought we knew about the microbial ecology of EBPR, what we think we now know, and what still needs to be elucidated before these processes can be operated and controlled more reliably than is currently possible. It looks at the history of EBPR, the currently available biochemical models, the structure of the microbial communities found in EBPR systems, possible identities of the bacteria responsible, and the evidence why these systems might operate suboptimally. The review stresses the need to extend what have been predominantly laboratory-based studies to full-scale operating plants. It aims to encourage microbiologists and process engineers to collaborate more closely and to bring an interdisciplinary approach to bear on this complex ecosystem.

The microbiology of biological phosphorus removal in activated sludge systems.

Large environmental simulation models are usually overparameterized with respect to given sets of observations. This results in poorly identifiable or nonidentifiable model parameters. For small models, plots of sensitivity functions have proven to be useful for the analysis of parameter identifiability. For models with many parameters, however, near-linear dependence of sensitivity functions can no longer be assessed graphically. In this paper a systematic approach for tackling the parameter identifiability problem of large models based on local sensitivity analysis is presented. The calculation of two identifiability measures that are easy to handle and interpret is suggested. The first accounts for the sensitivity of model results to single parameters, and the second accounts for the degree of near-linear dependence of sensitivity functions of parameter subsets. It is shown how these measures provide identifiability diagnosis for parameter subsets, how they are able to guide the selection of identifiable parameter subsets for parameter estimation, and how they facilitate the interpretation of the correlation matrix of the parameter estimate with respect to parameter identifiability. In addition, we show how potential bias of the parameter estimates, due to a priori fixing of some of the parameters, can be analyzed. Finally, two case studies are presented in order to illustrate the suggested approach.

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Roland Brun

Papers

Practical identifiability analysis of large environmental simulation models

Practical identifiability of ASM2d parameters—systematic selection and tuning of parameter subsets

Biogeochemical model of Lake Zürich : sensitivity, identifiability and uncertainty analysis

Microbial competition for the organic substrates and its impact on EBPR systems under conditions of changing carbon feed