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2020 | Buch

Complex Systems, Data and Inference Kapitel lesen Erstes Kapitel lesen

Identifiability and Regression Analysis of Biological Systems Models

Statistical and Mathematical Foundations and R Scripts

verfasst von: Paola Lecca

Verlag: Springer International Publishing

Buchreihe : SpringerBriefs in Statistics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This richly illustrated book presents the objectives of, and the latest techniques for, the identifiability analysis and standard and robust regression analysis of complex dynamical models. The book first provides a definition of complexity in dynamic systems by introducing readers to the concepts of system size, density of interactions, stiff dynamics, and hybrid nature of determination. In turn, it presents the mathematical foundations of and algorithmic procedures for model structural and practical identifiability analysis, multilinear and non-linear regression analysis, and best predictor selection.

Although the main fields of application discussed in the book are biochemistry and systems biology, the methodologies described can also be employed in other disciplines such as physics and the environmental sciences. Readers will learn how to deal with problems such as determining the identifiability conditions, searching for an identifiable model, and conducting their own regression analysis and diagnostics without supervision.

Featuring a wealth of real-world examples, exercises, and codes in R, the book addresses the needs of doctoral students and researchers in bioinformatics, bioengineering, systems biology, biophysics, biochemistry, the environmental sciences and experimental physics. Readers should be familiar with the fundamentals of probability and statistics (as provided in first-year university courses) and a basic grasp of R.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Complex Systems, Data and Inference
Abstract
The concepts of complexity and networks are recurrent in modern systems biology. They are intimately linked to the very nature of biological processes governed by mathematically complex laws and orchestrated by thousands of interactions among thousands of molecular components. In this chapter, we explain what it means that a system is complex, what are the mathematical tools and the abstract data structures that we can use to describe a complex system, and finally what challenges the scientific community must face today to deduce a mathematical or computational model from observations experimental.
Paola Lecca
Chapter 2. Dynamic Models
Abstract
A graph or hypergraph is a static representation of all possible interactions between nodes. However, due to these same interactions, the network topology evolves over time. The abundances of the chemical and/or molecular species they represent in nodes change over time and if they fall below a critical threshold, they cause the disappearance of any connected arches and then determine their reappearance if they return to exceed this critical threshold. The description of the dynamics of a network consists of a mathematical model often constituted by differential equations that express the speed of variation of the abundances of the biological entities represented by the nodes. The dynamics of a network can be deterministic, or stochastic or stochastic/deterministic hybrid. Depending on the nature of its determination, the dynamics is modelled by deterministic differential equations, stochastic differential equations, master equations, and in cases where the numerical solution of the latter is difficult to calculate, from stochastic simulation algorithms. In this chapter, we give an overview of the most used dynamic models for simulating the temporal evolution of a network.
Paola Lecca
Chapter 3. Model Identifiability
Abstract
Once we have built a model to describe the dynamics of a network, in order to simulate this dynamic, that is, the evolution in the time of the network, we need to know the parameters of the model. Very often the values of the kinetic constants in a network of biochemical interactions, or more generally the arcs’ weights on the network define the force and direction of the interaction between nodes, are obtained from experimental data through various regression and inference techniques. In this chapter, we will tackle a problem that is upstream of the parameter estimation, that is, the possibility to infer them from the data. The problem is known as identifiability. Identifiability is a fundamental prerequisite for model identification. It concerns uniqueness of the model parameters determined from experimental observations. This paper specifically deals with structural or a priori identifiability: whether or not parameters can be identified from a given model structure and experimental measurements. Since experimental data are usually affected by uncertainties, this question is known as practical identifiability. Non-identifiability of parameters induces non-observability of trajectories, reducing the predictive power of the model. We will discuss here a method of parameter identifiability based on the observability rank test and how much it is suitable to handle noisy observations.
Paola Lecca
Chapter 4. Regression and Variable Selection
Abstract
Regression is used for explaining the relationship between a variable Y called response, and a set of one or more variables \(X_1, X_2, \dots , X_N\) called explanatory variables. The variable selection is the process that choose a reduced number of explanatory variables to describe a response variable in a regression models. Variable selection is used to (i) make the model easier to interpret, removing redundant non-informative variables; (ii) reduce the size of the problem to enable algorithms to run faster; and (iii) reduce the overfitting and, consequently, make the model predictive.
Paola Lecca
Chapter 5. R Scripts
Abstract
In this chapter, we report the R scripts implemented to perform identifiability analysis and regression, mentioned in the previous chapters. The input files are only available upon request to the author.
Paola Lecca
Backmatter
Metadaten
Titel
Identifiability and Regression Analysis of Biological Systems Models
verfasst von
Paola Lecca
Copyright-Jahr
2020
Electronic ISBN
978-3-030-41255-5
Print ISBN
978-3-030-41254-8
DOI
https://doi.org/10.1007/978-3-030-41255-5

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