Stochastic Modelling for Systems Biology, Third Edition

Darren J. Wilkinson

• Editorial: Chapman and Hall/CRC
• Año: 2018
• ISBN:
  9781351000895
• Edición: 3
• Categoría: Mathématiques
• Categoría: Probabilités et statistiques

Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Having been thoroughly updated to reflect this, this third edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context. New methods and applications are included in the book, and the use of R for practical illustration of the algorithms has been greatly extended. There is a brand new chapter on spatially extended systems, and the statistical inference chapter has also been extended with new methods, including approximate Bayesian computation (ABC). Stochastic Modelling for Systems Biology, Third Edition is now supplemented by an additional software library, written in Scala, described in a new appendix to the book.

New in the Third Edition

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• New chapter on spatially extended systems, covering the spatial Gillespie algorithm for reaction diffusion master equation models in 1- and 2-d, along with fast approximations based on the spatial chemical Langevin equation

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• Significantly expanded chapter on inference for stochastic kinetic models from data, covering ABC, including ABC-SMC

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• Updated R package, including code relating to all of the new material

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• New R package for parsing SBML models into simulatable stochastic Petri net models

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• New open-source software library, written in Scala, replicating most of the functionality of the R packages in a fast, compiled, strongly typed, functional language

Keeping with the spirit of earlier editions, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership. An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling.

PART II

Stochastic processes and simulation

CHAPTER 3

Probability models

3.1 Probability

3.1.1 Sample spaces, events, and sets

The models and representations considered in the previous chapter provide a framework for thinking about the state of a biochemical network, the reactions that can take place, and the change in state that occurs as a result of particular chemical reactions. As yet, however, little has been said about which reactions are likely to occur or when. The state of a biochemical network evolves continuously through time with discrete changes in state occurring as the result of reaction events. These reaction events are random, governed by probabilistic laws. It is therefore necessary to have a fairly good background in probability theory in order to properly understand these processes. In a short text such as this, it is impossible to provide complete coverage of all of the necessary material. However, this chapter is meant to provide a quick summary of the essential concepts in a form that should be accessible to anyone with a high school mathematics education who has ever studied some basic probability and statistics. Readers with a strong background in probability will want to skip through this chapter. Note, however, that particular emphasis is placed on the properties of the exponential distribution, as these turn out to be central to understanding the various stochastic simulation algorithms that will be examined in detail in later chapters.

Any readers finding this chapter difficult should go back to a classic introductory text such as Ross (2009). The material in this chapter should provide sufficient background for the next few chapters (concerned with stochastic processes and simulation of biochemical networks). However, it does not cover sufficient statistical theory for the later chapters concerned with inference from data. Suitable a...