Inference for Diffusion Processes
With Applications in Life Sciences
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Beschreibung
Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.
Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.
Explicit instructions for diffusion modelling enable practitioners to apply this powerful class of processes Both stochastic modelling and statistical inference for diffusion processes are comprehensively covered in one book Explains in detail a Bayesian approach which enables parameter estimation for diffusion models in many applications in life sciences Graphical illustrations facilitate the understanding of Bayesian imputation techniques and associated convergence considerations Methods are illustrated on complex real data applications from epidemic modelling and fluorescence microscopy Required knowledge on stochastic calculus is provided in a special chapter Includes supplementary material: sn.pub/extras
Autor*in
Christiane Fuchs
Themen in »Inference for Diffusion Processes«
Bayesian inference diffusion approximations epidemic modelling fluorescence recovery after photobleaching (FRAP) stochastic differential equations (SDE)
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From the reviews:
“The book under review is aimed at introducing both modelling and inference for diffusions and applying the statistical estimation of complex diffusion models to real data sets. It addresses to theoreticians (e.g., mathematicians and statisticians) as well as practitioners (e.g., bioinformaticians and biologists) with basic knowledge about deterministic differential equations, probability theory and statistics. … the book under review is recommended to researchers with strong background through deterministic differential equations, probability theory and statistics.” (Iris Burkholder, zbMATH, Vol. 1276, 2014)()