Inference for Diffusion Processes : With Applications in Life Sciences

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. Front Matter....Pages i-xix Introduction....Pages 1-5 Front Matter....Pages 7-7 Stochastic Modelling in Life Sciences....Pages 9-30 Stochastic Differential Equations and Diffusions in a Nutshell....Pages 31-53 Approximation of Markov Jump Processes by Diffusions....Pages 55-100 Diffusion Models in Life Sciences....Pages 101-129 Front Matter....Pages 131-131 Parametric Inference for Discretely-Observed Diffusions....Pages 133-169 Bayesian Inference for Diffusions with Low-Frequency Observations....Pages 171-278 Front Matter....Pages 279-279 Application I: Spread of Influenza....Pages 281-303 Application II: Analysis of Molecular Binding....Pages 305-369 Summary and Future Work....Pages 371-373 Back Matter....Pages 375-430