Conducting Inference and Analysis on Non-Linear Diffusion Processes in R
Etienne Pienaar, a PhD student in the Department of Statistical Sciences will present the Department of Statistical Sciences seminar with his talk entitled, "Conducting Inference and analysis on non-linear diffusion processes in R
Stochastic calculus has found application in numerous scientific fields ranging from ecology and biology to finance and engineering. The science centres around conducting analysis on diffusion processes which are defined in terms of systems of stochastic differential equations (SDEs). As such diffusion models can be used to accurately describe the dynamics of complex systems of stochastic processes in a compact and coherent way. Unfortunately, diffusion models rarely have analytically tractable dynamics, often forcing the statistician to resort to using unrealistic models/assumptions in favour of making the analysis tractable. Alternatively a number of strategies have been developed for conducting analysis on non-linear systems of SDEs. However the mathematics that underpin these methods can be daunting and often require a good understanding of technical material from outside the discipline of pure statistics or the context of the desired application. Furthermore, these methods tend to be computationally intensive and often require hours of runtime on typical desktop configurations. In response to this we have endeavoured to develop a series of packages for the ubiquitous statistical software language, R, that aims to collect methods for performing inference and analysis on suitably general classes of diffusion processes. The packages focus on separating the user from the process of setting up the underlying mathematics, whilst maximizing computational efficiency through various programming and algorithmic techniques.
For purposes of the talk Etienne will be introducing two R packages currently under development:
DiffusionRgqd: A package that focuses on likelihood based inference and analysis for scalar and bivariate generalized quadratic diffusion processes (GQDs).
DiffusionRimp: A package that focuses on data imputation for reducible diffusions and PDE based analysis for highly non-linear diffusion processes.
Etienet will be demonstrating the software through some simulated and real-world applications and give a short outline of the software architecture where needed.