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This gives an overview of the different areas of research. In some cases more details can be obtained by selecting the releavnt links.
This project is about continuous time stochastic inference and learning (CTSIL). CTSIL is useful in continuously evolving environments that need to be modelled to fit with particular observations. Examples of this include weather systems where a stochastic model of the development of the local weather must explain the observed meteorological recordings well, and neural systems where models for neural spike patterns need to match intracellular recordings. Using CTSIL will provide models that can predict future data better and enable more accurate scientific explanations. In general, the capability of doing inference in continuous time stochastic systems reaps benefits in situations where:
By moving from simulation to continuous time stochastic inference, it is possible to perform rigourous parameter and model estimation that produces better models than matching limited simulation runs with observational statistics. By using stochastic instead of deterministic systems, the poor fit that results from trying to model a stochastic signal by a limited deterministic model is avoided. Consider a trivial example: fitting a deterministic oscillator (i.e. sinusoidal signal) to observations of a \emph{noisy} oscillator. Due to the various phase shifts that the noisy oscillator produces the fit of the deterministic oscillator will be poor, even if the parameters are exactly correct.
Continuous-time rather than discrete-time inference results in greater accuracy, especially in non-linear systems where the dynamics of the discrete iterated system can poorly match the underlying nonlinear dynamical system as the underlying attractors, limit cycles and chaotic dynamics will be potentially be different. In dynamic rather than static models, temporal constraints on causality can be used: even limited information from time-indexed signals can help establish causal relationships between variables that are indistinguishable in static models due to the large equivalence classes.
More recently I have been working in this area. Watch this space!