the Efficient modelling of individual animal movement in continuous time

In my work, we rigorously approximate the work of Blackwell (2020) by assuming that no more than two behavioural changes may occur between observations. This has previously been shown to lead to a close approximation of the truth in a PhD thesis by Alkhezi (2019) in an MCMC algorithm. When calculating the ‘local’ likelihood between observations, we may integrate the animal’s movement density over the time until potential behavioural changes occur. We do this for each possible case (no changes in behaviour, one change, and two changes in behaviour), weighting the diffusion rate of the animal in each case using algorithms in Hobolth and Stone (2019). These local likelihoods are then combined to produce a global likelihood via the aforementioned forward algorithm. 

We refer to this new method as the ‘Fast InCH’ (FInCH) approach. By simplifying the model in this way, we may make inference on an animal’s movement and behavioural ecology using maximum likelihood estimation, rather than MCMC. This is a key step if models formulated in continuous time are to one day be as accessible as their discrete-time counterparts. To achieve computational feasibility for large data sets, we have developed a method for spatially homogeneous data whereby we approximate the ‘local’ likelihood between observations using a spline interpolation.

 Please feel free to contact me at dpdgrainger1[at]sheffield.ac.uk