B1021
Title: State-switching varying-coefficient stochastic differential equations
Authors: Timo Adam - University of St Andrews (United Kingdom) [presenting]
Richard Glennie - University of St Andrews (United Kingdom)
Theo Michelot - University of St Andrews (United Kingdom)
Abstract: Stochastic differential equations (SDEs) are popular tools for uncovering mechanistic relationships underlying time series data. By modelling the parameters of the process of interest as potentially smooth functions of a given set of covariates, varying-coefficient SDEs provide an extension of basic SDEs that allows us to capture more detailed, non-stationary features of the data-generating process. However, in practice, these parameters often vary at multiple time scales, which will be illustrated using dive data of Bairds beaked whales: while changes in pitch, roll, and heading exhibited within some dives can be described by some varying-coefficient SDE, other dives can be better characterised by other varying-coefficient SDEs; a pattern that is not readily accommodated for by the existing approach. To account for such state-switching patterns between dives while simultaneously allowing to make inference on the underlying behavioural processes that occur within dives, we propose a Markov chain operating at the between-dives scale that selects among a finite set of varying-coefficient SDEs to model the behaviour at the within-dive scale. The resulting class of state-switching varying-coefficient SDEs thus allows us to simultaneously model time-series data at multiple time scales in a joint modelling framework.
