This thesis aims to identify appropriate methods for the modelling of animal behaviour data, and in the wider context, any time series of categorical data. We make extensive use of a large dataset of cow feeding behaviour, consisting of full feeding records for a number of cows over one month, the data taking the form of binary time series, i.e. feeding/non-feeding periods. After initial exploratory data analysis, we go on to investigate three classes of model: latent Gaussian, hidden Markov and semi-Markov. The latent Gaussian model assumes the binary data occur from the thresholding of an underlying continuous variable. We identify the one-to-one relationship between the autocorrelation of the observed and latent variables and consider techniques for parameter estimation. For a multivariate stationary Gaussian process we show the asymptotic equivalence of the likelihood written in its spectral and conventional forms, and provide a proof that for short-term memory processes such as ARMA models, a good approximation for the spectral form is obtained using Fourier transforms of correlations at only the first few lags. A simulation study highlights the saving in computing time that this offers, and also shows that, in contrast to the least squares methods considered, the number of lags to retain is not crucial for obtaining efficient parameter estimates. Hidden Markov models also directly model the underlying state of the animal, but the latent variable here is discrete and follows a Markov chain, observations being dependent only on the current state. However, this type of model constrains the durations between feeding events to follow a mixture of geometric distributions, which is seen to be inappropriate for the data considered. Semi-Markov models simply involve the animal moving between a set of feeding and non-feeding states according to a set of transition probabilities, the marginal distributions for durations in each state being specified directly.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:640407 |
| Date | January 2001 |
| Creators | Allcroft, David John |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/11132 |
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