Hidden Markov models for geolocation of fish |
| | Abstract | The present thesis strives to estimate the geographical location (geolocation) and movement of demersal fish based on tidal data extracted from electronic data storage tags (DSTs).
The theory of the underlying diffusion model is presented with emphasis on the connection between the partial differential equation governing its time evolution and a homogeneous random walk. The paradigm of a hidden Markov model is applied to the DST data considering the global coordinates as the hidden states furnishing the observable tidal output. A Bayesian filter offers a straightforward framework for maximum likelihood estimation of model parameters. The most probable sequence of hidden states, i.e. the Most Probable Track, is found by employment of the Viberti algorithm.
A simulation study is conducted to examine the method performance in terms of computation time and parameter estimation. Furthermore it is sought to elucidate the filtering step in greater detail and evaluate the influence of spatial variation in environmental variables such as depth. Conclusively, the maximum likelihood estimator is tested for bias and precision followed by an analysis of the optimal track representation.
The dataset considered in the project consists primarily of depth and temperature records from Atlantic cod (Gadus morhua) tagged in the southern North Sea and eastern English Channel. The initial data preprocessing extracts the pertinent tidal information and depth to be transferred to the filtering algorithm. The variance structure of the observed time series is assessed by means of stationary tags at known geographical positions.
The geolocation method is implemented in the Matlab v. 7.0 computing environment that offers a flexible presentation of the geolocation. Animating the time evolution of the marginal posterior distributions in an avi-file gives a detailed visualisation of the uncertainty in each discrete time step. The Most Probable Track images the mode of the joint posterior distribution and is a representation that can be contained in a single figure thereby easing interpretation of the results. Explicit estimation of the joint posterior distribution is unique for the method and opens for a wide range of applications.
The presented results concurred with the general pattern of previous studies of the data but excelled in terms of detail and computation time. The method showed flexibility and was prone to extensions of which some were implemented in simplified forms for illustrative purposes.
The estimated fish behaviour is based on statistical rigor and can serve as substantial argumentation in future decisions related to stock assessment and fisheries management. | | Keywords | Geolocation, diffusion process, Atlantic cod, data storage tags, hidden Markov model, maximum likelihood estimation, Most Probable Track | | Type | Master's thesis [Academic thesis] | | Year | 2007 | | Publisher | Informatics and Mathematical Modelling, Technical University of Denmark, DTU | | Address | Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby | | Series | IMM-Thesis-2007-22 | | Note | Supervised by Uffe H. Thygesen and Henrik Madsen, IMM, DTU, and colleagues Ken Haste Andersen and David Righton. I am indebted to the kind people at the CEFAS Laboratory for sharing their wisdom and for providing the DST and environmental data. This work was supported by Oticon Fonden. | | Electronic version(s) | [pdf] | | BibTeX data | [bibtex] | | IMM Group(s) | Mathematical Statistics |
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