Abstract
We model the points of the detection along the transect line by a Markov modulated Poisson process (MMPP). The MMPP can accommodate the spatial cluster structure typical of many line transect surveys. The basic idea is that animal density switches between a low and a high level according to a latent Markov process. The MMPP is attractive from a mathematical point of view, as it provides an explicit expression for the likelihood function and other important quantities. We focus on estimating the level of overdispersion in the number of detected animals, as this is important for quantifying the precision of the line transect estimator of animal abundance. The approach is illustrated using both simulated data and data from a minke whale sighting survey conducted in the North Atlantic.
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References
PK Andersen O Borgan RD Gill N Keiding (1993) Statistical models based on counting processes Springer-Verlag New York
S Asmussen (2000) ArticleTitleMatrix-analytic models and their analysis Scand J Stat 27 193–226 Occurrence Handle10.1111/1467-9469.00186
LE Baum T Petrie G Soules N Weiss (1970) ArticleTitleA maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains Ann Math Stat 41 167–174
BM Brown A Cowling (1998) ArticleTitleClustering and abundance estimation for Neyman-Scott models and line transect surveys Biometrika 85 427–438 Occurrence Handle10.1093/biomet/85.2.427
ST Buckland DR Anderson KP Burnham JL Laake DL Borchers L Thomas (2001) Introduction to distance sampling; estimating abundance of biological populations Oxford University Press Oxford
ST Buckland DR Anderson KP Burnham JL Laake DL Borchers L Thomas (Eds) (2004) Advanced distance sampling Oxford University Press Oxford
A Cowling (1998) ArticleTitleSpatial methods for line transect surveys Biometrics 54 828–839
DR Cox V Isham (1980) Point processes Chapman and Hall London
DJ Daley D Vere-Jones (1988) An introduction to the theory of point processes Springer-Verlag New York
Davison AC, Ramesh NI (1993). A stochastic model for times of exposures to air pollution from a point source. In: El-Shaarawi A, Piegorsch W (eds) Statistics for the environment. V. Barnett and K. F. Turkman, pp 123–138
A Griewank (2000) Evaluating derivatives: principles and techniques of algorithmic differentiation SIAM Philadelphia
G Hagen T Schweder (1994) Point clustering of minke whales in the northeastern Atlantic AS Blix L Walloe Ulltang (Eds) Whales, seals, fish and man. developments in marine biology Elsevier Amsterdam 27–34
S Hedley S Buckland (2004) ArticleTitleSpatial models for line transect sampling J Agric Biol Environ Stat 9 181–199 Occurrence Handle10.1198/1085711043578
H Heffes D Lucantoni (1986) ArticleTitleA Markov modulated characterization of packetized voice and data traffic related statistical performance IEEE J Sel areas Commun 4 856–868 Occurrence Handle10.1109/JSAC.1986.1146393
H Hogmander (1991) ArticleTitleA random field approach to transect counts of wildlife populations Biometrical J 33 1013–1023
JF Piatt DA Methven (1992) ArticleTitleThreshold foraging behavior of baleen whales Mar Ecol Prog Ser 84 205–210
NI Ramesh (1995) ArticleTitleStatistical-analysis on Markov-modulated Poisson processes Environmetrics 6 165–179
T Ryden (1994) ArticleTitleParameter estimation for Markov modulated Poisson processes Communi Stat—Stoch Models 10 795–829
T Ryden (1996) ArticleTitleAn EM algorithm for estimation in Markov-modulated Poisson processes Comput Stat Data Anal 21 431–447 Occurrence Handle10.1016/0167-9473(95)00025-9
T Schweder (1977) Point process models for line transect experiments J Barra (Eds) Recent developments in statistics North Holland Amsterdam 221–242
HJ Skaug N Oien G Bothun T Schweder (2004) ArticleTitleCurrent abundance of minke whales (Balaenoptera acutorostrata) in the Northeast Atlantic; variability in time and space Can J Fish Aquat Sci 61 870–886 Occurrence Handle10.1139/f04-020
H Taylor S Karlin (1984) An introduction to stochastic modeling Academic Press Orlando
J Ver Hoef N Cressie (1997) ArticleTitleUsing hidden Markov chains and empirical Bayes change-point estimation for transect data Environ Ecol Stat 4 247–264 Occurrence Handle10.1023/A:1018582614125
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Received: August 2004 / Revised: August 2005
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Skaug, H.J. Markov Modulated Poisson Processes for Clustered Line Transect Data. Environ Ecol Stat 13, 199–211 (2006). https://doi.org/10.1007/s10651-005-0006-0
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DOI: https://doi.org/10.1007/s10651-005-0006-0