Environmental and Ecological Statistics

, Volume 13, Issue 2, pp 199–211 | Cite as

Markov Modulated Poisson Processes for Clustered Line Transect Data

  • Hans J. SkaugEmail author


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.


Point process Line transect survey Minke whale Overdispersion 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andersen, PK, Borgan, O, Gill, RD, Keiding, N 1993Statistical models based on counting processesSpringer-VerlagNew YorkGoogle Scholar
  2. Asmussen, S 2000Matrix-analytic models and their analysisScand J Stat27193226CrossRefGoogle Scholar
  3. Baum, LE, Petrie, T, Soules, G, Weiss, N 1970A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chainsAnn Math Stat41167174Google Scholar
  4. Brown, BM, Cowling, A 1998Clustering and abundance estimation for Neyman-Scott models and line transect surveysBiometrika85427438CrossRefGoogle Scholar
  5. Buckland, ST, Anderson, DR, Burnham, KP, Laake, JL, Borchers, DL, Thomas, L 2001Introduction to distance sampling; estimating abundance of biological populationsOxford University PressOxfordGoogle Scholar
  6. Buckland, STAnderson, DRBurnham, KPLaake, JLBorchers, DLThomas, L eds. 2004Advanced distance samplingOxford University PressOxfordGoogle Scholar
  7. Cowling, A 1998Spatial methods for line transect surveysBiometrics54828839Google Scholar
  8. Cox, DR, Isham, V 1980Point processesChapman and HallLondonGoogle Scholar
  9. Daley, DJ, Vere-Jones, D 1988An introduction to the theory of point processesSpringer-VerlagNew YorkGoogle Scholar
  10. 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 123–138Google Scholar
  11. Griewank, A 2000Evaluating derivatives: principles and techniques of algorithmic differentiationSIAMPhiladelphiaGoogle Scholar
  12. Hagen, G, Schweder, T 1994Point clustering of minke whales in the northeastern AtlanticBlix, ASWalloe, LUlltang,  eds. Whales, seals, fish and man. developments in marine biologyElsevierAmsterdam2734vol. 4Google Scholar
  13. Hedley, S, Buckland, S 2004Spatial models for line transect samplingJ Agric Biol Environ Stat9181199CrossRefGoogle Scholar
  14. Heffes, H, Lucantoni, D 1986A Markov modulated characterization of packetized voice and data traffic related statistical performanceIEEE J Sel areas Commun4856868CrossRefGoogle Scholar
  15. Hogmander, H 1991A random field approach to transect counts of wildlife populationsBiometrical J3310131023Google Scholar
  16. Piatt, JF, Methven, DA 1992Threshold foraging behavior of baleen whalesMar Ecol Prog Ser84205210Google Scholar
  17. Ramesh, NI 1995Statistical-analysis on Markov-modulated Poisson processesEnvironmetrics6165179Google Scholar
  18. Ryden, T 1994Parameter estimation for Markov modulated Poisson processesCommuni Stat—Stoch Models10795829Google Scholar
  19. Ryden, T 1996An EM algorithm for estimation in Markov-modulated Poisson processesComput Stat Data Anal21431447CrossRefGoogle Scholar
  20. Schweder, T 1977Point process models for line transect experimentsBarra, J eds. Recent developments in statisticsNorth HollandAmsterdam221242Google Scholar
  21. Skaug, HJ, Oien, N, Bothun, G, Schweder, T 2004Current abundance of minke whales (Balaenoptera acutorostrata) in the Northeast Atlantic; variability in time and spaceCan J Fish Aquat Sci61870886CrossRefGoogle Scholar
  22. Taylor, H, Karlin, S 1984An introduction to stochastic modelingAcademic PressOrlandoGoogle Scholar
  23. Ver Hoef, J, Cressie, N 1997Using hidden Markov chains and empirical Bayes change-point estimation for transect dataEnviron Ecol Stat4247264CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of MathematicsJohannes Brunsgate 12BergenNorway

Personalised recommendations