Bayesian Analysis

Model-based inferences from adaptive cluster sampling

V. E. Rapley and A. H. Welsh

Full-text: Open access


Adaptive cluster sampling is useful for exploring populations of rare plant and animal species which cluster together because it allows sampling effort to be concentrated in areas where observed values are high. This allows more useful data to be collected with less effort than simpler sampling methods which ignore the population structure. In this paper, we take a model based approach in a Bayesian framework to make inference about the number of individuals in a sparse, clustered population. This approach allows us to use knowledge of the population to inform both the sampling design and inference, thereby making coherent use of the data in the analysis and resulting in improved population estimates. The methodology is compared to the design-based modified Horvitz-Thompson estimator through analysis of the examples presented in the defining paper of Thompson (1990)

Article information

Bayesian Anal., Volume 3, Number 4 (2008), 717-736.

First available in Project Euclid: 22 June 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Informative sampling MCMC spatial sampling zero-inflated count data


Rapley, V. E.; Welsh, A. H. Model-based inferences from adaptive cluster sampling. Bayesian Anal. 3 (2008), no. 4, 717--736. doi:10.1214/08-BA327.

Export citation


  • A.H. Welsh, C. D., R.B. Cunningham and Lindenmayer, D. (1996). "Modelling the abundance of rare species - statistical models for counts with extra zeros." Ecological Modelling, 88: 297–308.
  • Breckling, J., Chambers, R., Dorfman, A., Tang, S., and Welsh, A. (1994). "Maximum likelihood inference from sample survey data." International Statistical Reviews, 62: 349–363.
  • Brewer, K. (1963). "Ratio estimation and finite populations: Some results deducible from the assumption of an underlying stochastic process." Australian Journal of Statistics, 5: 93–105.
  • Brooks, S. (1996). "Quantitative convergence diagnostics for MCMC via CUSUMS." Technical Report, University of Bristol.
  • Brus, D. and de Gruijter, J. (1997). "Random sampling or geostatistical modelling? Choosing between design-based and model-based sampling strategies for soil (with discussion)." Geoderma, 80: 1–44.
  • G. Kaufman, Y. B. and Kruyt, D. (1975). "A probabilistic model of oil and gas discovery." In Estimating the Volume of Undiscovered Oil and Gas Resources, 109–117. Tulsa, Oklahoma: American Association of Petroleum Geologists.
  • Heilbron, D. (1994). "Zero-altered and other models for count data with added zeros." Biometrical Journal, 36: 531–547.
  • Mullahy, J. (1986). "Specification and testing of some modified count data models." Journal of Econometrics, 33: 341–365.
  • Nair, V. and Wang, P. (1989). "Maximum likelihood estimation under a successive sampling discovery model." Technometrics, 31: 423–436.
  • R. Valliant, A. D. and Royall, R. (2000). Finite Population Sampling and Inference: A Prediction Approach. New York: John Wiley & Sons.
  • Rapley, V. (2004). Model-Based Adaptive Cluster Sampling, PhD Thesis. Univerity of Southampton.
  • Royall, R. (1976). "Current advances in sampling theory:Implications for human observational studies." American Journal of Epidemiology, 104: 463–477.
  • Tanner, M. (1996). Tools for Statistical Inference. New York: Springer, 3 edition.
  • Thompson, S. (1990). "Adaptive cluster sampling." Journal of the American Statistical Association, 85: 1050–1059.
  • –- (1991a). "Adaptive cluster sampling: Designs with primary and secondary units." Biometrics, 47: 1103–1115.
  • –- (1991b). "Stratified adaptive cluster sampling." Biometrika, 78: 389–397.
  • –- (1992). Sampling. New York: John Wiley & Sons.
  • –- (2002). "On sampling and experiments." Environmetrics, 13: 429–436.
  • Thompson, S. and Seber, G. (1996). Adaptive Sampling. New York: John Wiley & Sons.
  • West, M. (1996). "Inference in successive sampling discovery models." Journal of Econometrics, 75: 217–238.
  • Yu, B. and Mykland, P. (1998). "Looking at Markov samplers through CUSUM path plots: a simple diagnostic idea." Statistics and Computing, 8: 275–286.