Triangulation based inclusion probabilities: a design-unbiased sampling approach
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A probabilistic sampling approach for design-unbiased estimation of area-related quantitative characteristics of spatially dispersed population units is proposed. The developed field protocol includes a fixed number of 3 units per sampling location and is based on partial triangulations over their natural neighbors to derive the individual inclusion probabilities. The performance of the proposed design is tested in comparison to fixed area sample plots in a simulation with two forest stands. Evaluation is based on a general approach for areal sampling in which all characteristics of the resulting population of possible samples is derived analytically by means of a complete tessellation of the areal sampling frame. The example simulation shows promising results. Expected errors under this design are comparable to sample plots including a much greater number of trees per plot.
KeywordsDesign based inference Inclusion probability Delaunay Triangulation Plot design Continuous population
This research was supported by the German Research Foundation DFG (KL 894/ 13-1). We thank Sebastian Schnell for helpful methodological and technical discussions. Further we thank two anonymous reviewers. Their extensive contributions to formulate the idea was substantial. We appreciated constructive comments, help and valuable suggestions to improve the manuscript.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
- Barabesi L, Franceschi S (2010) Sampling properties of spatial total estimators under tessellation stratified designs. Environmetrics. doi: 10.1002/env.1046
- Cochran WG (1977) Sampling Techniques. Whiley, New YorkGoogle Scholar
- Condit R (1998) Tropical Forest Census Plots. Springer and R. G. Landes Company, Berlin, Germany, and Georgetown, TexasGoogle Scholar
- Errico D (1981) Some methods of sampling triangle based probability polygons for forestry applications. Master’s thesis, Department of forestry, University of British ColumbiaGoogle Scholar
- Fraser A (1977) Triangle-based probability polygons for forest sampling. For Sci 23: 111–121Google Scholar
- Gregoire TG, Valentine HT (2008) Sampling strategies for natural resources and the environment. Applied environmental statistics. Chapman Hall/CRC, LondonGoogle Scholar
- Kronenfeld BJ (2009) A plotless density estimator based on the asymptotic limit of ordered distance estimation values. For Sci 55(4): 283–292Google Scholar
- Lessard VC, Drummer TD, Reed DD (2002) Precision of density estimates from fixed-radius plots compared to n-tree distance sampling. For Sci 48(1): 1–6Google Scholar
- Magnussen S, Picard N, Kleinn C (2008b) A Gamma-Poisson distribution of point to k nearest event distance. For Sci 54(4): 429–441Google Scholar
- Mandallaz D (1991) A unified approach to sampling theory for forest inventory based on infinite population models. Phd thesis, ETH ZürichGoogle Scholar
- Okabe A, Boots B, Sugihara K, Chiu SN (1999) Spatial tesselations. concepts and applications of voronoi diagrams. Wiley Series in Probability and Statistics. Wiley, New yorkGoogle Scholar
- Picard N, Kouyate A, Dessard H (2005) Tree density estimations using a distance method in mali savanna. For Sci 51(1): 7–18Google Scholar
- Prodan M (1968) Punktstichprobe für die Forsteinrichtung. Forst und Holzwirt 23(11): 225–226Google Scholar
- Ripley BD (1977) Modelling spatial patterns. J Royal Stat Soc Ser B (Methodological) 39(2): 172–212Google Scholar
- Roesch FA, Green EJ, Scott CT (1993) An alternative view of forest sampling. Surv Methodol 19(2): 199–204Google Scholar
- Sibson R (1980) The dirichlet tessellation as an aid in data analysis. Scand J Stat 7(1): 14–20Google Scholar
- Staupendahl K (2008) The modified six-tree-sample—a suitable method for forest stand assessment. Allgemeine Forst und Jagdzeitung 179(2–3): 21–33Google Scholar