Forest inventory: further results for optimal sampling schemes based on the anticipated variance

2001 ◽  
Vol 31 (10) ◽  
pp. 1845-1853 ◽  
Author(s):  
Daniel Mandallaz ◽  
Adrian Lanz
Keyword(s):  
Forest Inventory ◽  
Optimal Allocation ◽  
Optimality Criterion ◽  
Second Phase ◽  
Optimal Sampling ◽  
Two Stage ◽  
Two Phase ◽  
Sampling Density ◽  
Sampling Schemes ◽  
Inclusion Probabilities

This work presents optimal allocation rules for two-phase, two-stage sampling schemes in which the sampling density and the costs of the second phase can vary over domains. The optimality criterion is based on the anticipated variance. It also gives an improved version of discrete approximation for the resulting inclusion probabilities. An example illustrates the theory.

Forest inventory with optimal two-phase two-stage sampling schemes based on the anticipated variance

1999 ◽  
Vol 29 (11) ◽  
pp. 1691-1708 ◽  
Author(s):  
Daniel Mandallaz ◽  
Ronghua Ye
Keyword(s):  
Spatial Distribution ◽  
Forest Inventory ◽  
Poisson Model ◽  
Optimal Sampling ◽  
Two Stage ◽  
Two Phase ◽  
Sampling Schemes ◽  
One Stage ◽  
Sampling Procedures

This work presents optimal sampling schemes for forest inventory. The sampling procedures are optimal in the sense that they minimize the anticipated variance for given costs or conversely, the anticipated variance is the average of the design-based variance under a local Poisson model for the spatial distribution of the trees. The resulting optimal inclusion rules are either probability proportional to size, in one-stage procedures, or a combination of probability proportional to prediction and probability proportional to error, in two-stage procedures. Best feasible approximations of the exact optimal sampling schemes are also given.

scholarly journals Optimal sampling schemes based on the anticipated variance with lack of fit

2002 ◽  
Vol 32 (12) ◽  
pp. 2236-2243 ◽  
Author(s):  
D Mandallaz
Keyword(s):  
Estimation Procedure ◽  
Cluster Sampling ◽  
Second Phase ◽  
Optimal Sampling ◽  
Two Phase ◽  
Sampling Schemes ◽  
Lack Of Fit ◽  
Important Improvement ◽  
Phase Sampling ◽  
Simple Stochastic Model

This note presents an important improvement for optimal sampling schemes based on the anticipated variance. The anticipated variance is defined as the average of the design-based variance under a simple stochastic model in which the trees are assumed to be uniformly and independently distributed within a given number of so-called Poisson strata. We consider two-phase two-stage cluster sampling schemes in which costs and terrestrial second-phase sampling density can vary over domains. The estimation procedure is based on post-stratification with respect to so-called working strata that do not need to be identical with the Poisson strata, usually unknown, which induces a lack of fit. It is then possible to derive analytically the optimal sampling schemes. Data from the Swiss National Inventory illustrates the method.

Multi-phase sampling

2019 ◽  
pp. 200-218
Author(s):  
David G. Hankin ◽  
Michael S. Mohr ◽  
Ken B. Newman
Keyword(s):  
Optimal Allocation ◽  
Cost Effective ◽  
Auxiliary Variable ◽  
Sampling Effort ◽  
Second Phase ◽  
Two Phase ◽  
Phase Errors ◽  
The Mean ◽  
Phase Sample ◽  
Multi Phase

Attention is restricted to two-phase or double sampling. A large first-phase sample is used to generate a very good estimate of the mean or total of an auxiliary variable, x, which is relatively cheap to measure. Then, a second-phase sample is selected, usually from the first-phase sample, and both auxiliary and target variables are measured in selected second-phase population units. Two-phase ratio or regression estimators can be used effectively in this context. Errors of estimation reflect first-phase uncertainty in the mean or total of the auxiliary variable, and second-phase errors reflect the nature of the relation and correlation between auxiliary and target variables. Accuracy of the two-phase estimator of a proportion depends on sensitivity and specificity. Sensitivity is the probability that a unit possessing a trait (y = 1) will be correctly classified as such whenever the auxiliary variable, x, has value 1, whereas specificity is the probability that a unit not possessing a trait (y = 0) will be correctly classified as such whenever the auxiliary variable, x, has value 0. Optimal allocation results for estimation of means, totals, and proportions allow the most cost-effective allocation of total sampling effort to the first- and second-phases. In double sampling with stratification, a large first-phase sample estimates stratum weights, a second-phase sample estimates stratum means, and a stratified estimator gives an estimate of the overall population mean or total.

New regression estimators in forest inventories with two-phase sampling and partially exhaustive information: a design-based Monte Carlo approach with applications to small-area estimation

2013 ◽  
Vol 43 (11) ◽  
pp. 1023-1031 ◽  
Author(s):  
Daniel Mandallaz ◽  
Jochen Breschan ◽  
Andreas Hill
Keyword(s):  
Auxiliary Information ◽  
Cluster Sampling ◽  
Lidar Data ◽  
Second Phase ◽  
Regression Estimator ◽  
Two Phase ◽  
Sampling Schemes ◽  
Forest Inventories ◽  
Phase Sampling ◽  
Two Phase Sampling

We consider two-phase sampling schemes where one component of the auxiliary information is known in every point (“wall-to-wall”) and a second component is available only in the large sample of the first phase, whereas the second phase yields a subsample with the terrestrial inventory. This setup is of growing interest in forest inventory thanks to the recent advances in remote sensing, in particular, the availability of LiDAR data. We propose a new two-phase regression estimator for global and local estimation and derive its asymptotic design-based variance. The new estimator performs better than the classical regression estimator. Furthermore, it can be generalized to cluster sampling and two-stage tree sampling within plots. Simulations and a case study with LiDAR data illustrate the theory.

Die antizipierte Varianz: ein Werkzeug für die Optimierung von Waldinventuren | The anticipated variance: a tool for the optimization of forest inventory

2003 ◽  
Vol 154 (3-4) ◽  
pp. 117-121 ◽  
Author(s):  
Daniel Mandallaz
Keyword(s):  
Spatial Distribution ◽  
Forest Inventory ◽  
Random Sampling ◽  
Poisson Model ◽  
Simple Algebra ◽  
Simple Random Sampling ◽  
Two Stage ◽  
Two Phase ◽  
Forest Inventories ◽  
Mathematical Review

This paper gives a non-mathematical review of the concept of anticipated variance which allows to solve entirely the optimisation problem for two-phase two-stage forest inventories with cluster or simple random sampling, in the sense that the anticipated variance is minimised for given costs. The anticipated variance is the average of the design-based variance under a local Poisson-model for the spatial distribution of the trees. The resulting sampling rules have a clear intuitive background and require only simple algebra to be implemented. The required parameters can be estimated from any pre-existing two-phase inventory. An example based on the Swiss National Inventory illustrates the method.

A Comparison of Tem and Apfim to the Interpretation of Modulated Microstructures

1985 ◽  
Vol 43 ◽  
pp. 70-71
Author(s):  
M.G. Burke ◽  
M.K. Miller
Keyword(s):  
Low Temperature ◽  
Microstructural Characterization ◽  
Superlattice Reflection ◽  
High Volume ◽  
Atom Probe ◽  
Dark Field ◽  
Miscibility Gap ◽  
Second Phase ◽  
Two Phase ◽  
Probe Field

Interpretation of fine-scale microstructures containing high volume fractions of second phase is complex. In particular, microstructures developed through decomposition within low temperature miscibility gaps may be extremely fine. This paper compares the morphological interpretations of such complex microstructures by the high-resolution techniques of TEM and atom probe field-ion microscopy (APFIM).The Fe-25 at% Be alloy selected for this study was aged within the low temperature miscibility gap to form a <100> aligned two-phase microstructure. This triaxially modulated microstructure is composed of an Fe-rich ferrite phase and a B2-ordered Be-enriched phase. The microstructural characterization through conventional bright-field TEM is inadequate because of the many contributions to image contrast. The ordering reaction which accompanies spinodal decomposition in this alloy permits simplification of the image by the use of the centered dark field technique to image just one phase. A CDF image formed with a B2 superlattice reflection is shown in fig. 1. In this CDF micrograph, the the B2-ordered Be-enriched phase appears as bright regions in the darkly-imaging ferrite. By examining the specimen in a [001] orientation, the <100> nature of the modulations is evident.

THE DYNAMIC FRACTURE OF TWO PHASE ALLOYS WITH SECOND PHASE INCLUSIONS

1985 ◽  
Vol 46 (C5) ◽  
pp. C5-251-C5-255
Author(s):  
S. Pytel ◽  
L. Wojnar
Keyword(s):  
Dynamic Fracture ◽  
Second Phase ◽  
Two Phase
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