Aspects of statistical bias due to the forest edge: horizontal point sampling

1981 ◽  
Vol 11 (2) ◽  
pp. 335-342 ◽  
Author(s):  
Gary W. Fowler ◽  
Loukas G. Arvanitis
Keyword(s):  
Spatial Distribution ◽  
Edge Effect ◽  
Unbiased Estimator ◽  
Basal Area ◽  
Forest Edge ◽  
Mean Square ◽  
Statistical Bias ◽  
Point Sampling ◽  
Mean Square Errors ◽  
Horizontal Point Sampling

A tree-concentric procedure is presented to eliminate edge effect statistical bias for horizontal point sampling. For known forest populations, the exact mean of the unbiased (adjusted for edge effect) and biased (unadjusted for edge effect) estimators of a forest characteristic can be determined along with the exact bias. Edge-effect bias is investigated for three forests that vary in area, four basal area factors (BAF), and three forest characteristics. Exact and estimated results based on 5000 random points were compared. Edge effect bias increases as the BAF decreases and varies with forest size, size and spatial distribution of trees, percentage of edge trees, and forest characteristic. The variance of the biased estimator was always smaller than the variance of the unbiased estimator. Using mean square errors, the biased estimator was found to be, in general, more accurate and the distortion of probability statements caused by the bias negligible for small to moderate sample sizes, especially for larger BAF's and certain forest characteristics.

Aspects of statistical bias due to the forest edge: fixed-area circular plots

1979 ◽  
Vol 9 (3) ◽  
pp. 383-389 ◽  
Author(s):  
Gary W. Fowler ◽  
Loukas G. Arvanitis
Keyword(s):  
Spatial Distribution ◽  
Edge Effect ◽  
Unbiased Estimator ◽  
Forest Edge ◽  
Mean Square ◽  
Statistical Bias ◽  
Fixed Area ◽  
Plot Area ◽  
Small Plot ◽  
Mean Square Errors

A procedure is presented to eliminate edge-effect statistical bias for fixed-area circular plots when sampling forest areas. For known forest populations, the exact mean of the unbiased (adjusted for edge effect) and biased (unadjusted for edge effect) estimates of a forest characteristic can be determined along with the exact bias. Edge-effect bias is investigated for three forests that vary in area, four plot sizes, and three forest characteristics. Exact and estimated results based on 5000 random points were compared. Edge-effect bias increases with plot area and varies with forest size, spatial distribution of trees, percentage of edge trees, and forest characteristic. The variance of the biased estimator was always smaller than the variance of the unbiased estimator. Using mean square errors, the biased estimator was found to be more accurate and the distortion of probability statements caused by the bias negligible for moderate sample sizes and small-plot areas.

Is BAF 10 a Good Choice for Point Sampling?

1984 ◽  
Vol 1 (2) ◽  
pp. 23-24 ◽  
Author(s):  
Harry V. Wiant ◽  
David O. Yandle ◽  
Richard Andreas
Keyword(s):  
Basal Area ◽  
Good Choice ◽  
Hardwood Forest ◽  
Mean Square ◽  
Point Sampling ◽  
Volume Estimates ◽  
Mean Square Errors

Abstract The use of basal-area-factor (BAF)-5 and BAF-10 when point sampling in an Appalachian hardwood forest caused serious underestimation of sawtimber volume BAF's of 20 and 40 gave appropriate volume estimates and smallest mean-square errors. We recommend that BAF's 20 to 40 be used for sawtimber cruises. North. J. Appl. For. 2:23-24, June 1984.

A note on the relationship between the quadratic mean stand diameter and harmonic mean basal area under size-biased distribution theory

2003 ◽  
Vol 33 (8) ◽  
pp. 1587-1590 ◽  
Author(s):  
J H Gove
Keyword(s):  
Size Distribution ◽  
Graphical Representation ◽  
Basal Area ◽  
Distribution Theory ◽  
Harmonic Mean ◽  
Quadratic Mean ◽  
Point Sampling ◽  
The Relationship ◽  
Horizontal Point Sampling ◽  
Biased Distribution

This note seeks to extend the utility of size-biased distribution theory as applied to forestry through two relationships regarding the quadratic mean stand diameter. First, the quadratic mean stand diameter's relationship to the harmonic mean basal area for horizontal point sampling, which has been known algebraically from early on, is proved under size-biased distribution theory. Second, a new result, which may prove most valuable in viewing the graphical representation of assumed distributions, is also derived. The results are also shown to apply to the basal area – size distribution, providing a unique duality between the two means.

scholarly journals Vertical Point Sampling with a Camera

2011 ◽  
Vol 28 (2) ◽  
pp. 61-65 ◽  
Author(s):  
Mark J. Ducey ◽  
John A. Kershaw
Keyword(s):  
Basal Area ◽  
Stand Density ◽  
Double Sampling ◽  
Point Sampling ◽  
Field Techniques ◽  
Potential Applications ◽  
Stand Density Index ◽  
Detectable Bias ◽  
Horizontal Point Sampling

Abstract Vertical point sampling has seen relatively little use in practical forestry, in part because existing field techniques are difficult. We show how vertical point sampling can be implemented quickly and easily using a camera. We give tables and equations for calculating the height-squared factor, which plays a role similar to that of the basal area factor in horizontal point sampling. Some suggestions for choosing a height-squared factor are discussed, along with potential applications for further exploration. We illustrate the technique using a case study in southern Maine. Direct estimates with no statistically detectable bias were obtained using height-squared factors greater than 3. The results also suggested that the technique could be used as a correlate in double sampling for variables such as cubic volume, stand density index, and biomass, and possibly board foot volume as well.

scholarly journals Economic Impacts of Projecting Horizontal Angles to the Wrong Height When Conducting Point Sampling

2011 ◽  
Vol 35 (1) ◽  
pp. 33-38
Author(s):  
Curtis L. VanderSchaaf ◽  
Lewis Jordan
Keyword(s):  
Economic Impacts ◽  
Basal Area ◽  
Point Sampling ◽  
Breast Height ◽  
Area Estimate ◽  
Nonsampling Error ◽  
Taper Equation ◽  
Individual Trees ◽  
Horizontal Point Sampling ◽  
Stand Conditions

Abstract Horizontal point sampling selects sample trees by projecting horizontal angles. In many inventories, angles are to be projected to dbh, or the diameter at 4.5 ft, but because of user error, angles are often projected to heights other than breast height. Thus, errors are made as to which trees should be sampled, probabilities of sampling individual trees are incorrect, and the basal area estimate does not truly correspond to dbh. The objective of this study was to determine the potential economic impacts of projecting angles at heights other than breast height when breast height is the desired height. Projections for two planting densities (400 and 1,000 seedlings per acre) and two ages (20 and 30) were used to establish virtual plantations, and sampling was conducted using 10 and 20 basal area factor prisms by projecting horizontal angles to four heights, 4.5, 5.0, 5.5, and 6.0 ft. A taper equation was used to estimate changes in diameter along the stem. For the stand conditions examined in this study, incorrectly projecting angles to heights other than breast height reduced timber appraisals by as much as $190/ac. Across many acres and stands, this type of nonsampling error can result in serious errors in valuing stumpage.

Bias and Mean Square Errors of Estimators as Criteria for Evaluating Competing Analysis Strategies in Quasi-Experiments

1981 ◽  
Vol 6 (1) ◽  
pp. 33-53
Author(s):  
Stephen F. Olejnik ◽  
Andrew C. Porter
Keyword(s):  
Nonlinear Model ◽  
Unbiased Estimator ◽  
Small Sample ◽  
Academic Growth ◽  
Growth Patterns ◽  
Analysis Of Covariance ◽  
Small Samples ◽  
Mean Square ◽  
Analysis Strategies ◽  
Mean Square Errors

The evaluation of competing analysis strategies based on estimator bias and the mean square errors of estimators is demonstrated using gains in standard scores and analysis of covariance adjusted for errors of measurement procedures for quasi-experiments conforming to the fan spread hypothesis. Some confusion in the appropriateness of these analysis procedures is resolved by considering the fan spread model defined in latent and manifest variables, large and small sample properties of the estimators, and explicitly stating the nature of individual academic growth patterns. For a linear model of individual academic growth both procedures provide an unbiased estimator with equal mean square errors when the samples are large. With small samples, analysis of covariance adjusted for errors of measurement provides an unbiased estimator, while the gain in standard scores estimator is biased and has a spuriously low mean square error. Under a nonlinear model and large samples only gains in standard scores provide an unbiased estimator. Neither procedure is appropriate for a nonlinear model with small samples. A data example is provided to demonstrate the study's findings. It is recommended that both criteria of bias and mean square errors of estimators be considered when evaluating recently developed analytic strategies for quasi-experiments.

scholarly journals Histamine Control in Raw and Processed Tuna: A Rapid Tool Based on NIR Spectroscopy

Foods ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 885
Author(s):  
Sergio Ghidini ◽  
Luca Maria Chiesa ◽  
Sara Panseri ◽  
Maria Olga Varrà ◽  
Adriana Ianieri ◽  
...  
Keyword(s):  
Root Mean Square ◽  
Near Infrared ◽  
Nir Spectroscopy ◽  
Partial Least Square ◽  
Least Square ◽  
Partial Least Square Regression ◽  
Coefficient Of Determination ◽  
Mean Square ◽  
Tuna Fish ◽  
Mean Square Errors

The present study was designed to investigate whether near infrared (NIR) spectroscopy with minimal sample processing could be a suitable technique to rapidly measure histamine levels in raw and processed tuna fish. Calibration models based on orthogonal partial least square regression (OPLSR) were built to predict histamine in the range 10–1000 mg kg−1 using the 1000–2500 nm NIR spectra of artificially-contaminated fish. The two models were then validated using a new set of naturally contaminated samples in which histamine content was determined by conventional high-performance liquid chromatography (HPLC) analysis. As for calibration results, coefficient of determination (r2) > 0.98, root mean square of estimation (RMSEE) ≤ 5 mg kg−1 and root mean square of cross-validation (RMSECV) ≤ 6 mg kg−1 were achieved. Both models were optimal also in the validation stage, showing r2 values > 0.97, root mean square errors of prediction (RMSEP) ≤ 10 mg kg−1 and relative range error (RER) ≥ 25, with better results showed by the model for processed fish. The promising results achieved suggest NIR spectroscopy as an implemental analytical solution in fish industries and markets to effectively determine histamine amounts.

scholarly journals Automatic modelling of human musculoskeletal ligaments – Framework overview and model quality evaluation

2021 ◽  
pp. 1-14
Author(s):  
Noura Hamze ◽  
Lukas Nocker ◽  
Nikolaus Rauch ◽  
Markus Walzthöni ◽  
Matthias Harders ◽  
...  
Keyword(s):  
Statistical Model ◽  
Soft Tissues ◽  
Automatic Generation ◽  
Cadaveric Study ◽  
Patient Specific ◽  
Mean Square ◽  
Shape Modelling ◽  
Morphological Studies ◽  
Insertion Sites ◽  
Mean Square Errors

BACKGROUND: Accurate segmentation of connective soft tissues in medical images is very challenging, hampering the generation of geometric models for bio-mechanical computations. Alternatively, one could predict ligament insertion sites and then approximate the shapes, based on anatomical knowledge and morphological studies. OBJECTIVE: In this work, we describe an integrated framework for automatic modelling of human musculoskeletal ligaments. METHOD: We combine statistical shape modelling with geometric algorithms to automatically identify insertion sites, based on which geometric surface/volume meshes are created. As clinical use case, the framework has been applied to generate models of the forearm interosseous membrane. Ligament insertion sites in the statistical model were defined according to anatomical predictions following a published approach. RESULTS: For evaluation we compared the generated sites, as well as the ligament shapes, to data obtained from a cadaveric study, involving five forearms with 15 ligaments. Our framework permitted the creation of models approximating ligaments’ shapes with good fidelity. However, we found that the statistical model trained with the state-of-the-art prediction of the insertion sites was not always reliable. Average mean square errors as well as Hausdorff distances of the meshes could increase by an order of magnitude, as compared to employing known insertion locations of the cadaveric study. Using those, an average mean square error of 0.59 mm and an average Hausdorff distance of less than 7 mm resulted, for all ligaments. CONCLUSIONS: The presented approach for automatic generation of ligament shapes from insertion points appears to be feasible but the detection of the insertion sites with a SSM is too inaccurate, thus making a patient-specific approach necessary.

scholarly journals Improving a real-time helicopter simulator model with linear input filters

2021 ◽  
Author(s):  
Pavle Šćepanović ◽  
Frederik A. Döring
Keyword(s):  
Feedback Control ◽  
Time Domain ◽  
Flight Test ◽  
Flight Mechanics ◽  
Mean Square ◽  
Qualification Test ◽  
Model Inversion ◽  
Helicopter Flight ◽  
The Time Domain ◽  
Mean Square Errors

AbstractFor a broad range of applications, flight mechanics simulator models have to accurately predict the aircraft dynamics. However, the development and improvement of such models is a difficult and time consuming process. This is especially true for helicopters. In this paper, two rapidly applicable and implementable methods to derive linear input filters that improve the simulator model are presented. The first method is based on model inversion, the second on feedback control. Both methods are evaluated in the time domain, compared to recorded helicopter flight test data, and assessed based on root mean square errors and the Qualification Test Guide bounds. The best results were achieved when using the first method.

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