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.

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.

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.

MEAN SQUARE ERRORS OF POINT DETERMINATIONS

1944 ◽  
Vol 7 (53) ◽  
pp. 279-294
Author(s):  
G. H. Menzies
Keyword(s):  
Mean Square ◽  
Mean Square Errors

scholarly journals A Study on the Generalized Approximation Modeling Method Based on Fitting Sensitivity for Prediction of Engine Performance

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Lin Lin ◽  
Fang Wang ◽  
Shisheng Zhong
Keyword(s):  
Engine Performance ◽  
Grey Model ◽  
Model Parameters ◽  
Bayesian Regularization ◽  
Safety Engineering ◽  
The Novel ◽  
Mean Square ◽  
Approximation Model ◽  
Mean Square Errors ◽  
Fitting Accuracy

Prediction technology for aeroengine performance is significantly important in operational maintenance and safety engineering. In the prediction of engine performance, to address overfitting and underfitting problems with the approximation modeling technique, we derived a generalized approximation model that could be used to adjust fitting precision. Approximation precision was combined with fitting sensitivity to allow the model to obtain excellent fitting accuracy and generalization performance. Taking the Grey model (GM) as an example, we discussed the modeling approach of the novel GM based on fitting sensitivity, analyzed the setting methods and optimization range of model parameters, and solved the model by using a genetic algorithm. By investigating the effect of every model parameter on the prediction precision in experiments, we summarized the change regularities of the root-mean-square errors (RMSEs) varying with the model parameters in novel GM. Also, by analyzing the novel ANN and ANN with Bayesian regularization, it is concluded that the generalized approximation model based on fitting sensitivity can achieve a reasonable fitting degree and generalization ability.

scholarly journals Dynamics and Edge Effect of an Atlantic Forest Fragment in Brazil

2016 ◽  
Vol 23 (3) ◽  
pp. 340-349 ◽  
Author(s):  
Poliana Gabriella Araújo Mendes ◽  
Maria Amanda Menezes Silva ◽  
Tassiane Novacosque Feitosa Guerra ◽  
Ana Carolina Borges Lins-e-Silva ◽  
Airton de Deus Cysneiros Cavalcanti ◽  
...  
Keyword(s):  
Species Richness ◽  
Atlantic Forest ◽  
Edge Effect ◽  
Woody Plants ◽  
Response Times ◽  
Forest Edge ◽  
Northeastern Brazil ◽  
Forest Fragment ◽  
Canopy Tree ◽  
Forest Interior

ABSTRACT The woody plants in an edge area formed approximately 35 years ago in an Atlantic Forest fragment in northeastern Brazil were examined, and three environments defined: edge, intermediate, and interior. Canopy tree densities and basal areas were found to be similar in all three environments, and also similar to previous published studies in the same region; species richness was greatest at the forest edge. The understory showed greater species richness in the forest interior, but greater diversity and equitability in the intermediate environment. Understory environments close to the forest edge demonstrated larger stem diameters than in the forest interior, although at lesser densities and with smaller total basal areas. Our results indicated the existence of distinct patterns in canopy and understory that most likely reflect differences in the response times of these two vegetation layers, with the understory being more sensitive to alterations in environmental structure.

scholarly journals Uncertainties of ground-based microwave radiometer retrievals in zenith and off-zenith observations under snow conditions

2017 ◽  
Vol 10 (1) ◽  
pp. 155-165 ◽  
Author(s):  
Wengang Zhang ◽  
Guirong Xu ◽  
Yuanyuan Liu ◽  
Guopao Yan ◽  
Dejun Li ◽  
...  
Keyword(s):  
Relative Humidity ◽  
Microwave Radiometer ◽  
Retrieval Algorithm ◽  
Mean Square ◽  
Atmospheric Conditions ◽  
Vapor Density ◽  
Heavy Snowfall ◽  
Snow Conditions ◽  
The Impact ◽  
Mean Square Errors

Abstract. This paper is to investigate the uncertainties of microwave radiometer (MWR) retrievals in snow conditions and also explore the discrepancies of MWR retrievals in zenith and off-zenith observations. The MWR retrievals were averaged in a ±15 min period centered at sounding times of 00:00 and 12:00 UTC and compared with radiosonde observations (RAOBs). In general, the MWR retrievals have a better correlation with RAOB profiles in off-zenith observations than in zenith observations, and the biases (MWR observations minus RAOBs) and root mean square errors (RMSEs) between MWR and RAOB are also clearly reduced in off-zenith observations. The biases of temperature, relative humidity, and vapor density decrease from 4.6 K, 9 %, and 1.43 g m−3 in zenith observations to −0.6 K, −2 %, and 0.10 g m−3 in off-zenith observations, respectively. The discrepancies between MWR retrievals and RAOB profiles by altitude present the same situation. Cases studies show that the impact of snow on accuracies of MWR retrievals is more serious in heavy snowfall than in light snowfall, but off-zenith observation can mitigate the impact of snowfall. The MWR measurements become less accurate in snowfall mainly due to the retrieval algorithm, which does not consider the effect of snow, and the accumulated snow on the top of the radome increases the signal noise of MWR measurements. As the snowfall drops away by gravity on the sides of the radome, the off-zenith observations are more representative of the atmospheric conditions for RAOBs.

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