► Nearest neighbors techniques produce valid small area estimates and inferences. ► The Euclidean distance metric performs as well as optimized metrics. ► The bootstrap variance estimator is a valid ...alternative to a complex parametric estimator. ► Equal neighbor weighting produced predictions comparable to more complex schemes.
Nearest neighbors techniques have become extremely popular, particularly for use with forest inventory data. With these techniques, a population unit prediction is calculated as a linear combination of observations for a selected number of population units in a sample that are most similar, or nearest, in a space of ancillary variables to the population unit requiring the prediction. Nearest neighbors techniques are appealing for multiple reasons: they can be used with categorical response variables for which the objective is classification and with continuous response variables for which the objective is prediction; they can be used for both univariate and multivariate prediction; they are non-parametric in the sense that no assumptions regarding the distributions of response or predictor variables are necessary; they are synthetic in the sense that they can readily use information external to the geographic area for which an estimate is sought; they are useful for map construction, small area estimation, and inference; and they can be used with a wide variety of data sets. Recent advances and emerging issues in nearest neighbors techniques are reviewed for four topic areas: (1) distance metrics, (2) optimization, (3) diagnostic tools, and (4) inference. The focus of the study is estimation of mean forest stem volume per unit area for small areas using a combination of forest inventory observations and Landsat Thematic Mapper (TM) imagery. However, the concepts and techniques are generally applicable for all nearest neighbors problems.
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Information on land use and land cover (LULC) including forest cover is important for the development of strategies for land planning and management. Satellite remotely sensed data of varying ...resolutions have been an unmatched source of such information that can be used to produce estimates with a greater degree of confidence than traditional inventory estimates. However, use of these data has always been a challenge in tropical regions owing to the complexity of the biophysical environment, clouds, and haze, and atmospheric moisture content, all of which impede accurate LULC classification. We tested a parametric classifier (logistic regression) and three non-parametric machine learning classifiers (improved k-nearest neighbors, random forests, and support vector machine) for classification of multi-temporal Sentinel 2 satellite imagery into LULC categories in Dak Nong province, Vietnam. A total of 446 images, 235 from the year 2017 and 211 from the year 2018, were pre-processed to gain high quality images for mapping LULC in the 6516 km2 study area. The Sentinel 2 images were tested and classified separately for four temporal periods: (i) dry season, (ii) rainy season, (iii) the entirety of the year 2017, and (iv) the combination of dry and rainy seasons. Eleven different LULC classes were discriminated of which five were forest classes. For each combination of temporal image set and classifier, a confusion matrix was constructed using independent reference data and pixel classifications, and the area on the ground of each class was estimated. For overall temporal periods and classifiers, overall accuracy ranged from 63.9% to 80.3%, and the Kappa coefficient ranged from 0.611 to 0.813. Area estimates for individual classes ranged from 70 km2 (1% of the study area) to 2200 km2 (34% of the study area) with greater uncertainties for smaller classes.
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The scientific method has been characterized as having two distinct components,
Discovery and
Justification. Discovery emphasizes ideas and creativity, focuses on conceiving hypotheses and ...constructing models, and is generally regarded as lacking a formal logic. Justification begins with the hypotheses and models and ends with a valid scientific inference. Unlike Discovery, Justification has a formal logic whose rules must be rigorously followed to produce valid scientific inferences. In particular, when inferences are based on sample data, the rules of the logic of Justification require assessments of bias and precision. Thus, satellite image-based maps that lack such assessments for parameters of populations depicted by the maps may be of little utility for scientific inference; essentially, they may be just pretty pictures. Probability- and model-based approaches are explained, illustrated, and compared for producing inferences for population parameters using a map depicting three land cover classes: non-forest, coniferous forest, and deciduous forest. The maps were constructed using forest inventory data and Landsat imagery. Although a multinomial logistic regression model was used to classify the imagery, the methods for assessing bias and precision can be used with any classification method. For probability-based approaches, the difference estimator was used, and for model-based inference, a bootstrap approach was used.
► Inferences are constructed for parameters of populations depicted by maps. ► Map classes include non-forest, coniferous forest, and deciduous forest. ► Approaches use Landsat and forest inventory data with a logistic regression model. ► Probability-based inference uses simple random sampling and model-assisted estimators. ► Model-based inference uses bootstrap to estimate variances. ► Inferential techniques can be used with any classification technique.
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Forest inventory estimates of tree volume for large areas are typically calculated by adding model predictions of volumes for individual trees. However, the uncertainty in the model predictions is ...generally ignored with the result that the precision of the large area volume estimates is overestimated. The primary study objective was to estimate the effects of model residual variability and model parameter uncertainty on large area volume estimates and their uncertainties for a study area in northeastern Minnesota, USA. Monte Carlo simulation approaches were used because of the complexities associated with multiple sources of uncertainty and the nonlinear nature of the models. Two conclusions were important. First, for this study, the effects of uncertainty in model predictions on the large area volume estimates and their uncertainties were small when the models were calibrated using an average of 100 or more observations per species and when the average proportion of variance explained by the models was at least 0.95. Second, large area estimates and their uncertainties based on coniferous/deciduous and nonspecific models deviated very little from large area estimates based on species-specific models. PUBLICATION ABSTRACT
Information on Earth's land surface and change over time has never been easier to obtain, but making informed decisions to manage land well necessitates that this information is accurate and precise. ...In recent years, due largely to the inevitability of classification errors in remote sensing-based maps and the marked effects of these errors on subsequent area estimates, sample-based area estimates of land cover and land change have increased in importance and use. Area estimation of land cover and change by sampling is often made more efficient by a priori knowledge of the study area to be analyzed (e.g., stratification). Satellite data, obtained free of cost for virtually all of Earth's land surface, provide an excellent source for constructing landscape stratifications in the form of maps. Errors of omission, defined as sample units observed as land change but mapped as a stable class, may introduce considerable uncertainty in parameter estimates obtained from the sample data (e.g., area estimates of land change). The effects of omission errors are exacerbated in situations where the area of intact forest is large relative to the area of forest change, a common situation in countries that seek results-based payments for reductions in deforestation and associated carbon emissions. The presence of omission errors in such situations can preclude the acquisition of statistically valid evidence of a reduction in deforestation, and thus prevent payments. International donors and countries concerned with mitigating the effects of climate change are looking for guidance on how to reduce the effects of omission errors on area estimates of land change. This article presents the underlying reasons for the effects of omission errors on area estimates, case studies highlighting real-world examples of these effects, and proposes potential solutions. Practicable approaches to efficiently splitting large stable strata are presented that may reduce the effects of omission errors and immediately improve the quality of estimates. However, more research is needed before further recommendations can be provided on how to contain, mitigate and potentially eliminate the effects of omissions errors.
•Literature recommendations related to sampling-based estimation are augmented.•Omissions of land change in maps can introduce large uncertainty in area estimates.•If stratifying by map class, omissions of change tend to carry large area weight.•Substrata in forest strata unlikely to contain error mitigate effects of omissions.•Constructing efficient stratifications mitigate effects of omissions.
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Estimates of forest area are among the most common and useful information provided by national forest inventories. The estimates are used for local and national purposes and for reporting to ...international agreements such as the Montréal Process, the Ministerial Conference on the Protection of Forests in Europe, and the Kyoto Protocol. The estimates are usually based on sample plot data and are calculated using probability-based estimators. These estimators are familiar, generally unbiased, and entail only limited computational complexity, but they do not produce the maps that users are increasingly requesting, and they generally do not produce sufficiently precise estimates for small areas. Model-based estimators overcome these disadvantages, but they may be biased and estimation of variances may be computationally intensive. The study objective was to compare probability- and model-based estimators of mean proportion forest using maps based on a logistic regression model, forest inventory data, and Landsat imagery. For model-based estimators, methods for evaluating bias and reducing the computational intensity were also investigated. Four conclusions were drawn: the logistic regression model exhibited no serious lack of fit to the data; all the estimators produced comparable estimates for mean proportion forest, except for small areas; probability-based inferences enhanced using maps produced increased precision; and the computational intensity associated with estimating variances for model-based estimators can be greatly reduced with no detrimental effects.
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Due to the availability of good and reasonably priced auxiliary data, the use of model-based regression-synthetic estimators for small area estimation is popular in operational settings. Examples are ...forest management inventories, where a linking model is used in combination with airborne laser scanning data to estimate stand-level forest parameters where no or too few observations are collected within the stand. This paper focuses on different approaches to estimating the variances of those estimates. We compared a variance estimator which is based on the estimation of superpopulation parameters with variance estimators which are based on predictions of finite population values. One of the latter variance estimators considered the spatial autocorrelation of the residuals whereas the other one did not. The estimators were applied using timber volume on stand level as the variable of interest and photogrammetric image matching data as auxiliary information. Norwegian National Forest Inventory (NFI) data were used for model calibration and independent data clustered within stands were used for validation. The empirical coverage proportion (ECP) of confidence intervals (CIs) of the variance estimators which are based on predictions of finite population values was considerably higher than the ECP of the CI of the variance estimator which is based on the estimation of superpopulation parameters. The ECP further increased when considering the spatial autocorrelation of the residuals. The study also explores the link between confidence intervals that are based on variance estimates as well as the well-known confidence and prediction intervals of regression models.
•Uncertainty of timber volume estimates for stands using remote sensing is analyzed.•Some variance estimators for small area estimation have low coverage probabilities.•Variance estimators with improved coverage probabilities are described.•The link between confidence intervals (CI) for estimators and models is explored.•CI of the model is a simple-to-calculate indicator of uncertainty for large areas.
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Despite the popularity of random forests (RF) as a prediction algorithm, methods for constructing confidence intervals for population means using this technique are still only sparsely reported. For ...two regional study areas (Spain and Norway) RF was used to predict forest volume or aboveground biomass using remotely sensed auxiliary data obtained from multiple sensors. Additionally, the changes per unit area of these forest attributes were estimated using indirect and direct methods. Multiple inferential frameworks have attracted increased recent attention for estimating the variances required for confidence intervals. For this study, three different statistical frameworks, design-based expansion, model-assisted and model-based estimators, were used for estimating population parameters and their variances. Pairs and wild bootstrapping approaches at different levels were compared for estimating the variances of the model-based estimates of the population means, as well as for mapping the uncertainty of the change predictions. The RF models accurately represented the relationship between the response and remotely sensed predictor variables, resulting in increased precision for estimates of the population means relative to design-based expansion estimates. Standard errors based on pairs bootstrapping within or internal to RF were considerably larger than standard errors based on both pairs and wild external bootstrapping of the entire RF algorithm. Pairs and wild external bootstrapping produced similar standard errors, but wild bootstrapping better mimicked the original structure of the sample data and better preserved the ranges of the predictor variables.
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National forest inventory programs are tasked to produce timely and accurate estimates for a wide range of forest resource variables for a variety of users and applications. Time, cost, and precision ...constraints cause these programs to seek technological innovations that contribute to measurement and estimation efficiencies and that facilitate the production and distribution of an increasing array of inventory data, estimates, and derived products. Many of the recent innovations have involved remotely sensed data and related statistical estimation techniques. Current applications of remote sensing in support of national forest inventories are reviewed for three areas: (1) observation or measurement, meaning using remotely sensed data in lieu of field observations or measurements; (2) estimation, meaning calculation of traditional inventory areal estimates such as forest area or volume per unit area; and (3) mapping. Future applications focus on two areas: augmenting field measurements with remotely sensed data obtained from lidar sensors and Internet accessible map-based estimation.
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We report on the operational use of remotely sensed data by national forest inventory (NFI) programmes in 45 countries representing approximately 65% of the world's forest area. The analysis is based ...on responses to a questionnaire prepared under the auspices of COST Action FP1001 “Improving Data and Information on the Potential Supply of Wood Resources: A European Approach from Multisource National Forest Inventories (USEWOOD)”. Responses were received from NFI remote sensing experts from both European and non-European countries. Three major conclusions were drawn from the study: (1) remote sensing now plays an essential role in many NFI programmes and provides data that can be used to enhance estimates for the most meaningful and commonly reported forest resource parameters; (2) a wide spectrum of remote sensing methods are currently used by NFI teams; and (3) although substantial effort and attention has been focused on the use of aerial photography and spaceborne sensor data for mapping and enhancing estimation, integration of uncertainly estimation requires additional attention.
The operational use of remotely sensed data by NFI programmes is illustrated for three case studies: a case study for Switzerland focuses on digital aerial photography, a case study for Finland focuses on spaceborne sensor data for small area estimation, and a case study for the USA focuses on spaceborne sensor data for increasing the precision of large area estimates. Although use of remotely sensed data by NFI programmes may remain region-specific and some approaches are not readily transferable, generally applicable good practice guidelines were formulated on the basis of the questionnaire responses and the case studies. These guidelines are intended to promote better use of limited financial resources and to increase the accuracy and precision of NFI estimates.
•National forest inventory (NFI) use of remote sensing was assessed using a questionnaire.•Responses were received from countries representing 65% of the world's forest area.•Three case studies highlight state-of-the-art use of remotely sensed data.•Guidelines for NFI use of remotely sensed data are provided
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