This paper focuses on the use of models for increasing the precision of estimators in large-area forest surveys.It is motivated by the increasing availability of remotely sensed data,which facilitates the development ...This paper focuses on the use of models for increasing the precision of estimators in large-area forest surveys.It is motivated by the increasing availability of remotely sensed data,which facilitates the development of models predicting the variables of interest in forest surveys.We present,review and compare three different estimation frameworks where models play a core role:model-assisted,model-based,and hybrid estimation.The first two are well known,whereas the third has only recently been introduced in forest surveys.Hybrid inference mixes designbased and model-based inference,since it relies on a probability sample of auxiliary data and a model predicting the target variable from the auxiliary data.We review studies on large-area forest surveys based on model-assisted,modelbased,and hybrid estimation,and discuss advantages and disadvantages of the approaches.We conclude that no general recommendations can be made about whether model-assisted,model-based,or hybrid estimation should be preferred.The choice depends on the objective of the survey and the possibilities to acquire appropriate field and remotely sensed data.We also conclude that modelling approaches can only be successfully applied for estimating target variables such as growing stock volume or biomass,which are adequately related to commonly available remotely sensed data,and thus purely field based surveys remain important for several important forest parameters.展开更多
Background:Large area forest inventories often use regular grids(with a single random start)of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations.A design-unbiased est...Background:Large area forest inventories often use regular grids(with a single random start)of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations.A design-unbiased estimator of variance does not exist for this design.Oftentimes,a quasi-default estimator applicable to simple random sampling(SRS)is used,even if it carries with it the likely risk of overestimating the variance by a practically important margin.To better exploit the precision of systematic sampling we assess the performance of five estimators of variance,including the quasi default.In this study,simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends.We compared the results obtained with the SRS,Matern’s,successive difference replication,Ripley’s,and D’Orazio’s variance estimators.Results:The variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated,and in all study settings consistently closer to the target design variance than the estimator for SRS.The latter always produced the greatest overestimation.In populations with a near zero spatial autocorrelation,all estimators,performed equally,and delivered estimates close to the actual design variance.Conclusion:Without a linear trend,the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark;yet in terms of the least average absolute deviation,Matern’s estimator held a narrow lead.With a strong or moderate linear trend,Matern’s estimator is choice.In large populations,and a low sampling intensity,the performance of the investigated estimators becomes more similar.展开更多
A Norton-Rice distribution(NRD)is a versatile,flexible distribution for k ordered distances from a random location to the k nearest objects.In a context of plotless density estimation(PDE)with n randomly chosen sample...A Norton-Rice distribution(NRD)is a versatile,flexible distribution for k ordered distances from a random location to the k nearest objects.In a context of plotless density estimation(PDE)with n randomly chosen sample locations,and distances measured to the k=6 nearest objects,the NRD provided a good fit to distance data from seven populations with a census of forest tree stem locations.More importantly,the three parameters of a NRD followed a simple trend with the order(1,…,6)of observed distances.The trend is quantified and exploited in a proposed new PDE through a joint maximum likelihood estimation of the NRD parameters expressed as a functions of distance order.In simulated probability sampling from the seven populations,the proposed PDE had the lowest overall bias with a good performance potential when compared to three alternative PDEs.However,absolute bias increased by 0.8 percentage points when sample size decreased from 20 to 10.In terms of root mean squared error(RMSE),the new proposed estimator was at par with an estimator published in Ecology when this study was wrapping up,but otherwise superior to the remaining two investigated PDEs.Coverage of nominal 95%confidence intervals averaged 0.94 for the new proposed estimators and 0.90,0.96,and 0.90 for the comparison PDEs.Despite tangible improvements in PDEs over the last decades,a globally least biased PDE remains elusive.展开更多
We contrast a new continuous approach(CA)for estimating plot-level above-ground biomass(AGB)in forest inventories with the current approach of estimating AGB exclusively from the tree-level AGB predicted for each tree...We contrast a new continuous approach(CA)for estimating plot-level above-ground biomass(AGB)in forest inventories with the current approach of estimating AGB exclusively from the tree-level AGB predicted for each tree in a plot,henceforth called DA(discrete approach).With the CA,the AGB in a forest is modelled as a continuous surface and the AGB estimate for a fixed-area plot is computed as the integral of the AGB surface taken over the plot area.Hence with the CA,the portion of the biomass of in-plot trees that extends across the plot perimeter is ignored while the biomass from trees outside of the plot reaching inside the plot is added.We use a sampling simulation with data from a fully mapped two hectare area to illustrate that important differences in plot-level AGB estimates can emerge.Ideally CA-based estimates of mean AGB should be less variable than those derived from the DA.If realized,this difference translates to a higher precision from field sampling,or a lower required sample size.In our case study with a target precision of 5%(i.e.relative standard error of the estimated mean AGB),the CA required a 27.1%lower sample size for small plots of 100 m2 and a 10.4%lower sample size for larger plots of 1700 m2.We examined sampling induced errors only and did not yet consider model errors.We discuss practical issues in implementing the CA in field inventories and the potential in applications that model biomass with remote sensing data.The CA is a variation on a plot design for above-ground forest biomass;as such it can be applied in combination with any forest inventory sampling design.展开更多
Coverage of nominal 95% confidence intervals of a proportion estimated from a sample obtained under a complex survey design, or a proportion estimated from a ratio of two random variables, can depart significantly fro...Coverage of nominal 95% confidence intervals of a proportion estimated from a sample obtained under a complex survey design, or a proportion estimated from a ratio of two random variables, can depart significantly from its target. Effective calibration methods exist for intervals for a proportion derived from a single binary study variable, but not for estimates of thematic classification accuracy. To promote a calibration of confidence intervals within the context of land-cover mapping, this study first illustrates a common problem of under and over-coverage with standard confidence intervals, and then proposes a simple and fast calibration that more often than not will improve coverage. The demonstration is with simulated sampling from a classified map with four classes, and a reference class known for every unit in a population of 160,000 units arranged in a square array. The simulations include four common probability sampling designs for accuracy assessment, and three sample sizes. Statistically significant over- and under-coverage was present in estimates of user’s (UA) and producer’s accuracy (PA) as well as in estimates of class area proportion. A calibration with Bayes intervals for UA and PA was most efficient with smaller sample sizes and two cluster sampling designs.展开更多
文摘This paper focuses on the use of models for increasing the precision of estimators in large-area forest surveys.It is motivated by the increasing availability of remotely sensed data,which facilitates the development of models predicting the variables of interest in forest surveys.We present,review and compare three different estimation frameworks where models play a core role:model-assisted,model-based,and hybrid estimation.The first two are well known,whereas the third has only recently been introduced in forest surveys.Hybrid inference mixes designbased and model-based inference,since it relies on a probability sample of auxiliary data and a model predicting the target variable from the auxiliary data.We review studies on large-area forest surveys based on model-assisted,modelbased,and hybrid estimation,and discuss advantages and disadvantages of the approaches.We conclude that no general recommendations can be made about whether model-assisted,model-based,or hybrid estimation should be preferred.The choice depends on the objective of the survey and the possibilities to acquire appropriate field and remotely sensed data.We also conclude that modelling approaches can only be successfully applied for estimating target variables such as growing stock volume or biomass,which are adequately related to commonly available remotely sensed data,and thus purely field based surveys remain important for several important forest parameters.
文摘Background:Large area forest inventories often use regular grids(with a single random start)of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations.A design-unbiased estimator of variance does not exist for this design.Oftentimes,a quasi-default estimator applicable to simple random sampling(SRS)is used,even if it carries with it the likely risk of overestimating the variance by a practically important margin.To better exploit the precision of systematic sampling we assess the performance of five estimators of variance,including the quasi default.In this study,simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends.We compared the results obtained with the SRS,Matern’s,successive difference replication,Ripley’s,and D’Orazio’s variance estimators.Results:The variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated,and in all study settings consistently closer to the target design variance than the estimator for SRS.The latter always produced the greatest overestimation.In populations with a near zero spatial autocorrelation,all estimators,performed equally,and delivered estimates close to the actual design variance.Conclusion:Without a linear trend,the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark;yet in terms of the least average absolute deviation,Matern’s estimator held a narrow lead.With a strong or moderate linear trend,Matern’s estimator is choice.In large populations,and a low sampling intensity,the performance of the investigated estimators becomes more similar.
基金The work was supported by the Canadian Forest Service.
文摘A Norton-Rice distribution(NRD)is a versatile,flexible distribution for k ordered distances from a random location to the k nearest objects.In a context of plotless density estimation(PDE)with n randomly chosen sample locations,and distances measured to the k=6 nearest objects,the NRD provided a good fit to distance data from seven populations with a census of forest tree stem locations.More importantly,the three parameters of a NRD followed a simple trend with the order(1,…,6)of observed distances.The trend is quantified and exploited in a proposed new PDE through a joint maximum likelihood estimation of the NRD parameters expressed as a functions of distance order.In simulated probability sampling from the seven populations,the proposed PDE had the lowest overall bias with a good performance potential when compared to three alternative PDEs.However,absolute bias increased by 0.8 percentage points when sample size decreased from 20 to 10.In terms of root mean squared error(RMSE),the new proposed estimator was at par with an estimator published in Ecology when this study was wrapping up,but otherwise superior to the remaining two investigated PDEs.Coverage of nominal 95%confidence intervals averaged 0.94 for the new proposed estimators and 0.90,0.96,and 0.90 for the comparison PDEs.Despite tangible improvements in PDEs over the last decades,a globally least biased PDE remains elusive.
文摘We contrast a new continuous approach(CA)for estimating plot-level above-ground biomass(AGB)in forest inventories with the current approach of estimating AGB exclusively from the tree-level AGB predicted for each tree in a plot,henceforth called DA(discrete approach).With the CA,the AGB in a forest is modelled as a continuous surface and the AGB estimate for a fixed-area plot is computed as the integral of the AGB surface taken over the plot area.Hence with the CA,the portion of the biomass of in-plot trees that extends across the plot perimeter is ignored while the biomass from trees outside of the plot reaching inside the plot is added.We use a sampling simulation with data from a fully mapped two hectare area to illustrate that important differences in plot-level AGB estimates can emerge.Ideally CA-based estimates of mean AGB should be less variable than those derived from the DA.If realized,this difference translates to a higher precision from field sampling,or a lower required sample size.In our case study with a target precision of 5%(i.e.relative standard error of the estimated mean AGB),the CA required a 27.1%lower sample size for small plots of 100 m2 and a 10.4%lower sample size for larger plots of 1700 m2.We examined sampling induced errors only and did not yet consider model errors.We discuss practical issues in implementing the CA in field inventories and the potential in applications that model biomass with remote sensing data.The CA is a variation on a plot design for above-ground forest biomass;as such it can be applied in combination with any forest inventory sampling design.
文摘Coverage of nominal 95% confidence intervals of a proportion estimated from a sample obtained under a complex survey design, or a proportion estimated from a ratio of two random variables, can depart significantly from its target. Effective calibration methods exist for intervals for a proportion derived from a single binary study variable, but not for estimates of thematic classification accuracy. To promote a calibration of confidence intervals within the context of land-cover mapping, this study first illustrates a common problem of under and over-coverage with standard confidence intervals, and then proposes a simple and fast calibration that more often than not will improve coverage. The demonstration is with simulated sampling from a classified map with four classes, and a reference class known for every unit in a population of 160,000 units arranged in a square array. The simulations include four common probability sampling designs for accuracy assessment, and three sample sizes. Statistically significant over- and under-coverage was present in estimates of user’s (UA) and producer’s accuracy (PA) as well as in estimates of class area proportion. A calibration with Bayes intervals for UA and PA was most efficient with smaller sample sizes and two cluster sampling designs.
