Anton Grafström

Spatially Balanced Sampling through the Pivotal Method

A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also select spatially balanced samples in a space spanned by several auxiliary variables. Analysis and examples indicate that the suggested method achieves a high degree of spatial balance and is therefore efficient for populations with trends.

Hierarchical model-based inference for forest inventory utilizing three sources of information

Abstract∙ Key messageThe study presents novel model-based estimators for growing stock volume and its uncertainty estimation, combining a sparse sample of field plots, a sample of laser data, and wall-to-wall Landsat data. On the basis of our detailed simulation, we show that when the uncertainty of estimating mean growing stock volume on the basis of an intermediate ALS model is not accounted for, the estimated variance of the estimator can be biased by as much as a factor of three or more, depending on the sample size at the various stages of the design.∙ ContextThis study concerns model-based inference for estimating growing stock volume in large-area forest inventories, combining wall-to-wall Landsat data, a sample of laser data, and a sparse subsample of field data.∙ AimsWe develop and evaluate novel estimators and variance estimators for the population mean volume, taking into account the uncertainty in two model steps.∙ Methods Estimators and variance estimators were derived for two main methodological approaches and evaluated through Monte Carlo simulation. The first approach is known as two-stage least squares regression, where Landsat data were used to predict laser predictor variables, thus emulating the use of wall-to-wall laser data. In the second approach laser data were used to predict field-recorded volumes, which were subsequently used as response variables in modeling the relationship between Landsat and field data.Results∙ The estimators and variance estimators are shown to be at least approximately unbiased. Under certain assumptions the two methods provide identical results with regard to estimators and similar results with regard to estimated variances.∙ Conclusion We show that ignoring the uncertainty due to one of the models leads to substantial underestimation of the variance, when two models are involved in the estimation procedure.

Forecasting risk of tick-borne encephalitis (TBE): Using data from wildlife and climate to predict next year's number of human victims

Abstract Background: Over the past quarter century, the incidence of tick-borne encephalitis (TBE) has increased in most European nations. However, the number of humans stricken by the disease varies from year to year. A method for predicting major increases and decreases is needed. Methods: We assembled a 25-y database (1984–2008) of the number of human TBE victims and wildlife and climate data for the Stockholm region of Sweden, and used it to create easy-to-use mathematical models that predict increases and decreases in the number of humans stricken by TBE. Results: Our best model, which uses December precipitation and mink (Neovison vison, formerly Mustela vison) bagging figures, successfully predicted every major increase or decrease in TBE during the past quarter century, with a minimum of false alarms. However, this model was not efficient in predicting small increases and decreases. Conclusions: Predictions from our models can be used to determine when preventive and adaptive programmes should be implemented. For example, in years when the frequency of TBE in humans is predicted to be high, vector control could be intensified where infested ticks have a higher probability of encountering humans, such as at playgrounds, bathing lakes, barbecue areas and camping facilities. Because our models use only wildlife and climate data, they can be used even when the human population is vaccinated. Another advantage is that because our models employ data from previously-established databases, no additional funding for surveillance is required.

Size constrained unequal probability sampling with a non-integer sum of inclusion probabilities

More than 50 methods have been developed to draw unequal probability samples with fixed sample size. All these methods require the sum of the inclusion probabilities to be an integer number. There are cases, however, where the sum of desired inclusion probabilities is not an integer. Then, classical algorithms for drawing samples cannot be directly applied. We present two methods to overcome the problem of sample selection with unequal inclusion probabilities when their sum is not an integer and the sample size cannot be fixed. The first one consists in splitting the inclusion probability vector. The second method is based on extending the population with a phantom unit. For both methods the sample size is almost fixed, and equal to the integer part of the sum of the inclusion probabilities or this integer plus one.

Improved Prediction of Forest Variables Using Data Assimilation of Interferometric Synthetic Aperture Radar Data

ABSTRACT The statistical framework of data assimilation provides methods for utilizing new data for obtaining up-to-date forest data: existing forest data are forecasted and combined with each new remote sensing data set. This new paradigm for updating forest database, well known from other fields of study, will provide a framework for utilizing all available remote sensing data in proportion to their quality to improve prediction. It also solves the problem that not all remote sensing data sets provide information for the entire area of interest, since areas with no remote sensing data can be forecasted until new remote sensing data become available. In this study, extended Kalman filtering was used for assimilating data from 19 TanDEM-X InSAR images on 137 sample plots, each of 10-meter radius at a test site in southern Sweden over a period of 4 years. At almost all time points data assimilation resulted in predictions closer to the reference value than predictions based on data from that single time point. For the study variables Loreys mean height, basal area, and stem volume, the median reduction in root mean square error was 0.4 m, 0.9 m2/ha, and 15.3 m3/ha (2, 3, and 6 percentage points), respectively.

Logistic regression for clustered data from environmental monitoring programs

Large-scale surveys, such as national forest inventories and vegetation monitoring programs, usually have complex sampling designs that include geographical stratification and units organized in cl ...

Informative plot sizes in presence‐absence sampling of forest floor vegetation

1. Plant communities are attracting increased interest in connection with forest and landscape inventories due to society’s interest in ecosystem services. However, the acquisition of accurate info ...

Coordination of Conditional Poisson Samples

Abstract Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP) sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.