Apparent and real bias in numerical transfer functions in palaeolimnology

We present an evaluation of the procedure by which model prediction bias is examined in palaeolimnological transfer function inference models. We argue that most of the prediction biases commonly reported in the literature are, in fact, fallacious, and are the artificial consequence of the inappropriate manner in which residuals are traditionally examined. We show that the extent of the specious model bias is entirely predictable from first principles and is essentially determined by the strength of the predictive model. We suggest that the analysis of residuals should always be examined as a function of the model's predictions and we discuss the implications of the old and new approaches.     

大地电磁响应函数估算中改进的多道相关函数法及误差的综合评价

近年来,有关大地电磁响应函数估算中消除偏离误差、减少随机误差、评价结果质量方面已有许多研究。Lienert等（1980）提出的多道相关函数法以下式为基础:     

Integer estimation in the presence of biases

 Carrier phase ambiguity resolution is the key to fast and high-precision GNSS (Global Navigation Satellite System) kinematic positioning. Critical in the application of ambiguity resolution is the quality of the computed integer ambiguities. Unsuccessful ambiguity resolution, when passed unnoticed, will too often lead to unacceptable errors in the positioning results. Very high success rates are therefore required for ambiguity resolution to be reliable. Biases which are unaccounted for will lower the success rate and thus increase the chance of unsuccessful ambiguity resolution. The performance of integer ambiguity estimation in the presence of such biases is studied. Particular attention is given to integer rounding, integer bootstrapping and integer least squares. Lower and upper bounds, as well as an exact and easy-to-compute formula for the bias-affected success rate, are presented. These results will enable the evaluation of the bias robustness of ambiguity resolution. Received: 28 September 2000 / Accepted: 29 March 2001     

Remotely sensed estimation of forest canopy density: A comparison of the performance of four methods

In recent years, a number of alternative methods have been proposed to predict forest canopy density from remotely sensed data. To date, however, it remains difficult to decide which method to use, since their relative performance has never been evaluated. In this study the performance of: (1) an artificial neural network, (2) a multiple linear regression, (3) the forest canopy density mapper and (4) a maximum likelihood classification method was compared for prediction of forest canopy density using a Landsat ETM+ image. Comparison of confusion matrices revealed that the regression model performed significantly worse than the three other methods. These results were based on a z-test for comparison of weighted kappa statistics, which is an appropriate statistic for analysis of ranked categories. About 89% of the variance of the observed canopy density was explained by the artificial neural networks, which outperformed the other three methods in this respect. Moreover, the artificial neural networks gave an unbiased prediction, while other methods systematically under or over predicted forest canopy density. The choice of biased method could have a high impact on canopy density inventories.     

A source of bias in rates of surface soil movement as estimated from marked particles

When estimated from measurements of introduced tracer particles, the rate of surface soil movement tends to be greater than the natural rate for equivalent particles on the same site. This consistent overestimation is greatest in the period following tracer introduction and leads to a measurement bias that may be as high as 300 per cent. The magnitude of the bias decreases with time, as the tracer is incorporated into the surface material, but remains detectable statistically for more than a year on some low-angle sites.     

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基于FY-3C微波辐射成像仪海表温度产品的偏差订正方法研究

提出一种针对FY-3C搭载的微波辐射成像仪（MWRI）海表温度产品的分段回归偏差订正方法,该方法通过引进气候态海表温度数据,建立与关联实测海表温度相匹配的回归模型,并通过对模型中关联变量的误差分析,选择最优样本进行分段回归,以实现对海表温度数据的重新估计。通过对MWRI海表温度数据的偏差订正试验表明,采用分段回归方法获得的订正结果无论在误差指标的空间分布还是时间序列上,都要明显优于采用传统概率密度函数偏差订正方法的结果。其中,采用概率密度函数方法订正后的海表温度产品误差标准差和均方根误差从订正前的0.9—1.0℃,减小到0.8℃左右,而采用分段回归方法获得相应的订正误差仅为0.6℃左右,订正效果有明显改善。      

Bias and uncertainty in regression-calibrated models of groundwater flow in heterogeneous media

Groundwater models need to account for detailed but generally unknown spatial variability (heterogeneity) of the hydrogeologic model inputs. To address this problem we replace the large, m-dimensional stochastic vector β that reflects both small and large scales of heterogeneity in the inputs by a lumped or smoothed m-dimensional approximation γθ_∗, where γ is an interpolation matrix and θ_∗ is a stochastic vector of parameters. Vector θ_∗ has small enough dimension to allow its estimation with the available data. The consequence of the replacement is that model function f(γθ_∗) written in terms of the approximate inputs is in error with respect to the same model function written in terms of β, f(β), which is assumed to be nearly exact. The difference f(β) − f(γθ_∗), termed model error, is spatially correlated, generates prediction biases, and causes standard confidence and prediction intervals to be too small. Model error is accounted for in the weighted nonlinear regression methodology developed to estimate θ_∗ and assess model uncertainties by incorporating the second-moment matrix of the model errors into the weight matrix. Techniques developed by statisticians to analyze classical nonlinear regression methods are extended to analyze the revised method. The analysis develops analytical expressions for bias terms reflecting the interaction of model nonlinearity and model error, for correction factors needed to adjust the sizes of confidence and prediction intervals for this interaction, and for correction factors needed to adjust the sizes of confidence and prediction intervals for possible use of a diagonal weight matrix in place of the correct one. If terms expressing the degree of intrinsic nonlinearity for f(β) and f(γθ_∗) are small, then most of the biases are small and the correction factors are reduced in magnitude. Biases, correction factors, and confidence and prediction intervals were obtained for a test problem for which model error is large to test robustness of the methodology. Numerical results conform with the theoretical analysis.     

GPS接收机仪器偏差的长期变化特性分析

基于欧洲定轨中心2001-2009年发布的部分IGS测站接收机仪器偏差估值,分析了不同类型接收机DCB的长期变化特性.结果表明:各类接收机DCB的长期时变特征均具备一定的周期性,其中以月和年周期最为明显;接收机DCB的长期变化中还存在一定的波动,部分接收机DCB的稳定性随时间积累逐渐变差,甚至存在偏移.