Estimating the variance in before-after studies

Problem

To simplify the computation of the variance in before-after studies, it is generally assumed that the observed crash data for each entity (or observation) are Poisson distributed. Given the characteristics of this distribution, the observed value (x_i) for each entity is implicitly made equal to its variance. However, the variance should be estimated using the conditional properties of this observed value (defined as a random variable), that is, f(x_i|μ_i), since the mean of the observed value is in fact unknown.

Method

Parametric and non-parametric bootstrap methods were investigated to evaluate the conditional assumption using simulated and observed data.

Results

The results of this study show that observed data should not be used as a substitute for the variance, even if the entities are assumed to be Poisson distributed. Consequently, the estimated variance for the parameters under study in traditional before-after studies is likely to be underestimated.

Conclusions

The proposed methods offer more accurate approaches for estimating the variance in before-after studies.     

Testing hypotheses on shape and distribution of ecological response curves

Niche theory with hypotheses on shape and distribution of ecological response curves is used in the studies of resource sharing of competing plant species. Predictions based on theory should be applicable when, e.g., effects of competing species on the ecological tolerances are assessed or species’ diversity along a resource gradient is evaluated. We studied the ecological response curves of competing plant species along a resource gradient in boreal forests. The study was based on nation-wide soil and vegetation data collected from 455 sample plots on boreal forests in Finland. Species response curves along a soil fertility gradient (in terms of C/N ratio) were estimated using generalized additive models. Distribution of species optima and the relationship of niche width and skewness to the location of the optimum were analyzed with new bootstrap tests. The developed tests can account for the effects of truncation observed in the response curves of several species and for the uneven distribution of observations on the gradient.The estimated response curves of the major field layer species of boreal forests were not evenly distributed along soil C/N gradient. The density of optima peaked with relatively high nitrogen availability. Species with optima at low nitrogen availability had relatively broad realized niches. Niche width was negatively correlated with the density of optima. Species optima were packed and niches were narrow at high resource levels. This result suggests that a greater number of more specialized species can occur and interspecific competition decreases niche widths at high resource levels. Species were packed in the gradient where the C/N ratio was lower than 25, i.e., in conditions where nitrification can take place. This indicates that the majority of the vascular plants of boreal forests are favoured by the availability of NO₃⁻. Those few species thriving at high C/N ratios have broader realized niches.     

融合LRT的Bootstrap区间估计同质点识别方法研究*

针对传统同质点探测方法检验效率低以及在地物区分度不明显地区探测结果包含过多异质点的问题,提出融合似然比检验(LRT)与Bootstrap区间估计的同质点探测方法,通过模拟和实验对该方法进行验证,并对鄂尔多斯某煤矿地表形变进行探测和验证。研究结果表明:相比于传统方法,融合似然比检验(LRT)与Bootstrap区间估计的同质点探测方法具有较高的拒绝率和稳定的拒绝率标准差,比较适合地物区分度不明显的野外矿区同质点探测;在实验矿区发现1处明显下沉,最大累计沉降为-128.9 mm,通过与实测水准比较,发现实测水准结果与基于本文方法的DS-InSAR结果基本一致,2者均方根误差和平均绝对误差分别为14.4,12.0 mm。研究结果可实现对矿区的非接触、大范围、长时间监测,为DS-InSAR中同质点选取提供新思路。     

Confidence limits on one-stage model parameters in benchmark risk assessment

In modern environmental risk analysis, inferences are often desired on those low dose levels at which a fixed benchmark risk is achieved. In this paper, we study the use of confidence limits on parameters from a simple one-stage model of risk historically popular in benchmark analysis with quantal data. Based on these confidence bounds, we present methods for deriving upper confidence limits on extra risk and lower bounds on the benchmark dose. The methods are seen to extend automatically to the case where simultaneous inferences are desired at multiple doses. Monte Carlo evaluations explore characteristics of the parameter estimates and the confidence limits under this setting.

Bootstrap methods for simultaneous benchmark analysis with quantal response data

A primary objective in quantitative risk assessment is the characterization of risk which is defined to be the likelihood of an adverse effect caused by an environmental toxin or chemcial agent. In modern risk-benchmark analysis, attention centers on the “benchmark dose” at which a fixed benchmark level of risk is achieved, with a lower confidence limits on this dose being of primary interest. In practice, a range of benchmark risks may be under study, so that the individual lower confidence limits on benchmark dose must be corrected for simultaneity in order to maintain a specified overall level of confidence. For the case of quantal data, simultaneous methods have been constructed that appeal to the large sample normality of parameter estimates. The suitability of these methods for use with small sample sizes will be considered. A new bootstrap technique is proposed as an alternative to the large sample methodology. This technique is evaluated via a simulation study and examples from environmental toxicology.

地震活动性的自助统计分析及其在河南省及邻区地震预报中的应用

引用自助统计分析 ,对华北地区 17次中强地震前地震活动震级分布的离散度自助统计方差σBM值与地震活动的关系进行了分析和研究 ,总结出了中强地震前地震活动离散度自助统计方差σBM值的异常特征。同时 ,把该方法应用到了河南及邻区中等地震预报研究中 ,制定了预报规则 ,进行了预测内符检验和预报评分。结果表明 ,该方法是一种有效的中短期地震预报方法 ,具有推广应用价值     

Using biological data from field studies with multiple reference sites as a basis for environmental management: the risks for false positives and false negatives

Field surveys of biological responses can provide valuable information about environmental status and anthropogenic stress. However, it is quite usual for biological variables to differ between sites or change between two periods of time also in the absence of an impact. This means that there is an obvious risk that natural variation will be interpreted as environmental impact, or that relevant effects will be missed due to insufficient statistical power. Furthermore, statistical methods tend to focus on the risks for Type-I error, i.e. false positives. For environmental management, the risk for false negatives is (at least) equally important. The aim of the present study was to investigate how the probabilities for false positives and negatives are affected by experimental set up (number of reference sites and samples per site), decision criteria (statistical method and α-level) and effect size. A model was constructed to simulate data from multiple reference sites, a negative control and a positive control. The negative control was taken from the same distribution as the reference sites and the positive control was just outside the normal range. Using the model, the probabilities to get false positives and false negatives were calculated when a conventional statistical test, based on a null hypothesis of no difference, was used along with alternative tests that were based on the normal range of natural variation. Here, it is tested if an investigated site is significantly inside (equivalence test) and significantly outside (interval test) the normal range. Furthermore, it was tested how the risks for false positives and false negatives are affected by changes in α-level and effect size. The results of the present study show that the strategy that best balances the risks between false positives and false negatives is to use the equivalence test. Besides tests with tabulated p-values, estimates generated using a bootstrap routine were included in the present study. The simulations showed that the probability for management errors was smaller for the bootstrap compared to the traditional test and the interval test.     

Resampling methods for evaluating classification accuracy of wildlife habitat models

Predictive models of wildlife-habitat relationships often have been developed without being tested The apparent classification accuracy of such models can be optimistically biased and misleading. Data resampling methods exist that yield a more realistic estimate of model classification accuracy These methods are simple and require no new sample data. We illustrate these methods (cross-validation, jackknife resampling, and bootstrap resampling) with computer simulation to demonstrate the increase in precision of the estimate. The bootstrap method is then applied to field data as a technique for model comparison We recommend that biologists use some resampling procedure to evaluate wildlife habitat models prior to field evaluation.     

A methodology for calculating sample size to assess localized corrosion of process components

This paper proposes a methodology to estimate the required sample size to assess, with a specified precision, the localized corrosion of process components. The proposed methodology uses the extreme value and bootstrap methods. The results of estimated sample size ensure that the predicted maximum localized corrosion with the extreme value method is within an acceptable margin of error at a specified confidence level. Using the results of the proposed methodology, an equation is introduced to calculate sample size as a function of the acceptable margin of error, the population size, the standard deviation of corrosion data and the required confidence level. The probability of exceedance of critical limit of localized corrosion is also estimated. The methodology is explained through a case study of localized corrosion in process piping.     

Including model uncertainty in estimating variances in multiple capture studies

We present bootstrap-based methods which incorporate model uncertainty in estimating variances in multiple capture studies. Each of our three methods has a specific set of properties, and we discuss when each method should be used. Our first method can be used in any multiple capture setting, but it gives an estimate of the variance conditional on the number of observed animals. Our other two methods yield estimates of the unconditional variance; they require good estimates of part or all of the specific probability model, respectively. Smoothed estimated cell probabilities are utilized by the latter method. We contrast the three methods on a real-life data set, and then conduct simulations for a simple setting. Finally, we detail the use of our methodology for specific settings and discuss adaptations for tag-return studies.