Comparing computing formulas for estimating concentration ratios

The purpose of this paper is to provide guidance on the choice of computing formulas (estimators) for estimating average concentration ratios and other ratio-type measures of radionuclides and other environmental contaminant transfers between ecosystem components. Mathematical expressions for the expected value of three commonly used estimators (arithmetic mean of ratios, geometric mean of ratios, and the ratio of means) are obtained when the multivariate lognormal distribution is assumed. These expressions are used to explain why these estimators will not in general give the same estimate of the average concentration ratio. They illustrate that the magnitude of the discrepancies depends on the magnitude of measurement biases, and on the variance and correlations associated with spatial heterogeneity and measurement errors. This paper also reports on a computer simulation study that compares the accuracy of eight computing formulas for estimating a ratio relationship that is constant over time and/or space. Statistical models appropriate for both controlled spiking experiments and observational field studies for either normal or lognormal distributions are considered. Our results indicate that for either type of study the geometric mean is generally preferred if the lognormal distribution applies. However, the geometric mean has the disadvantage that its expected value depends on n, the number of measurements taken. Ricker's estimator, $\text{R}\text{?}{}_{\mathrm{rt}}$, appears to perform worse than the other estimators studied when the observations are lognormal. All eight estimators appear to be equally accurate for the controlled spiking study when data are normally distributed. For observational field studies when data are normally distributed the ratio of means or slight modifications thereof are preferred to other estimators investigated. Before one chooses a computing formula for estimating a concentration ratio, thought should be given to what target value needs to be estimated to satisfy study objectives, and to whether the normal or lognormal distribution is a more realistic model. The geometric mean performs well for lognormal distributions, but comparison of geometric means or of a geometric mean with environmental limits can be misleading if n is small. The arithmetic mean of ratios is a conservative choice in that it will always give a larger estimate than will the geometric mean. It may also be severely biased when data are lognormal and the variances of measurement errors are large. The ratio of the means is a reasonable choice if the distribution is normal. The median of the observed ratios, $\text{R}\text{?}{}_{\mathrm{<mtext>md</mtext>}}$, is useful estimate since it is easily obtained and has an easily understood interpretation as the point above which and below which 50% of the observed ratios lie. Also, it is appropriate no matter what the distribution of the observed ratios may be. Confidence limits on the median are also easily obtained. Finally, while this paper emphasizes applications in radionuclide research, our results should be applicable to a wide range of environmental contaminants since many contaminants have approximately lognormal distributions.     

一种改进的多学习教与学优化算法

针对传统教与学算法在解决复杂多峰函数优化问题时,具有局部最优且搜索开发能力较差的缺点,提出了一种改进的多学习教与学优化算法,新算法为学员的每一维加入不同的教学因子,设计了基于学员均值比较的教师选择策略和向教师及学员学习的多学习策略。基于多个单峰和多峰函数的仿真结果表明,新算法跟传统的、改进的教与学算法相比,在稳定性、寻优精度和收敛速度方面更具优势。     

Framework for participative reflection on the accomplishment of transdisciplinary research programs

In response to the increasingly complex social–ecological issues facing society, there is a growing trend to conduct environmental research in large collaborative programs. This approach is described as transdisciplinary research as it transcends formal disciplinary boundaries, explicitly acknowledges that many different perspectives are relevant to the resolution of complex problems, and actively involves the users of research. This poses challenges for the evaluation of “impact” as any evaluation process must take into consideration the different expectations, values, culture, language and reward structures of the main participating groups, the funders, researchers and end users. How can these participating groups learn about the progress of a transdisciplinary research program in a way that is purposeful and structured, continues through the life of the program, and includes explicit feedback mechanisms that facilitate adaptation during the course of the program? This paper presents a framework for co-reflecting on the accomplishment of transdisciplinary research programs. The framework incorporates the perspectives of funders, researchers and users, and recognizes that while they place different emphasis on measures of achievement such as efficiency, rigor and relevance, ultimate accomplishment in terms of translating knowledge into practice requires that the needs and expectations of all three groups are adequately addressed. What emerges from the framework is the importance of early investment in processes, behaviors and relationships that foster social learning and the co-production of the knowledge and understanding that are required to ensure relevance; while maintaining emphasis in the traditional areas of formally testing evidence and mentoring young researchers to ensure rigor and build confidence and capacity in transdisciplinary approaches.