Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models

The analysis of many physical and engineering problems involves running complex computational models (simulation models, computer codes). With problems of this type, it is important to understand the relationships between the input variables (whose values are often imprecisely known) and the output. The goal of sensitivity analysis (SA) is to study this relationship and identify the most significant factors or variables affecting the results of the model. In this presentation, an improvement on existing methods for SA of complex computer models is described for use when the model is too computationally expensive for a standard Monte-Carlo analysis. In these situations, a meta-model or surrogate model can be used to estimate the necessary sensitivity index for each input. A sensitivity index is a measure of the variance in the response that is due to the uncertainty in an input. Most existing approaches to this problem either do not work well with a large number of input variables and/or they ignore the error involved in estimating a sensitivity index. Here, a new approach to sensitivity index estimation using meta-models and bootstrap confidence intervals is described that provides solutions to these drawbacks. Further, an efficient yet effective approach to incorporate this methodology into an actual SA is presented. Several simulated and real examples illustrate the utility of this approach. This framework can be extended to uncertainty analysis as well.     

Renewal type bootstrap for Markov chains

In this paper we treat a renewal type of bootstrap for atomic Markov chains under minimal moment conditions on renewal times, i.e.Er ²<∞. Three main results are: a) if a Markov chain satisfies the CLT for the mean then it also satisfies a bootstrap CLT; b) if a Markov chain satisfies a uniform CLT over classes of functions then, it also satisfies bootstrap uniform CLT with minimal condition on envelope functionF; c) we establish second order correctness for this procedure. All results are for “in probability” bootstrap and constitute the final word in this setting.     

Estimation of demographic toxicity through the double bootstrap

Toxicity to organisms is usually expressed in terms of an observable effect on individuals from which a summary endpoint (such as the NOEC or ECx) is derived for risk assessment and environmental quality standards. However, toxicity evaluated in terms of a demographic endpoint may be more relevant to such regulatory applications. In this paper the effect of toxicity on population growth rate r is explored in tandem with a 'double bootstrap' to incorporate uncertainty. Exemplifying the approach with a set of individualized life table response data obtained for Daphnia magna exposed to zinc sulphate solution, the influence of increasing concentrations is assessed. A demographic-based metric for r, the ErCx (effect on r concentration percentage), is defined to permit alternative population level estimation of a 'safe effect' concentration.     

基于Bootstrap方法的独立分量分析可靠性研究

语音信号盲分离受到随机采样的数据所影响,产生统计可靠性问题,从而影响分离的效果.Bootstrap方法是以原始数据为基础的抽样统计推断法,可方便的应用于实际的数据处理之中,分析ICA的统计可靠性,但传统Bootstrap方法本身的计算特性限制了自助样本的生成范围,从而使得自助概率分布产生了一定的偏离,使之无法渐近于真实情形.本文通过对Bootstrap样本生成范围的拓展,改进了独立分量分析在语音信号应用的可靠性算法,获得了更加精确的可靠性参数.     

长贮雷管同步性的可靠性评定

针对库存雷管同步性无法通过大量试验进行可靠性评定,只能用少量作用时间数据定性做出估计这一问题,提出用小子样统计的Bootstrap方法估计样本参数值,再利用Monte Carlo方法进行同步性仿真来评定库存雷管同步性的可靠性.通过实例证明,该方法能有效评定长贮雷管同步性的可靠性.     

基于Bootstrap区间估计的中药指纹图谱相似度阈值确定方法研究

利用指纹图谱相似度评价中药质量时,色谱指纹图谱样本的数量有限。小样本条件下指纹图谱相似度值的分布难以满足正态分布或近似正态分布,不适合直接利用传统的区间估计方法来确定相似度的阈值。本文利用Bootstrap方法扩增样本,建立了小样本条件下的指纹图谱相似度阈值确定方法,并通过3个具体实例说明指纹图谱相似度阈值确定的具体过程。首先通过Bootstrap方法扩增样本,然后利用单侧区间估计方法确定相似度下限,得到相似度的阈值。以上3个实例说明了用该方法建立中药指纹图谱相似度阈值的合理性和可行性。此方法适用于由不同相似度计算方法所得相似度值。本文从理论、技术和应用的角度阐述了确定中药指纹图谱相似度阈值的方法,该方法将对指纹图谱技术的推广应用产生积极作用。     

Estimation of Relative SD

The relative SD is a measure that is now in common use in the pharmaceutical industry, for example, in pharmaceutical development and analytical chemistry, pharmacology, and quality control. This article comments on the usual point estimate of the true value; presents seven interval estimation methods, easily implemented on a desktop computer; and compares their individual merits and drawbacks. Finally, the question of determining an adequate sample size is addressed, and a possible solution is indicated.     

A Proposal for Estimation of the Parameters of Multivariate Moving-average Models

A method is proposed for the preliminary estimation of the parameters of multivariate moving-average processes. Initially, m independent white-noise series are generated. Then the parameters are estimated through an iterative procedure. The algorithm is fast and simple since it does not require specialized software for time series but a least squares routine. The estimators are consistent and a simulation experiment shows good performance in finite samples. An applicati on to real data is also illustrated     

Confidence interval for the mean of non‐normal data

The problem of constructing a confidence interval for the mean of non‐normal data is considered. The Bootstrap method and the Box–Cox transformation method of constructing the confidence interval are compared with the normal theory method. Simulation studies are used to evaluate the performance of these different methods of constructing confidence intervals. The result is not surprising; the Bootstrap method is more effective and efficient than the Box–Cox transformation method and the normal theory method in this simulation study. A real example demonstrates the ability of these methods to construct a confidence interval for the mean of audit accounting data. Copyright © 2001 John Wiley & Sons, Ltd.     

A bootstrap method of distribution mixture proportion determination

A simulation-based methodology for distribution mixture proportion determination is presented. A Monte Carlo study using Gaussian population data and cosmic-ray-experiments data proved the reliability of the methods proposed.