An Empirical Bayes Analysis of Volcanic Eruptions

This paper describes a simple empirical Bayes approach to inference about the eruption rate of a volcano under a Poisson process model. Under this approach, the prior distribution of the eruption rate is estimated from the eruption records of a group of similar volcanoes. The approach is illustrated using the eruption records of six Central American volcanoes.     

Sensitivity in volcanic hazard assessment for the Yucca Mountain high-level nuclear waste repository site: The model and the data

Both advocates and critics disagree on the significance and interpretation of critical geological features which relate to the safety and suitability of Yucca Mountain as a site for the construction of a high-level radioactive waste repository. Recent volcanism in the vicinity of Yucca Mountain is recognized readily by geologists and others with a knowledge of nuclear regulatory requirements as an important factor in determining future public and environmental safety. We regard basaltic volcanism as direct and unequivocal evidence of deep-seated geologic instability. Direct disruption of a repository site by basaltic volcanism therefore is a possibility. In this paper, sensitivity analysis of volcanic hazard assessment for the Yucca Mountain site is performed, taking into account some significant geological factors raised by experts. Three types of models are considered in the sensitivity data analysis. The first model assumes that both past and future volcanic activities follow a Homogeneous Poisson Process (HPP). The second model uses a Weibull Process (WP) to estimate the instantaneous recurrence rate based on the historical data at NTS (the Nevada Test Site). The model then switches from a WP of past events to a predictive HPP. The third model assumes that the prior historical trend based on a WP would continue for future activities. Hazards (at least one disruptive event during the next 10,000 years) using both classical and Bayesian approaches are evaluated based on the data for the following two observation periods: Pliocene and younger, and Quaternary. Combinations of various counts of events at volcanic centers of controversy and inclusion (or exclusion) of the youngest date at Lathrop Wells Center (=0.01 Ma) generate 90 different data sets. Sensitivity analysis is performed for each data set and the minimum and the maximum hazards for each model are summarized. We conclude that the estimated overall probability of at least one disruption of a repository at the Yucca Mountain site by basaltic volcanism during the next 10,000 years is bounded between 2.02×10⁵ and 6.57×10^–3.     

On estimating a relative safety loading for structures

This paper considers the reliability of a structure for earthquake load assuming that the number of earthquakes over a period [0, T] follows a truncated non-homogeneous Poisson process. It models the damage distribution along the line of a mixture of two distributions and derives an expression for the failure probability. It also estimates the value of a ‘relative safety loading’ that makes the failure probability as zero and investigates its asymptotic properties both theoretically and numerically.     

Statistics of Boulder Encounters during Shaft Excavation

Summary. We study the problem of boulder encounter during shaft excavation and the bias that results from directly using statistics from borehole samples without correction for probe diameter. We specifically focus on two quantities, the rate of boulder encounters λ₁ and the total length of obstructed shaft drilling L ₁. Assuming that boulders have spherical shape or cylindrical shape of a particular type, we evaluate how λ₁ and the mean and variance of L ₁ depend on the shaft diameter, the distribution of the boulder diameter, and the minimum boulder diameter that constitutes an obstruction to drilling. The statistics on L ₁ assume that the boulder centers are distributed according to a homogeneous Poisson process in space. Finally, we briefly discuss the problem of inferring the spatial density of boulders and their diameter distribution from borehole data. Both λ₁ and L ₁ increase significantly with increasing shaft diameter; hence the uncorrected statistics from borehole samples severely under-predict these two quantities during large-shaft drilling. Moreover, for typical parameter values, the mean value of L ₁ may be a significant fraction of the total shaft length.     

Selection of prior distributions and multiscale analysis in Bayesian temperature reconstructions based on fossil assemblages

It is possible to reconstruct the past variation of an environmental variable from measured historical indicators when the modern values of the variable and the indicators are known. In a Bayesian statistical approach, the selection of a prior probability distribution for the past values of the environmental variable can then be crucial and the selection therefore should be made carefully. This is particularly the case when the data are noisy and the statistical model used is complex since the influence of the prior on the results can then be especially strong. It can be difficult to elicit the prior probability distribution from the available information, since usually there are no measured data on the past values of the variable one wants to reconstruct and different reconstructions are typically consistent with each other only at a coarse level. To overcome these difficulties we propose to use a non-informative smoothing prior, possibly in combination with an informative prior, that simply penalizes for roughness of the reconstruction as measured by the variability of its values. We believe that it can sometimes be easier to set an overall prior distribution on the roughness than to agree on a prior for the actual values of the reconstructed variable. Note that by using a smoothing prior one incorporates into the model itself the smoothing step usually done before or after the actual numerical reconstruction. Another idea proposed in this paper is to integrate the reconstruction model with a multiscale feature analysis technique known as SiZer. Multiscale analysis of the posterior distribution of the reconstructed variable makes it possible to infer its statistically significant features such as trends, maxima and minima at several different time scales. While only temperature is considered in this paper, the technique can be applied to other environmental variables.     

Hazard area and probability of volcanic disruption of the proposed high-level radioactive waste repository at Yucca Mountain, Nevada, USA

Models that calculate the probability that a new volcano or a dike from a nearby eruption will intersect the footprint of the proposed high-level nuclear waste repository are generalized based on a conceptual model developed for the space transportation industry. The proposed hazard area, defined such that every new eruption that occurs there will disrupt the repository, plays a fundamental role in developing probability models. This hazard area is used not only to hedge the uncertainties in predicting patterns of future volcanic activity, but also to account for the characteristics of a new eruption during the post-closure performance period of an underground geologic repository. The paper discusses the advantages of probability comparisons, capabilities of conservativeness measurements and expert-elicitation on model parameters, and the implications to the proposed repository.Paper funded by a contract from the Agency for Nuclear Projects, State of Nevada, USA.     

地震危险性评价中余震活动的影响--以邢台余震区为例

目前通用的地震危险性模型在确定有关地震活动性参数时都强调删除余震,其理由是因为所应用的地震活动模型是泊松模型。但是在现实的地震灾害中,有些是因为余震活动所引起的。忽略余震活动的影响,可能会低估某些区域的地震危险。本文提出考虑余震活动的地震危险性分析模型,并从此模型出发,以邢台地震为例,对余震区内、余震区边界和余震区外等场点计算了考虑余震活动的地震危险性结果,同时,在原有模型的基础上,只改变余震区所处的潜在震源区的地震年发生率,计算相同场点的地震危险性结果,并把这两个结果与不考虑余震活动的结果进行比较,在此基础上讨论在某些区域考虑余震活动的必要性。     

区位通达性与在京外资企业的区位选择

利用北京市第二次基本单位普查资料,以邮政编码区为空间单元,采用泊松回归模型探讨了在京外资企业的城市内区位选择及其影响因素。研究涵盖了2001年全部的在京外资企业,模型估计中有效样本240个。外资企业具有显著的向中心城区集聚的分布态势,相对于制造业而言,服务业外资企业更为集中。分析结果表明,区位的通达性和城市结构对在京外资企业区位选择具有显著的影响。接近高速公路、高等院校、外国使馆以及工业园区等对外资企业具有显著吸引作用,离城市中心、火车站和机场距离过远则不利于吸引各类外资企业。研究也发现,制造业外资企业和服务业外资企业以及投资来源地不同的外资企业,在进行城市内部区位选择时存在显著的差异。