How to Choose Priors for Bayesian Estimation of the Discovery Process Model

The Bayesian version of the discovery process model provides an effective way to estimate the parameters of the superpopulation, the efficiency of the exploration effort, the number of pools and the undiscovered potential in a play. The posterior estimates are greatly influenced by the prior distribution of these parameters. Some empirical and statistical relationships for these parameters can be obtained from Monte Carlo simulations of the discovery model. For example, there is a linear relationship between the expectation of a pool size in logarithms and the order of its discovery, the slope of which is related to the discoverability factor. Some simple estimates for these unknown play parameters can be derived based upon these empirical and statistical conclusions and may serve as priors for the Bayesian approach. The priors and posteriors from this empirical Bayesian approach are compared with the estimates from Lee and Wang's modified maximum likelihood approach using the same data.     

A probabilistic model of petroleum discovery

We discuss a petroleum discovery model that greatly simplifies the approach initiated by Barouch and Kaufman (1976) in which exploration is viewed as a sampling without replacement process, and the probability of discovery of a pool is proportional to its size. Calculations that formerly required lengthy Monte Carlo simulations have been reduced to compact formulas.     

Forthcoming events

Spatial data uncertainty models (SDUM) are necessary tools that quantify the reliability of results from geographical information system (GIS) applications. One technique used by SDUM is Monte Carlo simulation, a technique that quantifies spatial data and application uncertainty by determining the possible range of application results. A complete Monte Carlo SDUM for generalized continuous surfaces typically has three components: an error magnitude model, a spatial statistical model defining error shapes, and a heuristic that creates multiple realizations of error fields added to the generalized elevation map. This paper introduces a spatial statistical model that represents multiple statistics simultaneously and weighted against each other. This paper's case study builds a SDUM for a digital elevation model (DEM). The case study accounts for relevant shape patterns in elevation errors by reintroducing specific topological shapes, such as ridges and valleys, in appropriate localized positions. The spatial statistical model also minimizes topological artefacts, such as cells without outward drainage and inappropriate gradient distributions, which are frequent problems with random field-based SDUM. Multiple weighted spatial statistics enable two conflicting SDUM philosophies to co-exist. The two philosophies are ‘errors are only measured from higher quality data’ and ‘SDUM need to model reality’. This article uses an automatic parameter fitting random field model to initialize Monte Carlo input realizations followed by an inter-map cell-swapping heuristic to adjust the realizations to fit multiple spatial statistics. The inter-map cell-swapping heuristic allows spatial data uncertainty modelers to choose the appropriate probability model and weighted multiple spatial statistics which best represent errors caused by map generalization. This article also presents a lag-based measure to better represent gradient within a SDUM. This article covers the inter-map cell-swapping heuristic as well as both probability and spatial statistical models in detail.     

Baptiste Lake,Alberta — A late Holocene history of changes in a lake and its catchment in the southern Boreal forest

Lead-210 assay and dating are subject to several sources of error, including natural variation, the statistical nature of measuring radioactivity, and estimation of the supported fraction. These measurable errors are considered in calculating confidence intervals for ²¹⁰Pb dates. Several sources of error, including the effect of blunders or misapplication of the mathematical model, are not included in the quantitative analysis. First-order error analysis and Monte Carlo simulation (of cores from Florida PIRLA lakes) are used as independent estimates of dating uncertainty. CRS-model dates average less than 1% older than Monte Carlo median dates, but the difference increases non-linearly with age to a maximum of 11% at 160 years. First-order errors increase exponentially with calculated CRS-model dates, with the largest 95% confidence interval in the bottommost datable section being 155±90 years, and the smallest being 128±8 years. Monte Carlo intervals also increase exponentially with age, but the largest 95% occurrence interval is 152±44 years. Confidence intervals calculated by first-order methods and ranges of Monte Carlo dates agree fairly well until the ²¹⁰Pb date is about 130 years old. Older dates are unreliable because of this divergence. Ninety-five per cent confidence intervals range from about 1–2 years at 10 years of age, 10–20 at 100 years, and 8–90 at 150 years old.This is the third of a series of papers to be published by this journal which is a contribution of the Paleoecological Investigation of Recent Lake Acidification (PIRLA) project. Drs. D.F. Charles and D.R. Whitehead are guest editors for this series.     

Leveraging parallel spatio-temporal computing for crime analysis in large datasets: analyzing trends in near-repeat phenomenon of crime in cities

ABSTRACT

Crime often clusters in space and time. Near-repeat patterns improve understanding of crime communicability and their space–time interactions. Near-repeat analysis requires extensive computing resources for the assessment of statistical significance of space–time interactions. A computationally intensive Monte Carlo simulation-based approach is used to evaluate the statistical significance of the space-time patterns underlying near-repeat events. Currently available software for identifying near-repeat patterns is not scalable for large crime datasets. In this paper, we show how parallel spatial programming can help to leverage spatio-temporal simulation-based analysis in large datasets. A parallel near-repeat calculator was developed and a set of experiments were conducted to compare the newly developed software with an existing implementation, assess the performance gain due to parallel computation, test the scalability of the software to handle large crime datasets and assess the utility of the new software for real-world crime data analysis. Our experimental results suggest that, efficiently designed parallel algorithms that leverage high-performance computing along with performance optimization techniques could be used to develop software that are scalable with large datasets and could provide solutions for computationally intensive statistical simulation-based approaches in crime analysis.     

Using a maximum entropy model to optimize the stochastic component of urban cellular automata models

ABSTRACT

The stochastic perturbation of urban cellular automata (CA) model is difficult to fine-tune and does not take the constraint of known factors into account when using a stochastic variable, and the simulation results can be quite different when using the Monte Carlo method, reducing the accuracy of the simulated results. Therefore, in this paper, we optimize the stochastic component of an urban CA model by the use of a maximum entropy model to differentially control the intensity of the stochastic perturbation in the spatial domain. We use the kappa coefficient, figure of merit, and landscape metrics to evaluate the accuracy of the simulated results. Through the experimental results obtained for Wuhan, China, the effectiveness of the optimization is proved. The results show that, after the optimization, the kappa coefficient and figure of merit of the simulated results are significantly improved when using the stochastic variable, slightly improved when using Monte Carlo methods. The landscape metrics for the simulated results and actual data are much closer when using the stochastic variable, and slightly closer when using the Monte Carlo method, but the difference between the simulated results is narrowed, reflecting the fact that the results are more reliable.     

Geologic risk, economic assessment, and optimal decision making of petroleum plays in the Bohaiwan Basin, northern China

A system of play (trap) assessment based on the analysis of geological characteristics of five different types of petroleum plays in the Bohaiwan Basin, northern China, is proposed. The system makes use of conditional probability, fuzzy logic, and Monte Carlo simulation to assess geologic risk for estimating the undiscovered petroleum resources in a region. Combining the estimates of undiscovered resources with the subsequent economic evaluation of discovered resources by using techniques of optimization, the expected monetary value can be estimated to determine the overall benefits of an investment. A software program has been developed to carry out the calculations.     

Probabilistic methodology for estimation of undiscovered petroleum resources in play analysis of the United States

A geostochastic system called FASPF was developed by the U.S. Geological Survey for their 1989 assessment of undiscovered petroleum resources in the United States. FASPF is a fast appraisal system for petroleum play analysis using a field-size geological model and an analytic probabilistic methodology. The geological model is a particular type of probability model whereby the volumes of oil and gas accumulations are modeled as statistical distributions in the form of probability histograms, and the risk structure is bilevel (play and accumulation) in terms of conditional probability. The probabilistic methodology is an analytic method derived from probability theory rather than Monte Carlo simulation. The resource estimates of crude oil and natural gas are calculated and expressed in terms of probability distributions. The probabilistic methodology developed by the author is explained.The analytic system resulted in a probabilistic methodology for play analysis, subplay analysis, economic analysis, and aggregation analysis. Subplay analysis included the estimation of petroleum resources on non-Federal offshore areas. Economic analysis involved the truncation of the field size with a minimum economic cutoff value. Aggregation analysis was needed to aggregate individual play and subplay estimates of oil and gas, respectively, at the provincial, regional, and national levels.     

Evaluating the uncertainty caused by Post Office Box addresses in environmental health studies: A restricted Monte Carlo approach

A Monte Carlo approach is used to evaluate the uncertainty caused by incorporating Post Office Box (PO Box) addresses in point‐cluster detection for an environmental‐health study. Placing PO Box addresses at the centroids of postcode polygons in conventional geocoding can introduce significant error into a cluster analysis of the point data generated from them. In the restricted Monte Carlo method I presented in this paper, an address that cannot be matched to a precise location is assigned a random location within the smallest polygon believed to contain that address. These random locations are then combined with the locations of precisely matched addresses, and the resulting dataset is used for performing cluster analysis. After repeating this randomization‐and‐analysis process many times, one can use the variance in the calculated cluster evaluation statistics to estimate the uncertainty caused by the addresses that cannot be precisely matched. This method maximizes the use of the available spatial information, while also providing a quantitative estimate of the uncertainty in that utilization. The method is applied to lung‐cancer data from Grafton County, New Hampshire, USA, in which the PO Box addresses account for more than half of the address dataset. The results show that less than 50% of the detected cluster area can be considered to have high certainty.     

Multi-level temporal autoregressive modelling of daily activity satisfaction using GPS-integrated activity diary data

In this research, we match web-based activity diary data with daily mobility information recorded by GPS trackers for a sample of 709 residents in a 7-day survey in Beijing in 2012 to investigate activity satisfaction. Given the complications arising from the irregular time intervals of GPS-integrated diary data and the associated complex dependency structure, a direct application of standard (spatial) panel data econometric approaches is inappropriate. This study develops a multi-level temporal autoregressive modelling approach to analyse such data, which conceptualises time as continuous and examines sequential correlations via a time or space-time weights matrix. Moreover, we manage to simultaneously model individual heterogeneity through the inclusion of individual random effects, which can be treated flexibly either as independent or dependent. Bayesian Markov chain Monte Carlo (MCMC) algorithms are developed for model implementation. Positive sequential correlations and individual heterogeneity effects are both found to be statistically significant. Geographical contextual characteristics of sites where activities take place are significantly associated with daily activity satisfaction, controlling for a range of situational characteristics and individual socio-demographic attributes. Apart from the conceivable urban planning and development implications of our study, we demonstrate a novel statistical methodology for analysing semantic GPS trajectory data in general.     

Bias estimation and correction for triangle-based surface area calculations

The calculation of surface area is meaningful for a variety of space-filling phenomena, e.g., the packing of plants or animals within an area of land. With Digital Elevation Model (DEM) data we can calculate the surface area by using a continuous surface model, such as by the Triangulated Irregular Network (TIN). However, just as the triangle-based surface area discussed in this paper, the surface area is generally biased because it is a nonlinear mapping about the DEM data which contain measurement errors. To reduce the bias in the surface area, we propose a second-order bias correction by applying nonlinear error propagation to the triangle-based surface area. This process reveals that the random errors in the DEM data result in a bias in the triangle-based surface area while the systematic errors in the DEM data can be reduced by using the height differences. The bias is theoretically given by a probability integral which can be approximated by numerical approaches including the numerical integral and the Monte Carlo method; but these approaches need a theoretical distribution assumption about the DEM measurement errors, and have a very high computational cost. In most cases, we only have variance information on the measurement errors; thus, a bias estimation based on nonlinear error propagation is proposed. Based on the second-order bias estimation proposed, the variance of the surface area can be improved immediately by removing the bias from the original variance estimation. The main results are verified by the Monte Carlo method and by the numerical integral. They show that an unbiased surface area can be obtained by removing the proposed bias estimation from the triangle-based surface area originally calculated from the DEM data.     

Uncertainty propagation in wildland fire behaviour modelling

Rothermel's model is the most widely used fire behaviour model in wildland fire research and management. It is a complex model that considers 17 input variables describing fuel type, fuel moisture, terrain and wind. Uncertainties in the input variables can have a substantial impact on the resulting errors and have to be considered, especially when the results are used in spatial decision making. In this paper it is shown that the analysis of uncertainty propagation can be carried out with the Taylor series method. This method is computationally cheaper than Monte Carlo and offers easy-to-use, preliminary sensitivity estimations.     

Assessment of Exploration Bias in Data-Driven Predictive Models and the Estimation of Undiscovered Resources

The spatial distribution of discovered resources may not fully mimic the distribution of all such resources, discovered and undiscovered, because the process of discovery is biased by accessibility factors (e.g., outcrops, roads, and lakes) and by exploration criteria. In data-driven predictive models, the use of training sites (resource occurrences) biased by exploration criteria and accessibility does not necessarily translate to a biased predictive map. However, problems occur when evidence layers correlate with these same exploration factors. These biases then can produce a data-driven model that predicts known occurrences well, but poorly predicts undiscovered resources. Statistical assessment of correlation between evidence layers and map-based exploration factors is difficult because it is difficult to quantify the “degree of exploration.” However, if such a degree-of-exploration map can be produced, the benefits can be enormous. Not only does it become possible to assess this correlation, but it becomes possible to predict undiscovered, instead of discovered, resources. Using geothermal systems in Nevada, USA, as an example, a degree-of-exploration model is created, which then is resolved into purely explored and unexplored equivalents, each occurring within coextensive study areas. A weights-of-evidence (WofE) model is built first without regard to the degree of exploration, and then a revised WofE model is calculated for the “explored fraction” only. Differences in the weights between the two models provide a correlation measure between the evidence and the degree of exploration. The data used to build the geothermal evidence layers are perceived to be independent of degree of exploration. Nevertheless, the evidence layers correlate with exploration because exploration has preferred the same favorable areas identified by the evidence patterns. In this circumstance, however, the weights for the “explored” WofE model minimize this bias. Using these revised weights, posterior probability is extrapolated into unexplored areas to estimate undiscovered deposits.     

Inference of past climate from borehole temperature data using Bayesian Reversible Jump Markov chain Monte Carlo

Estimates of past climate derived from borehole temperatures are assuming a greater importance in context of the millennial temperature variation debate. However, recovery of these signals is usually performed with regularization which can potentially lead to underestimation of past variation when noise is present. In this work Bayesian inference is applied to this problem with no explicit regularization. To achieve this Reversible Jump Markov chain Monte Carlo is employed, and this allows models of varying complexity (i.e. variable dimensions) to be sampled so that it is possible to infer the level of ground surface temperature (GST) history resolution appropriate to the data. Using synthetic examples, we show that the inference of the GST signal back to more than 500 yr is robust given boreholes of 500 m depth and moderate noise levels and discuss the associated uncertainties. We compare the prior information we have used with the inferred posterior distribution to show which parts of the GST reconstructions are independent of this prior information. We demonstrate the application of the method to real data using five boreholes from southern England. These are modelled both individually and jointly, and appear to indicate a spatial trend of warming over 500 yr across the south of the country.     

Same space – different perspectives: comparative analysis of geographic context through sketch maps and spatial video geonarratives

ABSTRACT

The importance of including a contextual underpinning to the spatial analysis of social data is gaining traction in the spatial science community. The challenge, though, is how to capture these data in a rigorous manner that is translational. One method that has shown promise in achieving this aim is the spatial video geonarrative (SVG), and in this paper we pose questions that advance the science of geonarratives through a case study of criminal ex-offenders. Eleven ex-offenders provided sketch maps and SVGs identifying high-crime areas of their community. Wordmapper software was used to map and classify the SVG content; its spatial filter extension was used for hot spot mapping with statistical significance tested using Monte Carlo simulations. Then, each subject’s sketch map and SVG were compared. Results reveal that SVGs consistently produce finer spatial-scale data and more locations of relevance than the sketch maps. SVGs also provide explanation of spatial-temporal processes and causal mechanisms linked to specific places, which are not evident in the sketch maps. SVG can be a rigorous translational method for collecting data on the geographic context of many phenomena. Therefore, this paper makes an important advance in understanding how environmentally immersive methods contribute to the understanding of geographic context.     

基于滨海环境资源特点的大连旅游承载状态评价

旅游环境承载力涉及多维度属性相互制约影响,而传统方法中对于各属性间影响程度及游客偏好选择的判定则较多依赖于个体的主观感知。因此,针对处理多属性综合评价中存在的模糊性及主观性,提出基于蒙特卡罗模拟修正的模糊综合评价模型。结果表明,借助上述模糊综合评价修正模型针对大连滨海旅游环境承载力进行解释与分析,成功缓解了在模型度量与数据分析环节所出现的主观偏误缺陷,从而有效提升了大连市滨海旅游景区有关阈值综合评价体系的科学性与稳健性。评价结果表明,当前大连市滨海旅游环境承载力状态可以判定为“适载”;在影响滨海旅游环境承载力的6项要素中,游憩环境要素与气候要素的评价分数较高,最低评分数值指标为景区游客管理状态。     

A TEST OF SIGNIFICANCE FOR PARTIAL LEAST SQUARES REGRESSION

Partial least squares (PLS) regression is a commonly used statistical technique for performingmultivariate calibration, especially in situations where there are more variables than samples. Choosingthe number of factors to include in a model is a decision that all users of PLS must make, but iscomplicated by the large number of empirical tests available. In most instances predictive ability is themost desired property of a PLS model and so interest has centred on making this choice based on aninternal validation process. A popular approach is the calculation of a cross-validated r~2 to gauge howmuch variance in the dependent variable can be explained from leave-one-out predictions. Using MonteCarlo simulations for different sizes of data set, the influence of chance effects on the cross-validationprocess is investigated. The results are presented as tables of critical values which are compared againstthe values of cross-validated r~2 obtained from the user's own data set. This gives a formal test forpredictive ability of a PLS model with a given number of dimensions.     

切片采样算法在光释光年龄模型参数估计中的应用

光释光(OSL)年代学模型是基于数理统计学的一类概率密度模型,它根据特定的假设条件对样品等效剂量(De)分布进行数学解释,由此估计具有不同沉积历史或者能够代表样品实际埋藏年龄的De组分。年龄模型参数估计常通过极大似然估计(MLE)算法实现,本文尝试了切片采样算法在年龄模型参数优化中的应用。切片采样属于一种马尔科夫链蒙特卡罗采样(MCMC)算法,能根据测量数据与模型的联合似然函数进行随机采样,由此获得参数的采样分布。本文编写了实现年龄模型切片采样算法的应用程序,并使用模拟及实测De数据验证了该算法估计的可靠性。相对于MLE算法,MCMC算法具有对参数初值依赖性低、误差估计更准确的特点,切片采样算法提供了实现释光年龄模型参数估计的一种新方法。     

Discovery process modeling—A sensitivity study

Lognormal discovery process modeling characterizes oil and gas discovery as sampling from a lognormal parent distribution with probability proportional to size and without replacement. In this article, we present a sensitivity study that is based on simulated discovery sequences with different assumptions regarding discovery efficiency, exploration status, and the shape of the parent field size distribution. The results indicate that lognormal discovery process modeling provides good overall estimates of the lognormal parameters if the parent field size distribution is lognormal. If the parent field size distribution is Pareto, an underestimation of the play potential may occur if a lognormal discovery process model is applied. Failure of the likelihood value converging to a maximum is more frequent when sample size is small and/or discovery efficiency is low.     

基于基尼系数空间分解的江苏省经济发展差异分析

不平等性是区域研究的重点,空间集中作为衡量不平等性的重要手段,是非空间与空间属性的二维统一体。传统的研究仅仅关注了全局非空间上的不均衡性,而忽略了地理空间上的集聚特点,往往不利于识别地理属性的集中特点。引进基尼系数的空间分解这一概念,通过对其空间随机分布性的零假设采用蒙特卡罗方法进行检验,从而判定其分解形式是否内生衡量区域不平等与空间自相关的特性。以1978—2015年江苏省区域经济发展差异的演变进行案例分析,通过蒙特卡罗99次随机模拟检验后,将分解的非邻居项与Moran’s I值进行显著性检验,结果进一步证实了这一分解的有效性与简洁性,表明空间基尼系数可内生测度空间的集聚性与非空间的差异性。