Two-dimensional Monte Carlo Analysis Research Articles

Health risk assessment of nitrate using a probabilistic approach in groundwater resources of western part of Iran

A probabilistic risk assessment (PRA) using two-dimensional Monte Carlo analysis was followed to inspect the health risk associated with consumption of groundwater contaminated with nitrate in 26 wells located in rural areas of Malayer, Iran. In this technique, probability distributions were assigned to the concentration of nitrate in groundwater, daily intake rate of water, frequency of exposure together with total duration of exposure and the risk levels were worked out for adults and children, accordingly. In addition, four scenarios were investigated with an emphasis on the effect of correlation between exposure frequency and ingestion rate of water on estimated risk values. It was indicated that inclusion of correlation between parameters would influence the upper median quartile values of estimated risk however the total impact on the results of health risk assessment is not significant. Moreover, considering the 3rd quartile value of risk level for the total size of the study area, the risk level related to children was higher than that of the adults with respective values of 0.621 and 0.989. The spatial variation of nitrate was considered using ordinary kriging and a novel combined method of random forest and spatial proximity as covariate. It was concluded that the predictions made by ordinary kriging were more accurate than the random forest technique which can be attributed to the small data sets used in this research.

A Probabilistic Risk Assessment for Field Radiography Based on Expert Judgment and Opinion

A probabilistic approach was applied to assess radiation risk associated with the field radiography using gamma sources. The Delphi method based on the expert judgments and opinions was used in the process of characterization of parameters affecting risk, which are inevitably subject to large uncertainties. A mathematical approach applying the Bayesian inferences was employed for data processing to improve the Delphi results. This process consists of three phases: (i) setting prior distributions, (ii) constructing the likelihood functions and (iii) deriving the posterior distributions based on the likelihood functions. The approach for characterizing input parameters using the Bayesian inference is provided for improved risk estimates without intentional rejection of part of the data, which demonstrated utility of Bayesian updating of distributions of uncertain input parameters in PRA (Probabilistic Risk Assessment). The data analysis portion for PRA in field radiography is addressed for estimates of the parameters used to determine the frequencies and consequences of the various events modeled. In this study, radiological risks for the worker and the public member in the vicinity of the work place are estimated for field radiography system in Korea based on two-dimensional Monte Carlo Analysis (2D MCA).

Identification of key factors for uncertainty in the prediction of the thermal performance of an office building under climate change

There is growing concern about the potential impact of climate change on the thermal performance of buildings. Building simulation is well-suited to predict the behaviour of buildings in the future, and to quantify the risks for prime building functions like occupant productivity, occupant health, or energy use. However, on the time scales that are involved with climate change, different factors introduce uncertainties into the predictions: apart from uncertainties in the climate conditions forecast, factors like change of use, trends in electronic equipment and lighting, as well as building refurbishment / renovation and HVAC (heating, ventilation, and air conditioning) system upgrades need to be taken into account. This article presents the application of two-dimensional Monte Carlo analysis to an EnergyPlus model of an office building to identify the key factors for uncertainty in the prediction of overheating and energy use for the time horizons of 2020, 2050 and 2080. The office has mixed-mode ventilation and indirect evaporative cooling, and is studied using the UKCIP02 climate change scenarios. The results show that regarding the uncertainty in predicted heating energy, the dominant input factors are infiltration, lighting gain and equipment gain. For cooling energy and overheating the dominant factors for 2020 and 2050 are lighting gain and equipment gain, but with climate prediction becoming the one dominant factor for 2080. These factors will be the subject of further research by means of expert panel sessions, which will be used to gain a higher resolution of critical building simulation input.

Radiological risk assessment for field radiography based on two dimensional Monte Carlo analysis

Probabilistic risk assessment studies use probability distributions for one or more variables of the risk equation in order to quantitatively characterize the variability and uncertainty. In this study, an advanced technique called the two-dimensional Monte Carlo analysis (2D MCA) is applied to estimation of radiological risk for worker and member of the public in the vicinity of the work place for field radiological system in Korea. The variables of the risk model along with the parameters of these variables are described in terms of probability density functions (PDFs). Because the frequencies of normal tasks were far higher than those of accidents, the total risk associated with normal tasks was higher than the accidental risk. The result derived from this work can be used as guidance for the decision-making in controlling the radiological risk in the field of radiography area.

2D Monte Carlo Analysis of Radiological Risk Assessment for the Food Intake In Korea

Most public health risk assessments assume and combine a series of average, conservative and worst-case values to derive an acceptable point estimate of risk. To improve quality of risk information, insight of uncertainty in the assessments is needed and more emphasis is put on the probabilistic risk assessment. Probabilistic risk assessment studies use probability distributions for one or more variables of the risk equation in order to quantitatively characterize variability and uncertainty. In this study, an advanced technique called the two-dimensional Monte Carlo analysis (2D MCA) is applied to estimation of internal doses from intake of radionuclides in foodstuffs and drinking water in Korea. The variables of the risk model along with the parameters of these variables are described in terms of probability density functions (PDFs). In addition, sensitivity analyses were performed to identify important factors to the radiation doses.

2D Monte Carlo versus 2D Fuzzy Monte Carlo health risk assessment

Risk estimates can be calculated using crisp estimates of the exposure variables (i.e., contaminant concentration, contact rate, exposure frequency and duration, body weight, and averaging time). However, aggregate and cumulative exposure studies require a better understanding of exposure variables and uncertainty and variability associated with them. Probabilistic risk assessment (PRA) studies use probability distributions for one or more variables of the risk equation in order to quantitatively characterize variability and uncertainty. Two-dimensional Monte Carlo Analysis (2D MCA) is one of the advanced modeling approaches that may be used to conduct PRA studies. In this analysis the variables of the risk equation along with the parameters of these variables (for example mean and standard deviation for a normal distribution) are described in terms of probability density functions (PDFs). A variable described in this way is called a “second order random variable.” Significant data or considerable insight to uncertainty associated with these variables is necessary to develop the appropriate PDFs for these random parameters. Typically, available data and accuracy and reliability of such data are not sufficient for conducting a reliable 2D MCA. Thus, other theories and computational methods that propagate uncertainty and variability in exposure and health risk assessment are needed. One such theory is possibility analysis based on fuzzy set theory, which allows the utilization of incomplete information (incomplete information includes vague and imprecise information that is not sufficient to generate probability distributions for the parameters of the random variables of the risk equation) together with expert judgment. In this paper, as an alternative to 2D MCA, we are proposing a 2D Fuzzy Monte Carlo Analysis (2D FMCA) to overcome this difficulty. In this approach, instead of describing the parameters of PDFs used in defining the variables of the risk equation as random variables, we describe them as fuzzy numbers. This approach introduces new concepts and risk characterization methods. In this paper we provide a comparison of these two approaches relative to their computational requirements, data requirements and availability. For a hypothetical case, we also provide a comperative interpretation of the results generated.

Analysis and Portrayal of Uncertainty in a Food-Web Exposure Model

The results of quantitative risk assessments are key factors in a risk manager's decision of the necessity to implement actions to reduce risk. The extent of the uncertainty in the assessment will play a large part in the degree of confidence a risk manager has in the reported significance and probability of a given risk. The two main sources of uncertainty in such risk assessments are variability and incertitude. In this paper we use two methods, a second-order two-dimensional Monte Carlo analysis and probability bounds analysis, to investigate the impact of both types of uncertainty on the results of a food-web exposure model. We demonstrate how the full extent of uncertainty in a risk estimate can be fully portrayed in a way that is useful to risk managers. We show that probability bounds analysis is a useful tool for identifying the parameters that contribute the most to uncertainty in a risk estimate and how it can be used to complement established practices in risk assessment. We conclude by promoting the use of probability analysis in conjunction with Monte Carlo analyses as a method for checking how plausible Monte Carlo results are in the full context of uncertainty.

Effects of uncertainties on exposure estimates to methylmercury: a Monte Carlo analysis of exposure biomarkers versus dietary recall estimation.

This article presents a general model for estimating population heterogeneity and "lack of knowledge" uncertainty in methylmercury (MeHg) exposure assessments using two-dimensional Monte Carlo analysis. Using data from fish-consuming populations in Bangladesh, Brazil, Sweden, and the United Kingdom, predictive model estimates of dietary MeHg exposures were compared against those derived from biomarkers (i.e., [Hg]hair and [Hg]blood). By disaggregating parameter uncertainty into components (i.e., population heterogeneity, measurement error, recall error, and sampling error) estimates were obtained of the contribution of each component to the overall uncertainty. Steady-state diet:hair and diet:blood MeHg exposure ratios were estimated for each population and were used to develop distributions useful for conducting biomarker-based probabilistic assessments of MeHg exposure. The 5th and 95th percentile modeled MeHg exposure estimates around mean population exposure from each of the four study populations are presented to demonstrate lack of knowledge uncertainty about a best estimate for a true mean. Results from a U.K. study population showed that a predictive dietary model resulted in a 74% lower lack of knowledge uncertainty around a central mean estimate relative to a hair biomarker model, and also in a 31% lower lack of knowledge uncertainty around central mean estimate relative to a blood biomarker model. Similar results were obtained for the Brazil and Bangladesh populations. Such analyses, used here to evaluate alternative models of dietary MeHg exposure, can be used to refine exposure instruments, improve information used in site management and remediation decision making, and identify sources of uncertainty in risk estimates.

Application of a Probabilistic Risk Assessment Methodology to a Lead Smelter Site

Exposure of children to lead in the environment was assessed at the Murray Smelter Superfund site using both a deterministic risk assessment approach, the Integrated Exposure Uptake Biokinetic (IEUBK) model, and a probabilistic approach, the Integrated Stochastic Exposure (ISE) model. When site-specific data on lead in environmental media were input as point estimates into the IEUBK model, unacceptable risks were predicted for children living within five of eight study zones. The predicted soil cleanup goal was 550 ppm. Concentration and exposure data were then input into the ISE model as probability distribution functions and a one-dimensional Monte Carlo analysis (ID MCA) was run to predict the expected distribution of exposures and blood lead values. Uncertainty surrounding these predictions was examined in a two-dimensional Monte Carlo analysis (2-D MCA). The ISE model predicted risks that were in the same rank order as those predicted by the IEUBK model, although the probability estimates of exceeding a blood lead level of 10 µg/dl (referred to as the P10) from the ISE model were uniformly lower than those predicted by the IEUBK model. The 2-D MCA allowed evaluation of the confidence around each P10 level, and identified the main sources of both uncertainty and variability in exposure estimates. The ISE model suggested cleanup goals ranging from 1300 to 1500 ppm might be protective at this site.

Application of a Probabilistic Risk Assessment Methodology to a Lead Smelter Site

Exposure of children to lead in the environment was assessed at the Murray Smelter Superfund site using both a deterministic risk assessment approach, the Integrated Exposure Uptake Biokinetic (IEUBK) model, and a probabilistic approach, the Integrated Stochastic Exposure (ISE) model. When site-specific data on lead in environmental media were input as point estimates into the IEUBK model, unacceptable risks were predicted for children living within five of eight study zones. The predicted soil cleanup goal was 550 ppm. Concentration and exposure data were then input into the ISE model as probability distribution functions and a one-dimensional Monte Carlo analysis (ID MCA) was run to predict the expected distribution of exposures and blood lead values. Uncertainty surrounding these predictions was examined in a two-dimensional Monte Carlo analysis (2-D MCA). The ISE model predicted risks that were in the same rank order as those predicted by the IEUBK model, although the probability estimates of exceeding a blood lead level of 10 µg/dl (referred to as the P10) from the ISE model were uniformly lower than those predicted by the IEUBK model. The 2-D MCA allowed evaluation of the confidence around each P10 level, and identified the main sources of both uncertainty and variability in exposure estimates. The ISE model suggested cleanup goals ranging from 1300 to 1500 ppm might be protective at this site.