Two-stage Monte Carlo Simulation Research Articles

A probabilistic risk approach for the collision detection of multi-ships under spatiotemporal movement uncertainty

It is vital to analyse ship collision risk for preventing collisions and improving safety at sea. The state-of-the-art of ship collision risk analysis focuses on encountering conflict between ship pairs, subject to a strong assumption of the ships having no/little spatiotemporal motion uncertainty. This paper proposes a probabilistic conflict detection approach to estimate potential collision risk of various multi-vessel encounters, in which the spatiotemporal-dependent patterns of ship motions are newly taken into account through quantifying the trajectory uncertainty distributions using AIS data. The estimation accuracy and efficiency are assured by employing a two-stage Monte Carlo simulation algorithm, which provides the quantitative bounds on the approximation accuracy and allows for a fast estimation of conflict criticality. Several real experiments are conducted using the AIS-based trajectory data in Ningbo-Zhoushan Port to demonstrate the feasibility and superiority of the proposed new approach. The results show that it enables the effective detection of collision risk timely and reliably in a complicated dynamic situation. They therefore provide valuable insights on ship collision risk prediction as well as the formulation of risk mitigation measures.

Estimation of particulate matter exposure to construction workers using low-cost dust sensors

The construction industry is one of the significant sources which pollutes the environment. As 66 % of the world’s population will move towards urban areas within 2050, the rate of construction work happening in the cities will be enormous. Thus, construction practitioners should be aware of Particulate matter (PM) exposure and associated health impacts on society living in urban areas and focus on executing targeted countermeasures. Low-cost sensors with higher sensitivity and higher saturation point can be used for PM measurements during the construction works. This study measures PM produced from a construction activity using low-cost sensors. A total of 4635 exposure samples were collected during the experiment from which the PM concentrations for PM10, PM2.5, and PM1 were recorded as 7731.32, 532.14, and 113.68 μg/m3 with a standard deviation (σ) of 1990.39, 64.97, and 12.06 μg/m3. The two-stage Monte Carlo simulation (MCS) method supports the conclusion that even after implementing efficient control measures, the concentration of PM10 and PM2.5 remain 30 and 8 fold higher than their respective 24-hs exposure standards. Thus, future research work should focus on creating targeted control measures, further research exploring the distribution of particles produced from different construction activities should be monitored.

Gold nanoparticle enhanced proton therapy: A Monte Carlo simulation of the effects of proton energy, nanoparticle size, coating material, and coating thickness on dose and radiolysis yield.

Radiosensitizer enhanced radiotherapy provides the possibility of improved treatment outcomes by preferentially increasing the effectiveness of radiation within the tumor. Proton therapy offers improved sparing of tissue distal of the tumor along the beam path and reduced integral dose compared to conventional photon therapy. The combination of proton therapy with radiosensitizers offers the potential for an enhanced therapy with increased effect within the tumor and low integral dose. The simulations performed in this work determine the effect of nanoparticle characteristics and proton energy on the nanoscale dose and radiolysis yield enhancement for a single gold nanoparticle irradiated with a proton beam. This data can be used to determine optimal nanoparticle characteristics to enhance proton therapy. A two-stage Monte Carlo simulation was performed using Geant4. In the first stage of the simulation, the physical interactions of protons within a gold nanoparticle were modeled and the secondary electrons escaping the nanoparticle's surface were scored in a phase space file. In the second stage of the simulation, the phase space file was used as an input to model the physical interactions of the secondary electrons in water and the resulting production and chemical interactions of reactive species. By comparing a gold nanoparticle with an equivalent water nanoparticle, the nanoscale enhancement of dose and radiolysis yield was calculated. A large nanoscale enhancement of both the dose and radiolysis yield of up to a factor of 11 due to gold nanoparticles was found for most simulated conditions. For 50nm gold nanoparticles, a large enhancement factor of 9-11 was observed for high proton energies; however, the enhancement was reduced for proton energies below 10MeV. For 5MeV incident protons, it was found that the enhancement factor was approximately 9 for gold nanoparticles of sizes 5-25nm with a reduction in enhancement observed for nanoparticle sizes outside this range. Additionally, it was found that larger nanoparticle sizes resulted in greater total energy deposition and radiolysis yields per proton flux but with reduced efficiency per nanoparticle mass. It was observed that a large loss of enhancement occurred for thick nanoparticle coatings. However, for polyethylene glycol (PEG) coatings, coating density had a minimal effect on enhancement. A large enhancement in dose and radiolysis yield was observed. However, the low-energy secondary electrons produced within the gold for lower energy protons are susceptible to self-absorption and result in the loss of enhancement observed for larger nanoparticles and thicker coatings. The radiolysis yield and dose increase with nanoparticle size; however, the yield and dose per gold mass decrease due to self-absorption. Therefore, an intermediate nanoparticle size of approximately 10-25nm maximizes both the radiolysis yield and dose as well as the enhancement. Coatings should be kept to the minimum effective thickness to limit the loss of enhancement. For molecular coatings such as PEG, coating density should be maximized as this increases the coating's effectiveness with only a minimal effect on enhancement.

The signal in the noise: Robust detection of performance “outliers” in health services

To make the increasing amounts of data about the performance of public sector organisations digestible by decision makers, composite indicators are commonly constructed, from which a natural step is rankings and league tables. However, how much credence should be given to the results of such approaches? Studying English NHS maternity services (N = 130 hospital trusts), we assembled and used a set of 38 indicators grouped into four baskets of aspects of service delivery. In the absence of opinion on how the indicators should be aggregated, we focus on the uncertainty this brings to the composite results. We use a large two-stage Monte Carlo simulation to generate possible aggregation weights and examine the discrimination in the composite results. We find that positive and negative “outliers” can be identified robustly, of particular value to decision makers for investigation for learning or intervention, however results in between should be treated with great caution.

Monte Carlo method for determining the response of portable gamma detector for in situ measurement of terrestrial gamma ray field

A Monte Carlo method to study the response of portable detector to terrestrial gamma ray is proposed. This method is based on two-stage Monte Carlo simulation. First, the probability distributions of the phase space coordinates of the events that are most likely to be detected are reconstructed at the phase space shell level. The phase space shell is a closed surface enclosing the detector. The detector response to events originating from the phase space shell is then studied. The full absorption spectra as well as the partial absorption spectra are obtained for natural radionuclides uniformly distributed in the ground. For validation, this method is applied to a HpGe portable detector previously studied. The previous study is based on a semiempirical model. Good agreement is achieved when we compare the full-energy peak efficiencies and the total in situ spectra obtained by the two methods. As an application, the effective depth of the activity of the 137Cs artificial radionuclide in the soil is determined from the low-energy part of the total in situ spectrum.

Distributed computing approaches for large‐scale probit‐based stochastic user equilibrium problems

SUMMARYApplications of probit‐based stochastic user equilibrium (SUE) principle on large‐scale networks have been largely limited because of the overwhelming computational burden in solving its stochastic network loading problem. A two‐stage Monte Carlo simulation method is recognized to have satisfactory accuracy level when solving this stochastic network loading. This paper thus works on the acceleration of the Monte Carlo simulation method via using distributed computing system. Three distributed computing approaches are then adopted on the workload partition of the Monte Carlo simulation method. Wherein, the first approach allocates each processor in the distributed computing system to solve each trial of the simulation in parallel and in turns, and the second approach assigns all the processors to solve the shortest‐path problems in one trial of the Monte Carlo simulation concurrently. The third approach is a combination of the first two, wherein both different trials of the Monte Carlo simulation as well as the shortest path problems in one trial are solved simultaneously. Performances of the three approaches are comprehensively tested by the Sioux‐Falls network and then a randomly generated network example. It shows that computational time for the probit‐based SUE problem can be largely reduced by any of these three approaches, and the first approach is found out to be superior to the other two. The first approach is then selected to calculate the probit‐based SUE problem on a large‐scale network example. Copyright © 2011 John Wiley & Sons, Ltd.

Antiretroviral therapy in pregnancy: Balancing the risk of preterm delivery with prevention of mother-to-child HIV transmission

Highly active antiretroviral therapy (HAART) for pregnant HIV-positive women reduces the risk of mother-to-child transmission, but is associated with an increased risk of preterm delivery (<37 weeks gestation). We aimed to quantify the incremental risk-benefit ratio for HAART compared with zidovudine monotherapy with respect to these outcomes. Two-stage Monte Carlo simulation methods were used to estimate the risk-benefit ratio for HAART in pregnancy. Estimates of mother-to-child transmission and preterm delivery rates were obtained from UK and Ireland surveillance data collected through the National Study of HIV in Pregnancy and Childhood. At a population level, HAART was associated with a more than sevenfold reduction in mother-to-child transmission compared with zidovudine monotherapy (adjusted odds ratio [AOR] 0.13, 95% confidence interval [CI] 0.06-0.27), but with a 1.4-fold increased odds of preterm delivery (AOR 1.43, 95% CI 1.10-1.86) and twofold increased odds of severe preterm delivery (<32 weeks; AOR 2.06, 95% CI 1.09-3.88). The incremental risk-benefit ratio for HAART in pregnancy compared with monotherapy was 0.63 (95% simulation interval 0.06-1.96) additional preterm births and 0.23 (95% simulation interval -0.02-0.88) severe preterm births for each infection prevented. It is estimated that for every 100 HIV transmissions prevented through the use of HAART (rather than monotherapy), 63 additional preterm deliveries would occur, including 23 at <32 weeks gestation. Interpretation of these ratios is context-dependent and requires additional information about morbidity, mortality and costs associated with the outcomes.

Time Variant Reliability Analysis of Nonlinear Structural Dynamical Systems using combined Monte Carlo Simulations and Asymptotic Extreme Value Theory

Reliability of nonlinear vibrating systems under stochastic excitations is investigated using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis tests, and the next stage involves the estimation of parameters of the relevant extreme value distribution. Both these stages are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear systems with single/multiple degrees of freedom, driven by random excitations. The predictions from the proposed method are compared with the results from large-scale Monte Carlo simulations, and also with the classical analytical results, when available, from the theory of out-crossing statistics. Applications of the proposed method for large-scale problems and for vibration data obtained from field/laboratory conditions, are also discussed.

Economic evaluation of caspofungin vs liposomal amphotericin B for empirical therapy of suspected systemic fungal infection in the German hospital setting.

As antifungal agents are frequently used in hematology and oncology, economic data on the empirical therapy of suspected systemic fungal infection are pivotal. Data were analyzed according to: (1) the rate of nephrotoxicity related to treatment with caspofungin in comparison to liposomal amphotericin B (L-AmB) from a randomized clinical trial, (2) the effect of nephrotoxicity on length of hospital stay from a European observational study, and (3) an example of total bottom-up cost in a department of hematology in Germany. All estimates include 95% confidence intervals (CI) using two-stage Monte Carlo simulation on binominal and Gaussian random variables from separate studies with comparable populations. Overall, 8.9 (95% CI 5.9–12.1) fewer patients (of 100 randomized) experienced worsening of renal function with caspofungin vs L-AmB, giving a number needed to treat for one patient to be harmed by L-AmB of 12 (95% CI 8–17). This was estimated to translate into 5.3 extra days in hospital (95% CI 1.6–9.1) per event or 0.48 days (95% CI 0.14–0.88) worth €298 (95% CI 89–554) per patient receiving L-AmB rather than caspofungin. From the hospital perspective, use of caspofungin was estimated to be cost-neutral compared to L-AmB at a per diem total hospital cost of €428 with, and €1284 without, consideration of supplementary reimbursement (Zusatzentgelt) of both L-AmB and caspofungin. The data presented in this scenario show that use of caspofungin in hematology–oncology departments in Germany results in shorter hospital stays and is at least cost-neutral compared to use of L-AmB.

Estimating the expected value of partial perfect information: a review of methods

Value of information analysis provides a framework for the analysis of uncertainty within economic analysis by focussing on the value of obtaining further information to reduce uncertainty. The mathematical definition of the expected value of perfect information (EVPI) is fixed, though there are different methods in the literature for its estimation. In this paper these methods are explored and compared. Analysis was conducted using a disease model for Parkinson's disease. Five methods for estimating partial EVPIs (EVPPIs) were used: a single Monte Carlo simulation (MCS) method, the unit normal loss integral (UNLI) method, a two-stage method using MCS, a two-stage method using MCS and quadrature and a difference method requiring two MCS. EVPPI was estimated for each individual parameter in the model as well as for three groups of parameters (transition probabilities, costs and utilities). Using 5,000 replications, four methods returned similar results for EVPPIs. With 5 million replications, results were near identical. However, the difference method repeatedly gave estimates substantially different to the other methods. The difference method is not rooted in the mathematical definition of EVPI and is clearly an inappropriate method for estimating EVPPI. The single MCS and UNLI methods were the least complex methods to use, but are restricted in their appropriateness. The two-stage MCS and quadrature-based methods are complex and time consuming. Thus, where appropriate, EVPPI should be estimated using either the single MCS or UNLI method. However, where neither of these methods is appropriate, either of the two-stage MCS and quadrature methods should be used.

Probabilistic risk and uncertainty analysis for bioremediation of four chlorinated ethenes in groundwater

Groundwater contamination risk assessment for health-threatening compounds should benefit from a stochastic environmental risk assessment which considers the effects of biological, chemical, human behavioral, and physiological processes that involve elements of biotic and abiotic aquifer uncertainty, and human population variability. This paper couples a complex model of chemical degradation and transformation with movement in an aquifer undergoing bioremediation to generate a health risk analysis for different population cohorts in the community. A two-stage Monte Carlo simulation has separate stages for population variability and aquifer uncertainty yielding a computationally efficient and conceptually attractive algorithm. A hypothetical example illustrates how risk variance analysis can be conducted to determine the distribution of risk, and the relative impact of uncertainty and variability in different sets of parameters upon the variation of risk values for adults, adolescents, and children. The groundwater example considers a community water supply contaminated with chlorinated ethenes. Biodegradation pathways are enhanced by addition of butyrate. The results showed that the contribution of uncertainty to the risk variance is comparable to that of variability. Among the uncertain parameters considered, transmissivity accounted for the major part of the output variance. Children were the most susceptible and vulnerable population cohort.

Analytical Contaminant Transport Analysis System ( ACTS )—Multimedia Environmental Fate and Transport

The analytical contaminant transport analysis system (ACTS) is a computational analysis platform designed to assist environmental engineers and health scientists with assessing and quantifying environmental multimedia fate and transport of contaminants within four environmental transport pathways—air, soil, surface water, and groundwater. ACTS contains more than 100 models and associated analytical solutions that are available in the public domain. The solutions are provided under a unified computational platform and are accessed through an easy to learn and easy to use graphical user interface. A powerful feature of this analysis system is the ability to conduct probabilistic analyses using one- and two-stage Monte Carlo simulation that is dynamically linked to all pathway modules. External routines or third-party software are not required to conduct Monte Carlo simulations in ACTS. Publication-quality output for simulation results can be developed using the presentation utilities included in ACTS for al...

Monte Carlo simulation of the Leksell Gamma Knife®: I. Source modelling and calculations in homogeneous media

The Monte Carlo code PENELOPE has been used to simulate photon flux from the Leksell Gamma Knife®, a precision method for treating intracranial lesions. Radiation from a single 60Co assembly traversing the collimator system was simulated, and phase space distributions at the output surface of the helmet for photons and electrons were calculated. The characteristics describing the emitted final beam were used to build a two-stage Monte Carlo simulation of irradiation of a target. A dose field inside a standard spherical polystyrene phantom, usually used for Gamma Knife® dosimetry, has been computed and compared with experimental results, with calculations performed by other authors with the use of the EGS4 Monte Carlo code, and data provided by the treatment planning system Gamma Plan®. Good agreement was found between these data and results of simulations in homogeneous media. Owing to this established accuracy, PENELOPE is suitable for simulating problems relevant to stereotactic radiosurgery.

Modeled estimates of chlorpyrifos exposure and dose for the Minnesota and Arizona NHEXAS populations.

This paper presents a probabilistic, multimedia, multipathway exposure model and assessment for chlorpyrifos developed as part of the National Human Exposure Assessment Survey (NHEXAS). The model was constructed using available information prior to completion of the NHEXAS study. It simulates the distribution of daily aggregate and pathway-specific chlorpyrifos absorbed dose in the general population of the State of Arizona (AZ) and in children aged 3-12 years residing in Minneapolis-St. Paul, Minnesota (MSP). Pathways included were inhalation of indoor and outdoor air, dietary ingestion, non-dietary ingestion of dust and soil, and dermal contact with dust and soil. Probability distributions for model input parameters were derived from the available literature, and input values were chosen to represent chlorpyrifos concentrations and demographics in AZ and MSP to the extent possible. When the NHEXAS AZ and MSP data become available, they can be compared to the distributions derived in this and other prototype modeling assessments to test the adequacy of this pre-NHEXAS model assessment. Although pathway-specific absorbed dose estimates differed between AZ and MSP due to differences in model inputs between simulated adults and children, the aggregate model results and general findings for simulated AZ and MSP populations were similar. The major route of chlorpyrifos intake was food ingestion, followed by indoor air inhalation. Two-stage Monte Carlo simulation was used to derive estimates of both inter-individual variability and uncertainty in the estimated distributions. The variability in the model results reflects the difference in activity patterns, exposure factors, and concentrations contacted by individuals during their daily activities. Based on the coefficient of variation, indoor air inhalation and dust ingestion were most variable relative to the mean, primarily because of variability in concentrations due to use or no-use of pesticides. Uncertainty analyses indicated a factor of 10-30 for uncertainty of model predictions of 10th, 50th, and 90th percentiles. The greatest source of uncertainty in the model stems from the definition of no household pesticide use as no use in the past year. Because chlorpyrifos persists in the residential environment for longer than a year, the modeled estimates are likely to be low. More information on pesticide usage and environmental concentrations measured at different post-application times is needed to refine and evaluate this and other pesticide exposure models.

Simulating earthquake ground motion at a site, for given intensity and uncertain source location

Following a companion article, ground motion acceleration time histories during earthquakes can be described as realizations of non-stationary stochastic processes with evolutionary frequency content and instantaneous intensity. The parameters characterizing those processes can be handled as uncertain variables with probabilistic distributions that depend on the magnitude of each seismic event and the corresponding source-to-site distance. Accordingly, the generation of finite samples of artificial ground motion acceleration time histories for earthquakes of given intensities is formulated as a two-stage Monte Carlo simulation process. The first stage includes the simulation of samples of sets of the parameters of the stochastic process models of earthquake ground motion. The second stage includes the simulation of the time histories themselves, given the parameters of the associated stochastic process model. In order to account for the dependence of the probability distribution of the latter parameters on magnitude and source-to-site distance, the joint conditional probability distribution of these variables must be obtained for a given value of the ground motion intensity. This is achieved by resorting to Bayes Theorem about the probabilities of alternate assumptions. Two options for the conditional simulation of ground motion time histories are presented. The more refined option makes use of all the information about the conditional distribution of magnitude and distance for the purpose of simulating values of the statistical parameters of the ground motion stochastic process models. The second option considers all probabilities concentrated at the most likely combination of magnitude and distance for each of the seismic sources that contribute significantly to the seismic hazard at the site of interest.

Separating Variability and Uncertainty in Environmental Risk Assessment—Making Choices

This article reviews some of the current guidance concerning the separation of variability and uncertainty in presenting the results of human health and ecological risk assessments. Such guidance and some of the published examples of its implementation using two-stage Monte Carlo simulation methods have not emphasized the fact that there is considerable judgment involved in determining which input parameters can be modeled as purely variable or purely uncertain, and which require explicit treatment in both dimensions. Failure to discuss these choices leads to confusion and misunderstanding of the proposed methods. We conclude with an example illustrating some of the reasoning and statistical calculations that might be used to inform such choices.