Model-based Monte Carlo Simulation Research Articles

SARIMA Model-Based Monte Carlo Simulation of Option Contract Design for Maize Seasonal Heavy Precipitation in Shenyang

Agricultural production is highly dependent on weather conditions such as temperature, light, water and heat. The huge loss caused by extreme disaster weather makes the global insurance and reinsurance market overwhelmed, and seriously affects the enthusiasm of agricultural investment and the development of agricultural economy. With unique topography and vast territory, China is vulnerable to complex and diverse climate disasters. In recent years, the annual average economic loss caused by extreme weather disasters has reached about 200-300 billion yuan, among which floods caused by extreme heavy rainfall are the main agricultural disasters in China. In order to enhance the "farmer - insurance company - government" interest association to resist the risk of flood disaster caused by extreme heavy rainfall, financial hedging derivatives of weather disaster risk have gradually become a new hedging tool besides traditional insurance and reinsurance. This paper takes Shenyang, the main grain producing area in northeast China, as the sample of the study area, and uses the SARIMA model to obtain the distribution characteristics of seasonal rainfall time series. Different seasonal rainfall index option products (call option and put option contracts) are designed respectively, and the final option pricing is obtained by Monte Carlo stochastic simulation. The seasonal rainfall call option and put option contracts have opened up a new hedging model of agricultural extreme weather catastrophe outside the insurance and reinsurance market, which has enriched the varieties of weather financial derivatives market in China, reduced the severe impact of extreme weather disasters on agriculture, and enhanced the ability of agricultural stakeholders to resist the risk of extreme weather disasters.

GEOMETRIC UNCERTAINTY ANALYSIS OF A CENTRIFUGAL COMPRESSOR USING KRIGING MODEL

Centrifugal compressor, which is an important turbomachinery, plays a significant role in the gas turbine engine. Various uncertain factors in the manufacturing process can lead to the geometric variations, which often cause noticeable variations in compressor performance. In this paper, a surrogate-based uncertainty analysis method is used to investigate the effect of geometric uncertainty on the aerodynamic performance of a centrifugal compressor. Firstly, a scaled-up version of NASA DDA’s 404-III centrifugal compressor is chosen as the research object. Considering the structural features of the compressor, a parameterized model with 38 independent control parameters is established to define the geometry of the compressor, enabling rapid modification of the geometry. Then, a widely-used simulation method based on computational fluid dynamics is employed to predict the aerodynamic performance at a series of specified geometries generated using Latin Hypercube Design. Next, based on the sample data, two Kriging models are built to emulating the complex functional relationship between the control parameters and the performance of compressor. Finally, a Kriging model-based Monte Carlo simulation method is used to perform the geometric uncertainty analysis. After specifying a reasonable probability distribution for each control parameter, the statistical distributions of the compressor performance are obtained and analyzed. The analysis results yield new insights for compressor designers.

Population pharmacokinetics of the anti-PD-1 antibody camrelizumab in patients with multiple tumor types and model-informed dosing strategy.

Camrelizumab, a programmed cell death 1 (PD-1) inhibitor, has been approved for the treatment of patients with relapsed or refractory classical Hodgkin lymphoma, nasopharyngeal cancer and non-small cell lung cancer. The aim of this study was to perform a population pharmacokinetic (PK) analysis of camrelizumab to quantify the impact of patient characteristics and to investigate the appropriateness of a flat dose in the dosing regimen. A total of 3092 camrelizumab concentrations from 133 patients in four clinical trials with advanced melanoma, relapsed or refractory classical Hodgkin lymphoma and other solid tumor types were analyzed using nonlinear mixed effects modeling. The PKs of camrelizumab were properly described using a two-compartment model with parallel linear and nonlinear clearance. Then, covariate model building was conducted using stepwise forward addition and backward elimination. The results showed that baseline albumin had significant effects on linear clearance, while actual body weight affected intercompartmental clearance. However, their impacts were limited, and no dose adjustments were required. The final model was further evaluated by goodness-of-fit plots, bootstrap procedures, and visual predictive checks and showed satisfactory model performance. Moreover, dosing regimens of 200 mg every 2 weeks and 3 mg/kg every 2 weeks provided similar exposure distributions by model-based Monte Carlo simulation. The population analyses demonstrated that patient characteristics have no clinically meaningful impact on the PKs of camrelizumab and present evidence for no advantage of either the flat dose or weight-based dose regimen for most patients with advanced solid tumors.

System reliability analysis in spatially variable slopes using coupled Markov chain and MARS

The soil heterogeneity has a significant impact on the stability of geotechnical structures. The inherent variability of parameters in one soil type comes from different deposition and tectonic conditions. Furthermore, geological uncertainty could be described by the distribution of varying soil types. Therefore, considering both the inherent variability and geological uncertainty of soil parameters, we introduced a coupled Markov chain (CMC) model to simulate the soil heterogeneity utilizing the field borehole data. Additionally, we initiated an extended Multivariate Adaptive Regression Spline (MARS) model-based Monte Carlo simulation (MCS). This technique is used to overcome the limits of the traditional response surface method that assumed both order and type of polynomials to perform the probabilistic analysis, which occurred in slope reliability evaluation. Our results have shown that the proposed MARS-based MCS approach could effectively conduct the probabilistic analysis with enough accuracy. The comparison of the probabilities of failure obtained by the MARS-based MCS and the other methods suggested that both the robustness and high accuracy of the MARS-based MCS have been discussed in different spatially varied soils. Even though the differences between these three approaches are insignificant, the reliability results obtained by the MARS-based MCS agree better with the results of the direct MCS results. Thus, these calibrated results indicated that the proposed MARS-based MCS could perform the system reliability analysis effectively and accurately.

High-throughput discovery of high Curie point two-dimensional ferromagnetic materials

Databases for two-dimensional materials host numerous ferromagnetic materials without the vital information of Curie temperature since its calculation involves a manually intensive complex process. In this work, we develop a fully automated, hardware-accelerated, dynamic-translation based computer code, which performs first principles-based computations followed by Heisenberg model-based Monte Carlo simulations to estimate the Curie temperature from the crystal structure. We employ this code to conduct a high-throughput scan of 786 materials from a database to discover 26 materials with a Curie point beyond 400 K. For rapid data mining, we further use these results to develop an end-to-end machine learning model with generalized chemical features through an exhaustive search of the model space as well as the hyperparameters. We discover a few more high Curie point materials from different sources using this data-driven model. Such material informatics, which agrees well with recent experiments, is expected to foster practical applications of two-dimensional magnetism.

Uncertainty and global sensitivity analysis of bladed disk statics with material anisotropy and root geometry variations

Monocrystalline blades used in gas turbines exhibit material anisotropy, and the orientation of the anisotropy axis affects the deformation of the bladed disk. Considering the orientation of the anisotropy axis as a random design parameter, the uncertainty and sensitivity analysis for static blade deformations are presented for the first time. The following two cases are analyzed using a realistic bladed disk model with friction contacts: (i) deformation of the tuned bladed disks considering the uncertainty in anisotropy orientation and variations in fir tree root geometry and (ii) deformation of mistuned bladed disks with uncertain blade crystal orientations. For efficient uncertainty and sensitivity analysis, the applicability of the following surrogate models are explored: (i) an ensemble of regression trees (random forest) and (ii) gradient‐based polynomial chaos expansion. Faster convergence in statistical characteristics has been obtained using a surrogate model compared to that obtained from finite element model based Monte Carlo simulation. From sensitivity analysis, it has been inferred that the uncertainty in static displacements of a blade in a bladed disk is primarily due to the uncertainty in anisotropy angles of that blade itself and secondarily due to the interaction of different blade anisotropy angles.

Maximizing the Expected Information Gain of Cognitive Modeling via Design Optimization

To ensure robust scientific conclusions, cognitive modelers should optimize planned experimental designs a priori in order to maximize the expected information gain for answering the substantive question of interest. Both from the perspective of philosophy of science, but also within classical and Bayesian statistics, it is crucial to tailor empirical studies to the specific cognitive models under investigation before collecting any new data. In practice, methods such as design optimization, classical power analysis, and Bayesian design analysis provide indispensable tools for planning and designing informative experiments. Given that cognitive models provide precise predictions for future observations, we especially highlight the benefits of model-based Monte Carlo simulations to judge the expected information gain provided by different possible designs for cognitive modeling.

Hide-and-Seek with time-series filters: a model-based Monte Carlo study

Time-series filters have become a major tool for univariate and multivariate analysis of business cycles. Yet, the caveats of filtering, such as distortions in spectral density often mentioned in the literature, may have substantial implications for empirical analysis. This paper focuses on two main problems: univariate and multivariate spurious inferences. While detrending the real world data, the true cyclical component is unknown, which makes it problematic to assess the efficiency of time-series filters. Using model-based Monte Carlo simulations solves this issue by introducing four different scenarios with a known trend, cyclical components and shocks. The goal of this exercise is to create realistic long-run macroeconomic time-series. To assess the performance of the five well-established time-series filters, spectral densities of the detrended fluctuations are analyzed and changes in the cross-correlation structure and deviations from the original implied fluctuations are examined. Analysis confirms and complements findings from the existing literature and provides some new insights: (i) presence of the Gibbs–Wilbraham phenomenon (for the Christiano–Fitzgerald and Baxter–King filters), yet no obvious evidence of the Slutzky–Yule phenomenon; (ii) the erroneous choice of filtering bands may lead to spurious inferences about the spectral density peaks of the detrended fluctuations; (iii) preservation of the spectral pattern of the original regular and irregular components after detrending with minor changes in the magnitude of the spectral density peaks; (iv) substantial outlier changes in the cross-correlation structure. The latter distortion may have far-reaching implications for further time-series analysis and may lead to spurious inferences about the interaction between the detrended series.

PROBABILISTIC SHORELINE CHANGE MODELING AND RISK ESTIMATION OF EROSION

Prediction of long-term shoreline changes is a key task in planning and management of coastal zones and regional sediment management. Due to complex natural features of offshore waves, sediments, and longshore sediment transport, quantifying uncertainties of shoreline evolution and risks of extreme shoreline changes (erosion and accretion) is of vital importance for practicing uncertainty- or risk-based design of shorelines. This paper presents probabilistic shoreline change modeling to quantify uncertainties of shoreline variations by using numerical-model-based Monte-Carlo simulations. A shoreline evolution model, GenCade, is used to simulate longshore sediment transport and shoreline changes induced by random waves from offshore. A probability density function with a modified tail distribution is developed to capture stochastic features of wave heights under fair weather and storm conditions. It produces a time series of wave heights including small and extreme waves based on their probabilities (or frequencies of appearance). Probabilistic modeling of shoreline change is demonstrated by computing spatiotemporal variations of statistical parameters such as mean and variance of shoreline changes along an idealized coast bounded by two groins. Maximum shoreline changes in return years with a confidence range are also estimated by using maximum likelihood method. Reasonable results of obtained probabilistic shoreline changes reveal that this model-based Monte-Carlo simulation and uncertainty estimation approach are applicable to facilitate risk/uncertainty-based design and planning of shorelines.

Effect of battery longevity on costs and health outcomes associated with cardiac implantable electronic devices: a Markov model-based Monte Carlo simulation

IntroductionThe effects of device and patient characteristics on health and economic outcomes in patients with cardiac implantable electronic devices (CIEDs) are unclear. Modeling can estimate costs and outcomes for patients with CIEDs under a variety of scenarios, varying battery longevity, comorbidities, and care settings. The objective of this analysis was to compare changes in patient outcomes and payer costs attributable to increases in battery life of implantable cardiac defibrillators (ICDs) and cardiac resynchronization therapy defibrillators (CRT-D).Methods and resultsWe developed a Monte Carlo Markov model simulation to follow patients through primary implant, postoperative maintenance, generator replacement, and revision states. Patients were simulated in 3-month increments for 15 years or until death. Key variables included Charlson Comorbidity Index, CIED type, legacy versus extended battery longevity, mortality rates (procedure and all-cause), infection and non-infectious complication rates, and care settings. Costs included procedure-related (facility and professional), maintenance, and infections and non-infectious complications, all derived from Medicare data (2004–2014, 5% sample). Outcomes included counts of battery replacements, revisions, infections and non-infectious complications, and discounted (3%) costs and life years. An increase in battery longevity in ICDs yielded reductions in numbers of revisions (by 23%), battery changes (by 44%), infections (by 23%), non-infectious complications (by 10%), and total costs per patient (by 9%). Analogous reductions for CRT-Ds were 23% (revisions), 32% (battery changes), 22% (infections), 8% (complications), and 10% (costs).ConclusionBased on modeling results, as battery longevity increases, patients experience fewer adverse outcomes and healthcare costs are reduced. Understanding the magnitude of the cost benefit of extended battery life can inform budgeting and planning decisions by healthcare providers and insurers.

A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis

Surrogate models are often used to alleviate the computational burden for structural systems with expensively time-consuming simulations. In this paper, a new adaptive surrogate model based efficient reliability method is proposed to address the issues that many existing adaptive sequential sampling reliability methods are limited to the Kriging models and Krging model-based Monte Carlo simulation (MCS) reliability methods produce random results even without considering the uncertainty from initial samples. Three learning functions are developed for selecting the most suitable training sample points at each iteration, and the learning functions ψσ and ψm are generally suggested because they were found to perform a bit better in most of the cases. Furthermore, most of the newly selected training sample points are ensured to reside far away from existing sample points and reside as close to the limit-state functions as possible. Two stopping criterions are given to terminate the proposed adaptive sequential sampling algorithm. The main advantages of the proposed method are that it not only provides an efficient manner for structural reliability analysis with multiple failure modes to produce a determined result under without considering the uncertainty from initial samples, but also can be used, in principle, in any existing surrogate models. The accuracy and efficiency as well as applicability of the proposed method are demonstrated using three numerical examples.

Optimization of a Centrifugal Compressor Impeller for Robustness to Manufacturing Uncertainties

Compressor impellers for mass-market turbochargers are die-casted and machined with an aim to achieve high dimensional accuracy and acquire specific performance. However, manufacturing uncertainties result in dimensional deviations causing incompatible operational performance and assembly errors. Process capability limitations of the manufacturer can cause an increase in part rejections, resulting in high production cost. This paper presents a study on a centrifugal impeller with focus on the conceptual design phase to obtain a turbomachine that is robust to manufacturing uncertainties. The impeller has been parameterized and evaluated using a commercial computational fluid dynamics (CFDs) solver. Considering the computational cost of CFD, a surrogate model has been prepared for the impeller by response surface methodology (RSM) using space-filling Latin hypercube designs. A sensitivity analysis has been performed initially to identify the critical geometric parameters which influence the performance mainly. Sensitivity analysis is followed by the uncertainty propagation and quantification using the surrogate model based Monte Carlo simulation. Finally, a robust design optimization has been carried out using a stochastic optimization algorithm leading to a robust impeller design for which the performance is relatively insensitive to variability in geometry without reducing the sources of inherent variation, i.e., the manufacturing noise.

A Markov Model-based Monte Carlo Simulation to Assess Variation in Financial Burden and Health Outcomes for Cardiac Implantable Electronic Devices Based on Device and Patient Characteristics

A Markov Model-based Monte Carlo Simulation to Assess Variation in Financial Burden and Health Outcomes for Cardiac Implantable Electronic Devices Based on Device and Patient Characteristics

Modelling and forecasting wind speed intensity for weather risk management

The main interest of the wind speed modelling is on the short-term forecast of wind speed intensity and direction. Recently, its relationship with electricity production by wind farms has been studied. In fact, electricity producers are interested in long-range forecasts and simulation of wind speed for two main reasons: to evaluate the profitability of building a wind farm in a given location, and to offset the risks associated with the variability of wind speed for an already operating wind farm. Three approaches that are capable of forecasting and simulating the long run evolution of wind speed intensity are compared (wind direction is not a concern, given that the recent turbines can rotate to follow wind direction). The evaluated models are: the Auto Regressive Gamma process, the Gamma Auto Regressive process, and the ARFIMA–FIGARCH model. Both in-sample and out-of-sample comparisons are provided, as well as some examples for the pricing of wind speed derivatives using a model-based Monte Carlo simulation approach.

Modelling and Forecasting Wind Speed Intensity for Weather Risk Management

The modeling of wind speed is a traditional topic in meteorological researches where the main interest is on the short term forecast of wind speed intensity and direction. More recently this theme has received some interest in the quantitative finance literature for its relations with the electricity production by wind farms. In fact, electricity producers are interested in long range forecasts and simulation of wind speed for two main reasons: to evaluate the profitability of a wind farm to be built in a given location, and to offset the risks associated with the variability of wind speed for an already operating wind farm. In this paper we contribute to the increasing literature of environmental finance by comparing three approaches capable to forecast and simulate the long run evolution of wind speed intensity (direction is not a concern given that the recent turbines can rotate to follow wind speed): the Auto Regressive Gamma process, the Gamma Auto Regressive process, and the ARFIMA-FIGARCH model. We provide both in-sample and out-of-sample comparison of the models as well as some examples for the pricing of wind speed derivatives using a model based Monte Carlo simulation approach.