scholarly journals Product-form estimators: exploiting independence to scale up Monte Carlo

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Juan Kuntz ◽  
Francesca R. Crucinio ◽  
Adam M. Johansen
Keyword(s):  
Monte Carlo ◽  
Importance Sampling ◽  
Rapid Growth ◽  
Broad Class ◽  
Scale Up ◽  
Computational Cost ◽  
U Statistics ◽  
Class Of Estimators ◽  
Consistency And Asymptotic Normality ◽  
Independence Structure

AbstractWe introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target’s independence structure. We identify the most basic incarnations of these estimators with a class of generalized U-statistics and thus establish their unbiasedness, consistency, and asymptotic normality. Moreover, we show that they obtain the minimum possible variance amongst a broad class of estimators, and we investigate their computational cost and delineate the settings in which they are most efficient. We exemplify the merger of these estimators with other well known Monte Carlo estimators so as to better adapt the latter to the target’s independence structure and improve their performance. We do this via three simple mergers: one with importance sampling, another with importance sampling squared, and a final one with pseudo-marginal Metropolis–Hastings. In all cases, we show that the resulting estimators are well founded and achieve lower variances than their standard counterparts. Lastly, we illustrate the various variance reductions through several examples.

scholarly journals Drone Ground Impact Footprints with Importance Sampling: Estimation and Sensitivity Analysis

2021 ◽  
Vol 11 (9) ◽  
pp. 3871
Author(s):  
Jérôme Morio ◽  
Baptiste Levasseur ◽  
Sylvain Bertrand
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Importance Sampling ◽  
Loss Of Control ◽  
Minimum Volume ◽  
Multiple Importance Sampling ◽  
Impact Position ◽  
Engine Failure ◽  
Main Engine ◽  
Ground Impact

This paper addresses the estimation of accurate extreme ground impact footprints and probabilistic maps due to a total loss of control of fixed-wing unmanned aerial vehicles after a main engine failure. In this paper, we focus on the ground impact footprints that contains 95%, 99% and 99.9% of the drone impacts. These regions are defined here with density minimum volume sets and may be estimated by Monte Carlo methods. As Monte Carlo approaches lead to an underestimation of extreme ground impact footprints, we consider in this article multiple importance sampling to evaluate them. Then, we perform a reliability oriented sensitivity analysis, to estimate the most influential uncertain parameters on the ground impact position. We show the results of these estimations on a realistic drone flight scenario.

Multilevel Monte Carlo by using the Halton sequence

2020 ◽  
Vol 26 (3) ◽  
pp. 193-203
Author(s):  
Shady Ahmed Nagy ◽  
Mohamed A. El-Beltagy ◽  
Mohamed Wafa
Keyword(s):  
Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Computational Cost ◽  
Random Numbers ◽  
Multilevel Monte Carlo ◽  
Halton Sequence ◽  
Random Generator ◽  
Mc Simulation ◽  
Multilevel Monte Carlo Method

AbstractMonte Carlo (MC) simulation depends on pseudo-random numbers. The generation of these numbers is examined in connection with the Brownian motion. We present the low discrepancy sequence known as Halton sequence that generates different stochastic samples in an equally distributed form. This will increase the convergence and accuracy using the generated different samples in the Multilevel Monte Carlo method (MLMC). We compare algorithms by using a pseudo-random generator and a random generator depending on a Halton sequence. The computational cost for different stochastic differential equations increases in a standard MC technique. It will be highly reduced using a Halton sequence, especially in multiplicative stochastic differential equations.

Reliability Assessment of Power System Using Importance Sampling Technique Based on Layer Optimization Simulation

2011 ◽  
Vol 88-89 ◽  
pp. 554-558 ◽  
Author(s):  
Bin Wang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Power System ◽  
Importance Sampling ◽  
System Reliability ◽  
Sampling Method ◽  
Sampling Technique ◽  
Test System ◽  
Importance Sampling Method ◽  
Importance Sampling Technique

An improved importance sampling method with layer simulation optimization is presented in this paper. Through the solution sequence of the components’ optimum biased factors according to their importance degree to system reliability, the presented technique can further accelerate the convergence speed of the Monte-Carlo simulation. The idea is that the multivariate distribution’ optimization of components in power system is transferred to many steps’ optimization based on importance sampling method with different optimum biased factors. The practice is that the components are layered according to their importance degree to the system reliability before the Monte-Carlo simulation, the more forward, the more important, and the optimum biased factors of components in the latest layer is searched while the importance sampling is carried out until the demanded accuracy is reached. The validity of the presented is verified using the IEEE-RTS79 test system.

A new weighted fraction Monte Carlo method for particle coagulation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Xiao Jiang ◽  
Tat Leung Chan
Keyword(s):  
Monte Carlo ◽  
Design Methodology ◽  
Computational Cost ◽  
Particle Coagulation ◽  
Content Type ◽  
Aerosol Dynamics ◽  
Stochastic Error ◽  
Adjustable Weight ◽  
Initial Distributions ◽  
Coagulation Kernel

Purpose The purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method. Design/methodology/approach The weighted numerical particles are adopted in a similar manner to the multi-Monte Carlo (MMC) method, with the addition of a new fraction function (α). Probabilistic removal is also introduced to maintain a constant number scheme. Findings Three typical cases with constant kernel, free-molecular coagulation kernel and different initial distributions for particle coagulation are simulated and validated. The results show an excellent agreement between the Monte Carlo (MC) method and the corresponding analytical solutions or sectional method results. Further numerical results show that the critical stochastic error in the newly proposed WFMC method is significantly reduced when compared with the traditional MMC method for higher-order moments with only a slight increase in computational cost. The particle size distribution is also found to extend for the larger size regime with the WFMC method, which is traditionally insufficient in the classical direct simulation MC and MMC methods. The effects of different fraction functions on the weight function are also investigated. Originality Value Stochastic error is inevitable in MC simulations of aerosol dynamics. To minimize this critical stochastic error, many algorithms, such as MMC method, have been proposed. However, the weight of the numerical particles is not adjustable. This newly developed algorithm with an adjustable weight of the numerical particles can provide improved stochastic error reduction.

scholarly journals Uncertainties in estimating regional methane emissions from rice paddies due to data scarcity in the modeling approach

2014 ◽  
Vol 7 (3) ◽  
pp. 1211-1224 ◽  
Author(s):  
W. Zhang ◽  
Q. Zhang ◽  
Y. Huang ◽  
T. T. Li ◽  
J. Y. Bian ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Rice Variety ◽  
Scale Up ◽  
Methane Emissions ◽  
Data Availability ◽  
Scale Model ◽  
Anthropogenic Source ◽  
Rice Paddies ◽  
Data Scarcity

Abstract. Rice paddies are a major anthropogenic source of the atmospheric methane. However, because of the high spatial heterogeneity, making accurate estimations of the methane emission from rice paddies is still a big challenge, even with complicated models. Data scarcity is one of the substantial causes of the uncertainties in estimating the methane emissions on regional scales. In the present study, we discussed how data scarcity affected the uncertainties in model estimations of rice paddy methane emissions, from county/provincial scale up to national scale. The uncertainties in methane emissions from the rice paddies of China was calculated with a local-scale model and the Monte Carlo simulation. The data scarcities in five of the most sensitive model variables, field irrigation, organic matter application, soil properties, rice variety and production were included in the analysis. The result showed that in each individual county, the within-cell standard deviation of methane flux, as calculated via Monte Carlo methods, was 13.5–89.3% of the statistical mean. After spatial aggregation, the national total methane emissions were estimated at 6.44–7.32 Tg, depending on the base scale of the modeling and the reliability of the input data. And with the given data availability, the overall aggregated standard deviation was 16.3% of the total emissions, ranging from 18.3–28.0% for early, late and middle rice ecosystems. The 95% confidence interval of the estimation was 4.5–8.7 Tg by assuming a gamma distribution. Improving the data availability of the model input variables is expected to reduce the uncertainties significantly, especially of those factors with high model sensitivities.

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