Variance reduction by importance sampling and the method of splitting in Monte Carlo calculations
Variance reduction by importance sampling and method of splitting in Monte Carlo calculations
Rosenbaum, B. M.↗
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Monte Carlo variance reduction
Computer program incorporates technique that reduces variance of forward Monte Carlo method for given amount of computer time in determining radiation environment in complex organic and inorganic systems exposed to significant amounts of radiation.
Byrn, N. R.↗
Variance reduction in Monte Carlo analysis of rarefied gas diffusion
The present analysis uses the Monte Carlo method to solve the problem of rarefied diffusion between parallel walls. The diffusing molecules are evaporated or emitted from one of two parallel walls and diffused through another molecular species. The analysis treats the diffusing molecule as undergoing a Markov random walk and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs the expected Markov walk payoff is retained but its variance is reduced so that the M. C. result has a much smaller error.
Perlmutter, M.↗
Variance reduction in Monte Carlo analysis of rarefied gas diffusion.
The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.
Perlmutter, M.↗
Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks
Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.
Perlmutter, M.↗
Monte Carlo variance reduction study
A mathematical analysis of the transport of nuclear radiation through matter is presented. A computer test bed that was developed is shown, along with flow charts.
Byrn, N. R.↗
Multi-Output Approximate Control Variate Estimation for Enhanced Variance Reduction
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Thomas Dixon↗
Dynamic and Regression Modeling of Ocean Variability in the Tide-Gauge Record at Seasonal and Longer Periods
Comparison of monthly mean tide-gauge time series to corresponding model time series based on a static inverted barometer (IB) for pressure-driven fluctuations and a ocean general circulation model (OM) reveals that the combined model successfully reproduces seasonal and interannual changes in relative sea level at many stations. Removal of the OM and IB from the tide-gauge record produces residual time series with a mean global variance reduction of 53%. The OM is mis-scaled for certain regions, and 68% of the residual time series contain a significant seasonal variability after removal of the OM and IB from the tide-gauge data. Including OM admittance parameters and seasonal coefficients in a regression model for each station, with IB also removed, produces residual time series with mean global variance reduction of 71%. Examination of the regional improvement in variance caused by scaling the OM, including seasonal terms, or both, indicates weakness in the model at predicting sea-level variation for constricted ocean regions. The model is particularly effective at reproducing sea-level variation for stations in North America, Europe, and Japan. The RMS residual for many stations in these areas is 25-35 mm. The production of "cleaner" tide-gauge time series, with oceanographic variability removed, is important for future analysis of nonsecular and regionally differing sea-level variations. Understanding the ocean model's strengths and weaknesses will allow for future improvements of the model.
Hill, Emma M.↗
Multi Model Monte Carlo with Python (MXMCPy)
Multi Model Monte Carlo with Python (\mxmc {}) is a software package developed as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Motivated by uncertainty propagation problems where classical Monte Carlo (MC) simulation is computationally intractable, various multi-model MC approaches have recently emerged that yield unbiased estimators with significantly reduced variance relative to MC for the same cost. These existing methods include multi-level Monte Carlo (MLMC), multi-fidelity Monte Carlo (MFMC), and approximate control variates (ACV). Given a fixed computational budget and a collection of models with varying cost/accuracy, each method seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. \mxmc {} is a versatile tool that enables convenient access to many existing multi-model MC approaches within one modular and extensible package. With \mxmc {}, users can easily compare existing methods to determine the best choice for their particular problem, while developers have a basis for implementing and sharing new variance reduction approaches. This report introduces the \mxmc {} software, providing a summary of the problem-solving workflow for users as well as a brief overview of the code layout for developers.
Geoffrey F Bomarito↗
Algorithm Performance Dataset from NASA Open-Source Software
NASA Langley Research Center has recently developed and released the open-source software Multi Model Monte Carlo with Python (MXMCPy- LAR-19756-1) as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Given a fixed computational budget and a collection of models with varying cost/accuracy, multi model Monte Carlo (MC) seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. MXMCPy is a versatile tool that enables convenient access to many existing multi-model MC approaches (over a dozen algorithms available) within one modular and extensible package [1]. With MXMCPy, users can easily compare existing methods to determine the best choice for their particular problem,while developers have a basis for implementing and sharing new variance reduction approaches. However,there is currently very little understanding about which algorithm will perform best for a given problem (defined by the correlation between and relative cost of the available models) without a brute force search.
Geoffrey F Bomarito↗
Long-Period Tidal Variations in the Length of Day
A new model of long-period tidal variations in length of day is developed. The model comprises 80 spectral lines with periods between 18.6 years and 4.7 days, and it consistently includes effects of mantle anelasticity and dynamic ocean tides for all lines. The anelastic properties followWahr and Bergen; experimental confirmation for their results now exists at the fortnightly period, but there remains uncertainty when extrapolating to the longest periods. The ocean modeling builds on recent work with the fortnightly constituent, which suggests that oceanic tidal angular momentum can be reliably predicted at these periods without data assimilation. This is a critical property when modeling most long-period tides, for which little observational data exist. Dynamic ocean effects are quite pronounced at shortest periods as out-of-phase rotation components become nearly as large as in-phase components. The model is tested against a 20 year time series of space geodetic measurements of length of day. The current international standard model is shown to leave significant residual tidal energy, and the new model is found to mostly eliminate that energy, with especially large variance reduction for constituents Sa, Ssa, Mf, and Mt.
LOD tidal oscillations↗
Monte Carlo Simulation of Nonlinear Radiation Induced Plasmas
A Monte Carlo simulation model for radiation induced plasmas with nonlinear properties due to recombination was, employing a piecewise linearized predict-correct iterative technique. Several important variance reduction techniques were developed and incorporated into the model, including an antithetic variates technique. This approach is especially efficient for plasma systems with inhomogeneous media, multidimensions, and irregular boundaries. The Monte Carlo code developed has been applied to the determination of the electron energy distribution function and related parameters for a noble gas plasma created by alpha-particle irradiation. The characteristics of the radiation induced plasma involved are given.
Wang, B. S.↗
Signal enhancement filters
Designed to smooth digital output of radar tracking system, two filters prevent noise-induced inaccuracies and result in input/output noise-variance reduction on order of 10:1. One filter is special purpose device with limited arithmetic-logic unit, and other is true programmable microprocessor.
Killen, H. B.↗
Microprocessor realizations of range rate filters
The performance of five digital range rate filters is evaluated. A range rate filter receives an input of range data from a radar unit and produces an output of smoothed range data and its estimated derivative range rate. The filters are compared through simulation on an IBM 370. Two of the filter designs are implemented on a 6800 microprocessor-based system. Comparisons are made on the bases of noise variance reduction ratios and convergence times of the filters in response to simulated range signals.
Source record↗
Waveform inversion of mantle Love waves: The born seismogram approach
Normal mode theory, extended to the slightly laterally heterogeneous Earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love waves (200-500 sec) for the Earth's lateral heterogeneity at l=2 and a spherically symmetric anelasticity (Q sub mu) structure. The data are from the Global Digital Seismograph Network (GDSN). The l=2 pattern is very similar to the results of other studies that used either different methods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analyzed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5% in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range can not constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.
Tanimoto, T.↗
Measurements of mantle wave velocities and inversion for lateral heterogeneity and anisotropy. I - Analysis of great circle phase velocities
The global lateral heterogeneity of the upper mantle is investigated using the classical Fourier-transform method of Sato(1958) and IDA/GDSN data from 25 1980 earthquakes. The great-circle phase velocities of 200 Love and 250 Rayleigh 100-330-sec-period fundamental-mode wave paths are determined and interpreted in terms of regional phase-velocity variation, using additional data on surface tectonics to extrapolate odd-harmonic information from the even-harmonic data. The results are presented in extensive tables, maps, and graphs. Regionalized inversion using the seven-region model of Okal (1977) is found to give maximum variance reductions of 65 percent for Love waves and 85 percent for Rayleigh waves, compared to 60 and 90 percent for l(max) = 2 inversion. Significant interregion differences are found in the regionalized Love-wave phase velocities.
Nakanishi, I.↗
Waveform inversion of mantle Love waves - The Born seismogram approach
Normal mode theory, extended to the slightly laterally heterogeneous earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love waves (200-500 sec) for the earth's lateral heterogeneity at l = 2 and a spherically symmetric anelasticity (Q sub mu) structure. The data are from the Global Digital Seismograph Network (GDSN). The l = 2 pattern is very similar to the results of other studies that used either different methods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analyzed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5 percent in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range can not constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.
Tanimoto, T.↗
On the evaluation of expected performance cost for partially observed closed-loop stochastic systems
New methods are presented for evaluating the expected performance cost of partially observed closed-loop stochastic systems. When the variances of the process statistics are small, a linearized model of the closed-loop stochastic system is defined for which the expected cost can be evaluated by recursion on a set of purely deterministic difference equations. When the variances of the process statistics are large, the linearized model can be used in the control variate method of variance reduction for reducing the number of sample paths required for effective Monte Carlo estimation.
Bayard, D. S.↗