scholarly journals Genz and Mendell-Elston Estimation of the High-Dimensional Multivariate Normal Distribution

Algorithms ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 296
Author(s):  
Lucy Blondell ◽  
Mark Z. Kos ◽  
John Blangero ◽  
Harald H. H. Göring
Keyword(s):  
Monte Carlo ◽  
Statistical Analysis ◽  
Execution Time ◽  
Absolute Error ◽  
High Dimensional ◽  
Multivariate Normal ◽  
Multinomial Data ◽  
Efficient Performance ◽  
Simulation Based ◽  
Scale Characteristics

Statistical analysis of multinomial data in complex datasets often requires estimation of the multivariate normal (mvn) distribution for models in which the dimensionality can easily reach 10–1000 and higher. Few algorithms for estimating the mvn distribution can offer robust and efficient performance over such a range of dimensions. We report a simulation-based comparison of two algorithms for the mvn that are widely used in statistical genetic applications. The venerable Mendell-Elston approximation is fast but execution time increases rapidly with the number of dimensions, estimates are generally biased, and an error bound is lacking. The correlation between variables significantly affects absolute error but not overall execution time. The Monte Carlo-based approach described by Genz returns unbiased and error-bounded estimates, but execution time is more sensitive to the correlation between variables. For ultra-high-dimensional problems, however, the Genz algorithm exhibits better scale characteristics and greater time-weighted efficiency of estimation.

scholarly journals Exact likelihood-free Markov chain Monte Carlo for elliptically contoured distributions

2015 ◽  
Vol 14 (4) ◽  
Author(s):  
Patrick Muchmore ◽  
Paul Marjoram
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Stationary Distribution ◽  
Large Family ◽  
Multivariate Normal ◽  
Elliptically Contoured Distributions ◽  
Simulation Based ◽  
A Chain ◽  
Elliptically Contoured

AbstractRecent results in Markov chain Monte Carlo (MCMC) show that a chain based on an unbiased estimator of the likelihood can have a stationary distribution identical to that of a chain based on exact likelihood calculations. In this paper we develop such an estimator for elliptically contoured distributions, a large family of distributions that includes and generalizes the multivariate normal. We then show how this estimator, combined with pseudorandom realizations of an elliptically contoured distribution, can be used to run MCMC in a way that replicates the stationary distribution of a likelihood based chain, but does not require explicit likelihood calculations. Because many elliptically contoured distributions do not have closed form densities, our simulation based approach enables exact MCMC based inference in a range of cases where previously it was impossible.

Energy-saving design of variable-displacement bi-directional pump-controlled electrohydraulic system

2020 ◽  
pp. 095965182097389
Author(s):  
Samir Kumar Hati ◽  
Nimai Pada Mandal ◽  
Dipankar Sanyal
Keyword(s):  
Energy Saving ◽  
Absolute Error ◽  
Fast Response ◽  
Maximum Energy ◽  
Radial Clearance ◽  
Simulation Based Design ◽  
Simulation Based ◽  
Displacement Pump ◽  
Variable Displacement ◽  
Axial Piston

Losses in control valves drag down the average overall efficiency of electrohydraulic systems to only about 22% from nearly 75% for standard pump-motor sets. For achieving higher energy efficiency in slower systems, direct pump control replacing fast-response valve control is being put in place through variable-speed motors. Despite the promise of a quicker response, displacement control of pumps has seen slower progress for exhibiting undesired oscillation with respect to the demand in some situations. Hence, a mechatronic simulation-based design is taken up here for a variable-displacement pump–controlled system directly feeding a double-acting single-rod cylinder. The most significant innovation centers on designing an axial-piston pump with an electrohydraulic compensator for bi-directional swashing. An accumulator is conceived to handle the flow difference in the two sides across the load piston. A solenoid-driven sequence valve with P control is proposed for charging the accumulator along with setting its initial gas pressure by a feedforward design. Simple proportional–integral–derivative control of the compensator valve is considered in this exploratory study. Appropriate setting of the gains and critical sizing of the compensator has been obtained through a detailed parametric study aiming low integral absolute error. A notable finding of the simulation is the achievement of the concurrent minimum integral absolute error of 3.8 mm s and the maximum energy saving of 516 kJ with respect to a fixed-displacement pump. This is predicted for the combination of the circumferential port width of 2 mm for the compensator valve and the radial clearance of 40 µm between each compensator cylinder and the paired piston.

scholarly journals Voronoi diagram and Monte-Carlo simulation based finite element optimization for cost-effective 3D printing

2021 ◽  
Vol 50 ◽  
pp. 101301
Author(s):  
A.Z. Zheng ◽  
S.J. Bian ◽  
E. Chaudhry ◽  
J. Chang ◽  
H. Haron ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
3D Printing ◽  
Voronoi Diagram ◽  
Cost Effective ◽  
Simulation Based

Monte Carlo Simulation of Texture and Microstructure Transformation during Annealing of Steel

2007 ◽  
Vol 129 ◽  
pp. 83-87
Author(s):  
Hua Long Li ◽  
Jong Tae Park ◽  
Jerzy A. Szpunar
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Grain Boundary ◽  
Computer Model ◽  
Graphical Representation ◽  
Structural Characteristics ◽  
Polycrystalline Materials ◽  
Virtual Experiments ◽  
Grain Boundary Character ◽  
Simulation Based

Controlling texture and microstructure evolution during annealing processes is very important for optimizing properties of steels. Theories used to explain annealing processes are complicated and always case dependent. An recently developed Monte Carlo simulation based model offers an effective tool for studying annealing process and can be used to verify the arbitrarily defined theories that govern such processes. The computer model takes Orientation Image Microscope (OIM) measurements as an input. The abundant information contained in OIM measurement allows the computer model to incorporate many structural characteristics of polycrystalline materials such as, texture, grain boundary character, grain shape and size, phase composition, chemical composition, stored elastic energy, and the residual stress. The outputs include various texture functions, grain boundary and grain size statistics that can be verified by experimental results. Graphical representation allows us to perform virtual experiments to monitor each step of the structural transformation. An example of applying this simulation to Si steel is given.

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