scholarly journals THE CAVALIERI ESTIMATOR WITH UNEQUAL SECTION SPACING REVISITED

2017 ◽  
Vol 36 (2) ◽  
pp. 135 ◽  
Author(s):  
Markus Kiderlen ◽  
Karl-Anton Dorph-Petersen
Keyword(s):  
Variance Reduction ◽  
Compact Object ◽  
Quadrature Rule ◽  
Special Situation ◽  
Randomized Sampling ◽  
Mild Conditions ◽  
Sampling Points ◽  
Random Variability ◽  
Simulation Results ◽  
Simpson's Rule

The Cavalieri method allows to estimate the volume of a compact object from area measurements in equidistant parallel planar sections. However, the spacing and thickness of sections can be quite irregular in applications. Recent publications have thus focused on the effect of random variability in section spacing, showing that the classical Cavalieri estimator is still unbiased when the stack of parallel planes is stationary, but that the existing variance approximations must be adjusted. The present paper considers the special situation, where the distances between consecutive section planes can be measured and thus where Cavalieri’s estimator can be replaced by a quadrature rule with randomized sampling points. We show that, under mild conditions, the trapezoid rule and Simpson’s rule lead to unbiased volume estimators and give simulation results that indicate that a considerable variance reduction compared to the generalized Cavalieri estimator can be achieved.

Asymptotic variance of Newton–Cotes quadratures based on randomized sampling points

2020 ◽  
Vol 52 (4) ◽  
pp. 1284-1307
Author(s):  
Mads Stehr ◽  
Markus Kiderlen
Keyword(s):  
Point Process ◽  
Asymptotic Variance ◽  
Compact Object ◽  
Quadrature Rule ◽  
Randomized Sampling ◽  
Riemann Sum ◽  
Sampling Points ◽  
Stationary Point Process ◽  
The Mean ◽  
Point Distance

AbstractWe consider the problem of numerical integration when the sampling nodes form a stationary point process on the real line. In previous papers it was argued that a naïve Riemann sum approach can cause a severe variance inflation when the sampling points are not equidistant. We show that this inflation can be avoided using a higher-order Newton–Cotes quadrature rule which exploits smoothness properties of the integrand. Under mild assumptions, the resulting estimator is unbiased and its variance asymptotically obeys a power law as a function of the mean point distance. If the Newton–Cotes rule is of sufficiently high order, the exponent of this law turns out to only depend on the point process through its mean point distance. We illustrate our findings with the stereological estimation of the volume of a compact object, suggesting alternatives to the well-established Cavalieri estimator.

Modeling for Optimization (MO-OP): Tools for Manufacturing and Design Engineering Problems

2001 ◽  
Author(s):  
Mohamed H. Gadallah ◽  
Hazim El-Mounayri
Keyword(s):  
Variance Reduction ◽  
Optimization Technique ◽  
Tolerance Allocation ◽  
Process Selection ◽  
Engineering Problems ◽  
Simulation Results ◽  
Standard Designs ◽  
Performance Of Algorithm ◽  
Composite Designs

Abstract In this paper, a new statistical optimization technique is proposed. The technique employs new variance reduction schemes (VRTs). The performance of three standard designs: L27/L27 OA, L54/L27 OA and L243 / L27 OA are studied. These designs, although both orthogonal and balanced, exhibit high variance reduction properties with questionable convergence in very short number of iterations. Four new composite designs are developed, implemented and compared with the standard ones. These designs are known as: 5-, 7-, 9- and 11-point composite L27 OA. The problem of tolerance allocation with optimal process selection is revisited as a case study for simulation. Results indicate the efficiency of these new designs to reduce variances to lower levels than standard designs and better convergence in fraction of experiments. These designs are then integrated in an optimization algorithm previously developed (Gadallah, M.H., 2000). The algorithm is then modified to deal with the least sensitive optimal solutions for standard and composite designs. Particularly, the parameters that affect the algorithm are varied and their effects on performance of algorithm are studied. A standard manufacturing case study is used for analysis and simulation results for the composite designs are also given.

scholarly journals Between-season attraction of cotton boll weevil, Anthonomus grandis Boh. (Coleoptera: Curculionidae) adults by its aggregation pheromone

2001 ◽  
Vol 58 (2) ◽  
pp. 229-234 ◽  
Author(s):  
Wedson Desidério Fernandes ◽  
Sérgio Luis de Carvalho ◽  
Mohamed Habib
Keyword(s):  
Aggregation Pheromone ◽  
Chemical Control ◽  
Prey Availability ◽  
Evaluation Process ◽  
Boll Weevil ◽  
Anthonomus Grandis ◽  
Cotton Boll ◽  
Randomized Sampling ◽  
Sampling Points ◽  
To Receive

The present study was undertaken to investigate the attractiveness of boll weevil adults by its aggregation pheromone under winter field conditions. Two experimental fields were utilized at "Casa Branca", SP, Brazil. For each one, three areas were established near the refuge vegetation, sparated 500 m from each other. Each area was divided in three sub-areas or blocks of 100 m² to receive pheromone applications (2.5 g per block). In addition to the pre-application counting, five additional evaluations were carried out after the pheromone applicaton. Ten randomized sampling points per block were considered in each evaluation process. A. grandis adults responded immediately to the pheromone applications, and were captured for 14 days . The highest level of attractiveness was observed 24 hours after application. The application of the boll weevil aggregation pheromone during winter could increase the predation by natural enemies, due to the increase of prey availability. Chemical control can be recommended 24 hours after pheromone applications in small plots as a between-season strategy for the suppression of boll weevil adults.

scholarly journals AN ADAPTIVE METHOD FOR EVALUATING MULTIDIMENSIONAL CONTINGENT CLAIMS: PART II

2003 ◽  
Vol 06 (04) ◽  
pp. 327-353 ◽  
Author(s):  
LARS O. DAHL
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
Variance Reduction ◽  
Adaptive Method ◽  
Unit Cube ◽  
Random Numbers ◽  
Quasi Monte Carlo ◽  
Low Discrepancy Sequences ◽  
Pricing Problems ◽  
Simulation Results

This is part two of a work on adaptive integration methods aimed at multidimensional option pricing problems in finance. It presents simulation results of an adaptive method developed in the companion article [3] for the evaluation of multidimensional integrals over the unit cube. The article focuses on a rather general test problem constructed to give insights in the success of the adaptive method for option pricing problems. We establish a connection between the decline rate of the ordered eigenvalues of the pricing problem and the efficiency of the adaptive method relative to the non-adaptive. This gives criteria for when the adaptive method can be expected to outperform the non-adaptive for other pricing problems. In addition to evaluating the method for different problem parameters, we present simulation results after adding various techniques to enhance the adaptive method itself. This includes using variance reduction techniques for each sub-problem resulting from the partitioning of the integration domain. All simulations are done with both pseudo-random numbers and quasi-random numbers (low discrepancy sequences), resulting in Monte Carlo (MC) and quasi-Monte Carlo (QMC) estimators and the ability to compare them in the given setting. The results show that the adaptive method can give performance gains in the order of magnitudes for many configurations, but it should not be used incautious, since this ability depends heavily on the problem at hand.

Identification for Chaos and Subharmonic Responses in Coupled Forced Duffing's Oscillators

2011 ◽  
Vol 27 (1) ◽  
pp. 139-147 ◽  
Author(s):  
J.-D. Jeng ◽  
Y. Kang ◽  
Y.-P. Chang
Keyword(s):  
Nonlinear Oscillators ◽  
High Order ◽  
Quantitative Characterization ◽  
Section Method ◽  
Sampling Points ◽  
Integral Quantity ◽  
Simulation Results ◽  
Signal Response

ABSTRACTIn this paper, a response integral quantity method is proposed. This technique provides a quantitative characterization of system responses and can assist the role of the traditional stroboscopic technique (Poincaré section method) in observing bifurcations and chaos of the nonlinear oscillators. We numerically analyze and identify the chaos and subharmonic responses in the forced coupled Duffing's oscillators in which we find that chaotic behaviors and high-order subharmonic responses exist. Due to the signal response contamination of system, it is difficult to identify the high-order responses of the subharmonic motion because of the sampling points on Poincaré map being very close to each other. Even the system responses are subject to misjudgments. The simulation results, however, show that the highorder subharmonic and chaotic responses and their bifurcations can be observed effectively.

Non-uniform Randomized Sampling for Multivariate Approximation by High Order Parzen Windows

2011 ◽  
Vol 54 (3) ◽  
pp. 566-576
Author(s):  
Xiang-Jun Zhou ◽  
Lei Shi ◽  
Ding-Xuan Zhou
Keyword(s):  
Density Function ◽  
High Order ◽  
Multivariate Approximation ◽  
Probability Measures ◽  
Multivariate Functions ◽  
Uniform Sampling ◽  
Randomized Sampling ◽  
Parzen Windows ◽  
Sampling Points ◽  
Non Uniform Sampling

AbstractWe consider approximation of multivariate functions in Sobolev spaces by high order Parzen windows in a non-uniform sampling setting. Sampling points are neither i.i.d. nor regular, but are noised from regular grids by non-uniform shifts of a probability density function. Sample function values at sampling points are drawn according to probability measures with expected values being values of the approximated function. The approximation orders are estimated by means of regularity of the approximated function, the density function, and the order of the Parzen windows, under suitable choices of the scaling parameter.

Comparison of quadrature and regression based generalized polynomial chaos expansions for structural acoustics

2021 ◽  
Vol 263 (6) ◽  
pp. 863-874
Author(s):  
Gage Walters ◽  
Andrew Wixom ◽  
Sheri Martinelli
Keyword(s):  
Polynomial Chaos ◽  
Quadrature Rule ◽  
Test Problems ◽  
Random Input ◽  
Generalized Polynomial Chaos ◽  
Stochastic Sampling ◽  
Generalized Polynomial ◽  
Sampling Points ◽  
Input Variables ◽  
Polynomial Chaos Expansions

This work performs a direct comparison between generalized polynomial chaos (GPC) expansion techniques applied to structural acoustic problems. Broadly, the GPC techniques are grouped in two categories: , where the stochastic sampling is predetermined according to a quadrature rule; and , where an arbitrary selection of points is used as long as they are a representative sample of the random input. As a baseline comparison, Monte Carlo type simulations are also performed although they take many more sampling points. The test problems considered include both canonical and more applied cases that exemplify the features and types of calculations commonly arising in vibrations and acoustics. A range of different numbers of random input variables are considered. The primary point of comparison between the methods is the number of sampling points they require to generate an accurate GPC expansion. This is due to the general consideration that the most expensive part of a GPC analysis is evaluating the deterministic problem of interest; thus the method with the fewest sampling points will often be the fastest. Accuracy of each GPC expansion is judged using several metrics including basic statistical moments as well as features of the actual reconstructed probability density function.

Losses of atrazine, metolachlor, prosulfuron and triasulfuron in subsurface drain water. II. Simulation results

Agronomie ◽  
2002 ◽  
Vol 22 (4) ◽  
pp. 413-425 ◽  
Author(s):  
Matteo Balderacchi ◽  
Ghasam Alavi ◽  
Ettore Capri ◽  
Alberto Vicari ◽  
Cesare Accinelli ◽  
...  
Keyword(s):  
Drain Water ◽  
Simulation Results

Study and design of dual stator permanent magnet machine with spoke-type configurations using phase-group concentrated-coil windings

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1381-1389
Author(s):  
Dezhi Chen ◽  
Chengwu Diao ◽  
Zhiyu Feng ◽  
Shichong Zhang ◽  
Wenliang Zhao
Keyword(s):  
Permanent Magnet ◽  
Permanent Magnets ◽  
Low Cost ◽  
Dynamic Performance ◽  
Torque Ripple ◽  
Permanent Magnet Machine ◽  
Torque Density ◽  
Phase Group ◽  
High Torque ◽  
Simulation Results

In this paper, a novel dual-stator permanent magnet machine (DsPmSynM) with low cost and high torque density is designed. The winding part of the DsPmSynM adopts phase-group concentrated-coil windings, and the permanent magnets are arranged by spoke-type. Firstly, the winding structure reduces the amount of copper at the end of the winding. Secondly, the electromagnetic torque ripple of DsPmSynM is suppressed by reducing the cogging torque. Furthermore, the dynamic performance of DsPmSynM is studied. Finally, the experimental results are compared with the simulation results.

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