Antithetic Sampling with Multivariate Inputs

Wilson, James R.

doi:10.1080/01966324.1983.10737119

Cited by 18 publications

(6 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…But the problem is deeper than that. A result in measure theory (see p. 327 of Royden 1968; see Whitt 1976 andWilson 1983 for closely related applications) states that any "reasonable" probability space can be represented as the image of a measurable function on the unit interval with Lebesgue measure. This means that, in a precise sense, virtually any random object can be sampled by appropriately transforming a single uniform random variable, U.…”

Section: Optimality Of Crnmentioning

confidence: 99%

Some Guidelines and Guarantees for Common Random Numbers

1992

View full text Add to dashboard Cite

Common random numbers (CRN) is a widely-used technique for reducing variance in comparing stochastic systems through simulation. Its popularity derives from its intuitive appeal and ease of implementation. However, though CRN has been observed to work well with a broad range of models, the class of systems for which it is provably advantageous has remained rather limited. This paper has two purposes: We first discuss the effectiveness and optimality of CRN in a general setting, stressing the roles played by monotonicity and continuity properties. We then present specific, new classes of systems and comparisons for which CRN is beneficial and even optimal. Our conclusions for these systems are largely consistent with simulation practice and lend further theoretical support to folklore. Our results differ from those of previous analyses primarily because we put conditions on the timing of events, rather than the sequence of states, in a discrete-event simulation. We formulate our results in three settings corresponding to three applications of CRN: distributional comparisons, structural comparisons, and sensitivity analysis. In each case, we make use of conditions that simultaneously ensure monotonicity and continuity in the timing of events. These properties are established through explicit recursions for event epochs in terms of increasing, continuous functions.simulation, variance reduction techniques, stochastic ordering, common random numbers

show abstract

Section: Optimality Of Crnmentioning

confidence: 99%

Some Guidelines and Guarantees for Common Random Numbers

1992

View full text Add to dashboard Cite

show abstract

“…The mathematical basis for antithetic sampling is defined in work led by Hammersley (Hammersley and Morton, 1956;Hammersley and Mauldon, 1956;Hammersley and Handscomb, 1958) and Wilson (1979Wilson ( , 1983, and summarised by Fishman (1996). The method has mostly been applied within quantitative economics (Geweke, 1988) and finance (Paskov and Traub, 1995;Boyle et al, 1997).…”

Section: Antithetic Samplingmentioning

confidence: 99%

Comparison of the stochastic fields method and DQMoM-IEM as turbulent reaction closures

Akroyd¹,

Smith²,

McGlashan³

et al. 2010

Chemical Engineering Science

View full text Add to dashboard Cite

“…An image that captures fewer than 20 bands of the spectrum referred to as a multispectral image, and an image with 20 or more bands is called a hyperspectral image. All of this data is then stored in a three-dimensional hypermatrix , 8 referred to as a data cube, with the first two dimensions of the hypermatrix, x and y , being the location of the pixel in the image, and the third dimension, z , being the magnitude at each of the recorded EM bands. The image can be thought of as a series of vectors, one for each pixel location, that contains the wavelength magnitudes for each of the bands.…”

Section: Introductionmentioning

confidence: 99%

Outlier detection in hyperspectral imagery using closest distance to center with ellipsoidal multivariate trimming

Caulk

Reyes

Bauer

2011

Journal of Defense Modeling & Simulation

View full text Add to dashboard Cite

In this paper we examine the efficacy of using the closest distance to center algorithm in conjunction with ellipsoidal multivariate trimming (MVT) to find outliers in a hyperspectral image. MVT is applied here as a global anomaly detector on images that are pre-processed into clusters using a technique called X-means. Under the assumption that there are no more than 5% outliers in any given cluster set, we develop a method, based upon principal component analysis pre-processing, to create a flexible threshold for determining the percentage of data to retain with MVT. Using a retention percentage that more adequately reflects the actual number of outlier-free observations allows one to form estimates of the mean and covariance matrix that more effectively decrease the effects of swamping and masking as compared to using a set percentile for retention. These ideas are tested against real and synthetically generated hyperspectral imagery.

show abstract

Antithetic Sampling with Multivariate Inputs

Cited by 18 publications

References 8 publications

Some Guidelines and Guarantees for Common Random Numbers

Some Guidelines and Guarantees for Common Random Numbers

Comparison of the stochastic fields method and DQMoM-IEM as turbulent reaction closures

Outlier detection in hyperspectral imagery using closest distance to center with ellipsoidal multivariate trimming

Contact Info

Product

Resources

About