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14
Parallel Computation of Multivariate Normal Probabilities
"... We present methods for the computation of multivariate normal probabilities on parallel/ distributed systems. After a transformation of the initial integral, an approximation can be obtained using MonteCarlo or quasirandom methods. We propose a metaalgorithm for asynchronous sampling methods and d ..."
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Cited by 207 (9 self)
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We present methods for the computation of multivariate normal probabilities on parallel/ distributed systems. After a transformation of the initial integral, an approximation can be obtained using MonteCarlo or quasirandom methods. We propose a metaalgorithm for asynchronous sampling methods and derive efficient parallel algorithms for the computation of MVN distribution functions, including a method based on randomized Korobov and Richtmyer sequences. Timing results of the implementations using the MPI parallel environment are given. 1 Introduction The computation of the multivariate normal distribution function F (a; b) = j\Sigmaj \Gamma 1 2 (2) \Gamma n 2 Z b a e \Gamma 1 2 x \Sigma \Gamma1 x dx: (1) often leads to computationalintensive integration problems. Here \Sigma is an n \Theta n symmetric positive definite covariance matrix; furthermore one of the limits in each integration variable may be infinite. Genz [5] performs a sequence of transformations resu...
Numerical Computation of Rectangular Bivariate And Trivariate normal and t probabilities
 STATISTICS AND COMPUTING
, 2004
"... Algorithms for the computation of bivariate and trivariate normal and t probabilities for rectangles are reviewed. The algorithms use numerical integration to approximate transformed probability distribution integrals. A generalization of Plackett's formula is derived for bivariate and trivaria ..."
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Cited by 54 (1 self)
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Algorithms for the computation of bivariate and trivariate normal and t probabilities for rectangles are reviewed. The algorithms use numerical integration to approximate transformed probability distribution integrals. A generalization of Plackett's formula is derived for bivariate and trivariate t probabilities. New methods are described for the numerical computation of bivariate and trivariate t probabilities. Test results are provided, along with recommendations for the most efficient algorithms for single and double precision computations.
Probabilistic Complexity Analysis for a Class of Approximate DFT Algorithms
, 1996
"... We present a probabilistic complexity analysis of a class of multistage algorithms which incrementally refine DFT approximations. Each stage of any algorithm in this class improves the results of the previous stage by a fixed increment in one of three dimensions: SNR, frequency resolution, or frequ ..."
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Cited by 4 (3 self)
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We present a probabilistic complexity analysis of a class of multistage algorithms which incrementally refine DFT approximations. Each stage of any algorithm in this class improves the results of the previous stage by a fixed increment in one of three dimensions: SNR, frequency resolution, or frequency coverage. However, the complexity of each stage is probabilistically dependent upon certain characteristics of the input signal. Assuming that an algorithm has to be terminated before its arithmetic cost exceeds a given limit, we have formulated a method for predicting the probability of completion of each of the algorithm's stages. This analysis is useful for lowpower and realtime applications where FFT algorithms cannot meet the specified limits on arithmetic cost. I. Introduction While the palette of transforms available to the DSP system designer continues to broaden, the utility of the DFT across a broad range of applications remains unparalleled. This fact can be attributed in p...
Incremental Refinement Structures for Approximate Signal Processing
, 1997
"... This work investigates approximate signal processing as a design philosophy supporting the realization of efficient, robust, and flexible digital signal processing systems through the use of incremental refinement structures that allow tradeoffs to be easily made between the accuracy or optimality o ..."
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Cited by 4 (1 self)
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This work investigates approximate signal processing as a design philosophy supporting the realization of efficient, robust, and flexible digital signal processing systems through the use of incremental refinement structures that allow tradeoffs to be easily made between the accuracy or optimality of results and the utilization of computing resources such as time, power, and chip area. The value of this approach is demonstrated through the theoretical development of incremental refinement structures for signal detection using the fast Fourier transform (FFT), image decoding using the twodimensional inverse discrete cosine transform (2D IDCT), and spectral analysis using the discrete Fourier transform (DFT). Using both deterministic and probabilistic techniques, the theoretical performance of these structures under various resource constraints is quantified in terms of welldefined measures such as probability of detection, SNR, and frequency resolution. These analyses are verified for...
Power Optimization for Digital Signal Processing in Reconfigurable Logic: Newsletter 2
"... Welcome to the second project newsletter. We have now completed the first year of the project, and ..."
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Cited by 2 (1 self)
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Welcome to the second project newsletter. We have now completed the first year of the project, and
Contents Overview........................................ 2 General Classes 3
, 2008
"... This package provides tools to compute densities, mass functions, distribution functions ..."
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This package provides tools to compute densities, mass functions, distribution functions
Contents Overview........................................ 2 General Classes 3
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Contents Overview........................................ 2 General Classes 3
, 2010
"... This package provides tools to compute densities, mass functions, distribution functions ..."
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This package provides tools to compute densities, mass functions, distribution functions