Advertisement

Fundamentals of Statistical Analysis

  • Ruijing Shen
  • Sheldon X.-D. Tan
  • Hao Yu
Chapter

Abstract

To make this book self-contained, this chapter will review relevant mathematical concepts used in this book. We first review basic probability and statistical concepts used in this book. Then we introduce mathematic notations for statistical processes with multiple variable and variable reduction methods. We will then go through some statistical analysis approaches such as the MC method and the spectral stochastic method. Finally, we will discuss some fast techniques to compute some of random variables with log-normal distributions.

Keywords

Hermite Polynomial Quadrature Point Sparse Grid Gate Oxide Thickness Exponential Convergence Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 13.
    H. Chang and S. S. Sapatnekar, “Full-chip analysis of leakage power under process variations, including spatial correlations,” in Proc. IEEE/ACM Design Automation Conference (DAC), 2005, pp. 523–528.Google Scholar
  2. 41.
    G. F. Fishman, Monte Carlo, concepts, algorithms, and Applications. Springer, 1996.Google Scholar
  3. 44.
    R. Ghanem, “The nonlinear Gaussian spectrum of log-normal stochastic processes and variables,” Journal of Applied Mechanics, vol. 66, pp. 964–973, December 1999.CrossRefGoogle Scholar
  4. 45.
    R. G. Ghanem and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach. Dover Publications, 2003.Google Scholar
  5. 70.
    A. Iserles, A First Course in the Numerical Analysis of Differential Equations, 3rd ed. Cambridge University, 1996.Google Scholar
  6. 74.
    R. Jiang, W. Fu, J. M. Wang, V. Lin, and C. C.-P. Chen, “Efficient statistical capacitance variability modeling with orthogonal principle factor analysis,” in Proc. Int. Conf. on Computer Aided Design (ICCAD), 2005, pp. 683–690.Google Scholar
  7. 75.
    I. T. Jolliffe, Principal Component Analysis. Springer-Verlag, 1986.Google Scholar
  8. 95.
    P. Li and W. Shi, “Model order reduction of linear networks with massive ports via frequency-dependent port packing,” in Proc. Design Automation Conf. (DAC), 2006, pp. 267–272.Google Scholar
  9. 101.
    Y. Liu, S. Nassif, L. Pileggi, and A. Strojwas, “Impact of interconnect variations on the clock skew of a gigahertz microprocessor,” in Proc. IEEE/ACM Design Automation Conference (DAC), 2000, pp. 168–171.Google Scholar
  10. 109.
    N. Mi, J. Fan, S. X.-D. Tan, Y. Cai, and X. Hong, “Statistical analysis of on-chip power delivery networks considering lognormal leakage current variations with spatial correlations,” IEEE Trans. on Circuits and Systems I: Fundamental Theory and Applications, vol. 55, no. 7, pp. 2064–2075, Aug 2008.MathSciNetCrossRefGoogle Scholar
  11. 126.
    E. Novak and K. Ritter, “Simple cubature formulas with high polynomial exactness,” Constructive Approximation, vol. 15, no. 4, pp. 449–522, Dec 1999.MathSciNetCrossRefGoogle Scholar
  12. 132.
    A. Papoulis and S. Pillai, Probability, Random Variables and Stochastic Processes. McGraw-Hill, 2001.Google Scholar
  13. 169.
    A. Srivastava, R. Bai, D. Blaauw, and D. Sylvester, “Modeling and analysis of leakage power considering within-die process variations,” in Proc. Int. Symp. on Low Power Electronics and Design (ISLPED), Aug 2002, pp. 64–67.Google Scholar
  14. 187.
    S. Vrudhula, J. M. Wang, and P. Ghanta, “Hermite polynomial based interconnect analysis in the presence of process variations,” IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, vol. 25, no. 10, 2006.Google Scholar
  15. 196.
    D. Xiu and G. Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Scientific Computing, vol. 24, no. 2, pp. 619–644, Oct 2002.MathSciNetMATHCrossRefGoogle Scholar
  16. 197.
    D. Xiu and G. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. of Computational Physics, vol. 187, no. 1, pp. 137–167, May 2003.MathSciNetMATHCrossRefGoogle Scholar
  17. 204.
    W. Yu, C. Hu, and W. Zhang, “Variational capacitance extraction of on-chip interconnects based on continuous surface model,” in Proc. IEEE/ACM Design Automation Conference (DAC), July 2009, pp. 758–763.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Ruijing Shen
    • 1
  • Sheldon X.-D. Tan
    • 1
  • Hao Yu
    • 2
  1. 1.Department of Electrical EngineeringUniversity of CaliforniaRiversideUSA
  2. 2.Department of Electrical and ElectronicNanyang Technological UniversitySingaporeSingapore

Personalised recommendations