Sensitivity analysis via likelihood ratios

ABSTRACT

We present a new method of obtaining derivatives of expectations with respect to various parameters. For example, if &lgr; is the rate of a Poisson process, NT is the number of Poisson events in (0, T),and &psgr; is nearly any function of the sample path (e.g. a performance measure in a queuing network), then we show that d/d&lgr; E&lgr;(&psgr;) = E&lgr; ((NT/&lgr; - T)&psgr;), which yields an obvious algorithm. We have proven that the method works for a wide class of parameters and performance measures in regenerative simulation. We also report on the method's limitations and on some numerical experiments.

REFERENCES

• 1: Bickel, P. J~ and Doksum, K. A. "'Mathematical Statistics: Basic Ideas with Selected Topics," Holden- Day, San Francisco, 1977.
• 2: Reiman, M. I. and Weiss, A. "Sensitivity Analysis for Simulations via Likelihood Ratios," submitted for publication, 1986.
• 3: Rubinstein, R. "'Sensitivity Analysis and Performance Extrapolation for Computer Simulation Models," submitted for publication, 1986.
• 4: Siegmund, D. "Importance Sampling in the Monte Carlo Study of Sequential Tests," Ann. Star., Vol. 14, No. 4, pp. 673-684, 1976.
• 5: Tolman, R. C. "The Principles of Statistical Mechanics," Dover, New York, 1979.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

Additional Classification:
  G. Mathematics of Computing

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

General Terms:
Design, Experimentation, Measurement, Performance, Theory, Verification