Counterexamples in importance sampling for large deviations probabilities

Glasserman, Paul; Wang, Yashan

doi:10.1214/aoap/1034801251

Cited by 125 publications

(153 citation statements)

References 24 publications

Supporting

Mentioning

147

Contrasting

Order By: Relevance

“…Though this seems natural, it is not trivial. Further, we could not find references, except for special cases of mixing exponentially tilted importance sampling densities, for instance Sadowsky and Bucklew (1990) and Glassermann and Wang (1997). Therefore we shall give sufficient conditions the mixed estimator to inherit efficiency from its component estimators, and prove the given results.…”

Section: Efficiency Of Mixed Importance Sampling Estimatorsmentioning

confidence: 95%

“…Furthermore, we let the mixing probabilities to be determined by an appropriate MCE program. We compare our estimator with these three other algorithms, and we find a large improvement over Glassermann and Wang (1997); Dupuis and Wang (2007), and a small improvement over Dupuis and Wang (2004).…”

mentioning

confidence: 91%

“…The importance sampling density for the jumps in this problem given in (3) is fixed throughout the sampling process, irrespective of the state S j = X 1 + · · · + X j after the first j jumps. Such state-independent importance sampling algorithms are known to be inefficient for models with nontrivial rare events (Glassermann and Wang 1997) or for queueing network models with buffer overflow rare events (de Boer 2006). Efficiency may be defined as follows (Heidelberger 1995;Bucklew 2004;L'Ecuyer et al 2008).…”

mentioning

confidence: 99%

“…jumps, and where a < E[X] < b such that state-independent importance sampling algorithms without mixing are inefficient (Glassermann and Wang 1997). We consider the estimator obtained by mixing two of our one-tailed estimators.…”

mentioning

confidence: 99%

“…The two-tailed problem has been studied before as a typical example where the 'naive' large deviations approach tends to fail logarithmic efficiency. These studies give resolutions as well: Glassermann and Wang (1997) propose a mixed importance sampling estimator; also Bucklew (2004) in Example 5.2.13 involving Gaussian jumps comes up with the same mixed estimator; Dupuis and Wang (2004) pursue another approach to construct a time-and state-dependent importance sampling algorithm based on the solution of an Isaacs equation; Dupuis and Wang (2007) give an algorithm based on a subsolution of an Isaacs equation. These three algorithms are proven to be logarithmically efficient.…”

mentioning

confidence: 99%

See 4 more Smart Citations

State-dependent importance sampling schemes via minimum cross-entropy

Ridder

Taimre

2009

Ann Oper Res

View full text Add to dashboard Cite

We present a method to obtain state-and time-dependent importance sampling estimators by repeatedly solving a minimum cross-entropy (MCE) program as the simulation progresses. This MCE-based approach lends a foundation to the natural notion to stop changing the measure when it is no longer needed. We use this method to obtain a stateand time-dependent estimator for the one-tailed probability of a light-tailed i.i.d. sum that is logarithmically efficient in general and strongly efficient when the jumps are Gaussian. We go on to construct an estimator for the two-tailed problem which is shown to be similarly efficient. We consider minor variants of the algorithm obtained via MCE, and present some numerical comparisons between our algorithms and others from the literature.

show abstract

Section: Efficiency Of Mixed Importance Sampling Estimatorsmentioning

confidence: 95%

mentioning

confidence: 91%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

State-dependent importance sampling schemes via minimum cross-entropy

Ridder

Taimre

2009

Ann Oper Res

View full text Add to dashboard Cite

show abstract

Monte Carlo Methods for Portfolio Credit Risk

Brereton

Kroese

Chan

2013

Credit Securitizations and Derivatives

View full text Add to dashboard Cite

Quantitative Differentiation: A General Formulation

Cheeger

2012

Comm Pure Appl Math

View full text Add to dashboard Cite

Let dx denote Lebesgue measure on R n . With respect to the measure C D r 1 dr dx on the collection of balls B r .x/ R n , the subcollection of balls B r .x/ B 1 .0/ has infinite measure. Let f W B 1 .0/ ! R have bounded gradient, jrf j Ä 1. For any B r .x/ B 1 .0/ there is a natural scale-invariant quantity that measures the deviation of f j B r .x/ from being an affine linear function. The most basic case of quantitative differentiation (due to Peter Jones) asserts that for all > 0, the measure of the collection of balls on which the deviation from linearity is is finite and controlled by , independent of the particular function f . The purpose of this paper is to explain the sense in which this model case is actually a particular instance of a general phenomenon that is present in many different geometric/analytic contexts. Essentially, in each case that fits the framework, to prove the relevant quantitative differentiation theorem, it suffices to verify that the family of relative defects is monotone and coercive. We indicate one recent application to theoretical computer science and others to partial regularity theory in geometric analysis and nonlinear PDEs.

show abstract

Counterexamples in importance sampling for large deviations probabilities

Cited by 125 publications

References 24 publications

State-dependent importance sampling schemes via minimum cross-entropy

State-dependent importance sampling schemes via minimum cross-entropy

Monte Carlo Methods for Portfolio Credit Risk

Quantitative Differentiation: A General Formulation

Contact Info

Product

Resources

About