A sequential Monte Carlo approach to computing tail probabilities in stochastic models

Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential Monte Carlo estimators, we show how resampling weights can be chosen to yield logarithmically efficient Monte Carlo estimates of large deviation probabilities for multidimensional Markov random walks.Comment: Published in at http://dx.doi.org/10.1214/10-AAP758 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities

Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given examples in which importance sampling measures that are consistent with large deviations can perform much worse than direct Monte Carlo. We address this problem by using certain mixtures of exponentially twisted measures for importance sampling. Their asymptotic optimality is established by using a new class of likelihood ratio martingales and renewal theory.Comment: Published at http://dx.doi.org/10.1214/105051606000000664 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices

Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices, multivariate empirical processes, and scan statistics in change-point and signal detection as special cases. Some key ingredients in these extensions are moderate deviation approximations to marginal tail probabilities and weak convergence of the conditional distributions of certain ``clumps'' around high-level crossings. We also discuss how these results are related to the Poisson clumping heuristic and tube formulas of Gaussian random fields, and describe their applications to laws of the iterated logarithm in the form of the Kolmogorov--Erd\H{o}s--Feller integral tests.Comment: Published at http://dx.doi.org/10.1214/009117905000000378 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A model for parton distributions in hadrons

The non-perturbative parton distributions in hadrons are derived from simple physical arguments resulting in an analytical expression for the valence parton distributions. The sea partons arise mainly from pions in hadronic fluctuations. The model gives new insights and a good description of structure function data.Comment: 3 pages, 4 figures, LaTeX. Contribution to DIS 99 worksho

Surgery for pelvic organ prolapse: the quest to reduce failure rates

Female pelvic organ prolapse (FPOP) is a debilitating condition. In Australia, 19% of women require prolapse surgery in their lifetime and recurrence rates range as high as 40 – 60% in the anterior compartment. Given the high surgical failure rate, this thesis aimed to identify the use of mesh to improve surgical outcomes utilising translabial ultrasound as the principal study method. In a retrospective analysis of mesh use in vaginal repair, anterior mesh proved to have a lower recurrence rate compared to native tissue repair, and anterior anchored mesh such as the PerigeeTM was of maximum benefit only in women who had a levator avulsion, a risk factor for prolapse recurrence. Apical anchoring supports were also evaluated in this thesis. Vaginally, the anterior ElevateTM was found to be inferior compared to the PerigeeTM, highlighting the possible poorer load-bearing capability of the self-fixating anterior ElevateTM anchors, whilst abdominally, there was still a very high rate of cystocele recurrence (>80%) despite excellent apical support in those that had laparoscopic sacrocolpopexy. Regardless of anchoring methods, mesh repair did not seem to completely compensate for the effect of levator avulsion and it did not confer additional benefit in women with an enlarged levator hiatal area, another risk factor for prolapse recurrence. The Puborectalis sling was designed to prevent excessive levator hiatal enlargement and proof of concept was achieved in a phase II observational pilot study of 110 women. There was a mean reduction of the levator hiatal area by 12cm2 sustained for over two years. During the course of this work, the rise in reported mesh related complications had also led to heated debates over its use in urogynaecology. Prolapse repair with mesh shifted from being readily embraced to complete withdrawal of use in many countries. This work hopes to contribute to the evolving mesh literature and to outline an alternative operative approach in women at high risk of prolapse recurrence