Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.

Saddlepoint approximations

The saddlepoint method provides accurate approximations for the distributions of many test statistics, estimators and for important probabilities arising in various stochastic models. The saddlepoint approximation is a large deviations technique which is substantially more accurate than limiting normal or Edgeworth approximations, especially in presence of very small sample sizes or very small probabilities. The outstanding accuracy of the saddlepoint approximation can be explained by the fact that it has bounded relative error.

Stochastic simulation of rare events

Stochastic simulation is an important and practical technique for computing probabilities of rare events, like the payoff probability of a financial option, the probability that a queue exceeds a certain level or the probability of ruin of the insurer's risk process. Rare events occur so infrequently, that they cannot be reasonably recorded during a standard simulation procedure: specifc simulation algorithms which thwart the rarity of the event to simulate are required. An important algorithm in this context is based on changing the sampling distribution and it is called importance sampling. Optimal Monte Carlo algorithms for computing rare event probabilities are either logarithmic eficient or possess bounded relative error.

The trouble with quality filtering based on relative Cramér-Rao lower bounds.

Cramér Rao Lower Bounds (CRLB) have become the standard for expression of uncertainties in quantitative MR spectroscopy. If properly interpreted as a lower threshold of the error associated with model fitting, and if the limits of its estimation are respected, CRLB are certainly a very valuable tool to give an idea of minimal uncertainties in magnetic resonance spectroscopy (MRS), although other sources of error may be larger. Unfortunately, it has also become standard practice to use relative CRLB expressed as a percentage of the presently estimated area or concentration value as unsupervised exclusion criterion for bad quality spectra. It is shown that such quality filtering with widely used threshold levels of 20% to 50% CRLB readily causes bias in the estimated mean concentrations of cohort data, leading to wrong or missed statistical findings-and if applied rigorously-to the failure of using MRS as a clinical instrument to diagnose disease characterized by low levels of metabolites. Instead, absolute CRLB in comparison to those of the normal group or CRLB in relation to normal metabolite levels may be more useful as quality criteria. Magn Reson Med, 2015. © 2015 Wiley Periodicals, Inc.

Bounded Seas: Island Parsing Without Shipwrecks

Imprecise manipulation of source code (semi-parsing) is useful for tasks such as robust parsing, error recovery, lexical analysis, and rapid development of parsers for data extraction. An island grammar precisely defines only a subset of a language syntax (islands), while the rest of the syntax (water) is defined imprecisely. Usually, water is defined as the negation of islands. Albeit simple, such a definition of water is naive and impedes composition of islands. When developing an island grammar, sooner or later a programmer has to create water tailored to each individual island. Such an approach is fragile, however, because water can change with any change of a grammar. It is time-consuming, because water is defined manually by a programmer and not automatically. Finally, an island surrounded by water cannot be reused because water has to be defined for every grammar individually. In this paper we propose a new technique of island parsing - bounded seas. Bounded seas are composable, robust, reusable and easy to use because island-specific water is created automatically. We integrated bounded seas into a parser combinator framework as a demonstration of their composability and reusability.

Relative estimate of accuracy in orbit determination from a short tracklet

The Astronomical Institute of the University of Bern (AIUB) is conducting several search campaigns for orbital debris. The debris objects are discovered during systematic survey observations. In general only a short observation arc, or tracklet, is available for most of these objects. From this discovery tracklet a first orbit determination is computed in order to be able to find the object again in subsequent follow-up observations. The additional observations are used in the orbit improvement process to obtain accurate orbits to be included in a catalogue. In this paper, the accuracy of the initial orbit determination is analyzed. This depends on a number of factors: tracklet length, number of observations, type of orbit, astrometric error, and observation geometry. The latter is characterized by both the position of the object along its orbit and the location of the observing station. Different positions involve different distances from the target object and a different observing angle with respect to its orbital plane and trajectory. The present analysis aims at optimizing the geometry of the discovery observation is depending on the considered orbit.

Bounded seas

Abstract Imprecise manipulation of source code (semi-parsing) is useful for tasks such as robust parsing, error recovery, lexical analysis, and rapid development of parsers for data extraction. An island grammar precisely defines only a subset of a language syntax (islands), while the rest of the syntax (water) is defined imprecisely. Usually water is defined as the negation of islands. Albeit simple, such a definition of water is naive and impedes composition of islands. When developing an island grammar, sooner or later a language engineer has to create water tailored to each individual island. Such an approach is fragile, because water can change with any change of a grammar. It is time-consuming, because water is defined manually by an engineer and not automatically. Finally, an island surrounded by water cannot be reused because water has to be defined for every grammar individually. In this paper we propose a new technique of island parsing —- bounded seas. Bounded seas are composable, robust, reusable and easy to use because island-specific water is created automatically. Our work focuses on applications of island parsing to data extraction from source code. We have integrated bounded seas into a parser combinator framework as a demonstration of their composability and reusability.