Large deviations for weighted empirical measures arising in importance sampling

Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted empirical measure, where the weights are given by the likelihood ratio between the original distribution and the sampling distribution. In this paper the efficiency of an importance sampling algorithm is studied by means of large deviations for the weighted empirical measure. The main result, which is stated as a Laplace principle for the weighted empirical measure arising in importance sampling, can be viewed as a weighted version of Sanov's theorem. The main theorem is applied to quantify the performance of an importance sampling algorithm over a collection of subsets of a given target set as well as quantile estimates. The analysis yields an estimate of the sample size needed to reach a desired precision as well as of the reduction in cost for importance sampling compared to standard Monte Carlo

Large deviations for multidimensional state-dependent shot noise processes

Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot noise processes. The result covers previously known large deviation results for one dimensional state-independent shot noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness

The Limnology of Two Dissimilar Subarctic Streams and Implications of Resource Development

Because of the relatively undeveloped condition of arctic and subarctic Alaska, an opportunity is presented to draw up water quality management plans before extensive perturbation. These plans cannot, unfortunately , be based upon those drawn up for more temperate regions where much is known about natural stream conditions, for in these Alaskan areas, little is known about the natural physical, chemical, and biological cycles of streams or about their ability to handle the stresses that will be exerted on them should development take place. The Chena River, in subarctic, interior Alaska, near the city of Fairbanks, has been studied to evaluate the impact of pending construction and operation of flood control structures (Frey, Mueller and Berry, 1970). This river however has already been developed, especially along its lower reaches where the city of Fairbanks is situated. The watersheds of the two streams chosen for this study roughly parallel each other, although the Chatanika River watershed is about twice as long as that of Goldstream Creek. In addition to the dissimilarity in size, these two streams also differ in regard to terrain, at least along the respective stretches that were studied. The Goldstream Creek study area runs through a bog and extensive muskeg. The Chatanika River, however, was for the most part sampled in the area of mountainous terrain. The intent of this study was to obtain comprehensive physical and chemical data, to survey the resident invertebrates, and to evaluate the assimilative capabilities of both streams.This project was supported in part by funds (Proj. B-017-ALAS) provided by the United States Department of the Interior, Office of Water Resources Research, as authorized under the Water Resources Act of 1964, as amended. Equal support was provided by the State of Alaska as research funds (University of Alaska 234-2503)

Redetermination of parameters for semi-empirical model for spallogenic He and Ne in chondrites

A semi-empirical model described previously satisfactorily reproduced a number of shielding-dependent variations in the relative production rates of spallogenic He and Ne in chondrites. However, data for cores of the Keyes and St. Severin meteorites showed a subsurface build-up in He-3 which was not predicted with the original model parameters and the model was not pursued. Renewed interest in the preatmospheric size of meteorites, spurred in part by the desirability of understanding the exposure history of the SNC meteorites, justifies redetermination of model parameters

A Survey of Lentic Waters with Respect to Dissolved and Particulate Lead

Some of the strongest temperature inversions in the world occur at Fairbanks, Alaska. Benson (1970) has reported that a temperature gradient of 10 to 30C/1OO m is common in the winter inversions that form at Fairbanks. Air pollution is especially severe during these inversions when it is accompanied by the formation of ice crystals in the air, a condition known as ice fog. This phenomenon occurs when the temperature drops below -20F (-35C) (Benson, 1970), and it intensifies with time if the inversion is not broken. The ice crystals in this fog have been found to adsorb dust and gasses, including the lead halides which are present in the air as a result of the combustion of tetraethyl lead and/or other lead-hydrocarbon compounds used as anti-knock additives in automotive gasoline. Lazrus et al. (1970) have found lead concentrations in precipitation to be highly significantly correlated with the amount of gasoline used in the area sampled. There are two factors that bring the concentration of lead to high levels in ice fogs. Evaporation of the ice crystals tends to concentrate pollutants in the air mass, especially over the core area of the city where precipitation is retarded by the heating effect of the city. Also, during the extreme cold weather accompanying this phenomenon, many people allow their cars to idle when they are parked to increase performance and for reasons of personal comfort. Eventually, much of the pollutants suspended in the ice fog is precipitated and causes unnaturally high levels of lead in the snow. (Winchester et al., 1967). It is suspected that some of this particulate lead collected in the snow may be carried along with the associated surface runoff into 1entic (standing) surface waters during thawing. The objectives of this project were: 1. to measure the amount of dissolved and particulate lead in a number of selected 1entic waters in the Fairbanks area, and 2. to measure the amount of lead that has been incorporated into net plankton organisms located in the selected lentic waters.The work upon which this report is based was supported by funds (Project A-035-ALAS) provided by the United States Department of the Interior, Office of Water Resources Research, as authorized under the Water Resources Act of 1964, as amended