4,019 research outputs found
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
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