7,113 research outputs found
Uniformisation techniques for stochastic simulation of chemical reaction networks
This work considers the method of uniformisation for continuous-time Markov
chains in the context of chemical reaction networks. Previous work in the
literature has shown that uniformisation can be beneficial in the context of
time-inhomogeneous models, such as chemical reaction networks incorporating
extrinsic noise. This paper lays focus on the understanding of uniformisation
from the viewpoint of sample paths of chemical reaction networks. In
particular, an efficient pathwise stochastic simulation algorithm for
time-homogeneous models is presented which is complexity-wise equal to
Gillespie's direct method. This new approach therefore enlarges the class of
problems for which the uniformisation approach forms a computationally
attractive choice. Furthermore, as a new application of the uniformisation
method, we provide a novel variance reduction method for (raw) moment
estimators of chemical reaction networks based upon the combination of
stratification and uniformisation
Minimum variance stratification of a finite population
This paper considers the combined problem of allocation and stratification in order to minimise the variance of the expansion estimator of a total, taking into account that the population is finite. The proof of necessary minimum variance conditions utilises the Kuhn-Tucker Theorem. Stratified simple random sampling with non-negligible sampling fractions is an important design in sample surveys. We go beyond limiting assumptions that have often been used in the past, such as that the stratification equals the study variable or that the sampling fractions are small. We discuss what difference the sampling fractions will make for stratification. In particular, in many surveys the sampling fraction equals one for some strata. The main theorem of this paper is applied to two populations with different characteristics, one of them being a business population and the other one a small population of 284 Swedish municipalities. We study empirically the sensitivity of deviations from the optimal solution
Matching on-the-fly in Sequential Experiments for Higher Power and Efficiency
We propose a dynamic allocation procedure that increases power and efficiency
when measuring an average treatment effect in sequential randomized trials.
Subjects arrive iteratively and are either randomized or paired via a matching
criterion to a previously randomized subject and administered the alternate
treatment. We develop estimators for the average treatment effect that combine
information from both the matched pairs and unmatched subjects as well as an
exact test. Simulations illustrate the method's higher efficiency and power
over competing allocation procedures in both controlled scenarios and
historical experimental data.Comment: 20 pages, 1 algorithm, 2 figures, 8 table
Heuristic Algorithm for Univariate Stratification Problem
In sampling theory, stratification corresponds to a technique used in
surveys, which allows segmenting a population into homogeneous subpopulations
(strata) to produce statistics with a higher level of precision. In particular,
this article proposes a heuristic to solve the univariate stratification
problem - widely studied in the literature. One of its versions sets the number
of strata and the precision level and seeks to determine the limits that define
such strata to minimize the sample size allocated to the strata. A
heuristic-based on a stochastic optimization method and an exact optimization
method was developed to achieve this goal. The performance of this heuristic
was evaluated through computational experiments, considering its application in
various populations used in other works in the literature, based on 20
scenarios that combine different numbers of strata and levels of precision.
From the analysis of the obtained results, it is possible to verify that the
heuristic had a performance superior to four algorithms in the literature in
more than 94% of the cases, particularly concerning the known algorithms of
Kozak and Lavallee-Hidiroglou.Comment: 25 pages and 7 figure
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