9,519 research outputs found
Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics
We consider the problem of constructing optimal designs for population
pharmacokinetics which use random effect models. It is common practice in the
design of experiments in such studies to assume uncorrelated errors for each
subject. In the present paper a new approach is introduced to determine
efficient designs for nonlinear least squares estimation which addresses the
problem of correlation between observations corresponding to the same subject.
We use asymptotic arguments to derive optimal design densities, and the designs
for finite sample sizes are constructed from the quantiles of the corresponding
optimal distribution function. It is demonstrated that compared to the optimal
exact designs, whose determination is a hard numerical problem, these designs
are very efficient. Alternatively, the designs derived from asymptotic theory
could be used as starting designs for the numerical computation of exact
optimal designs. Several examples of linear and nonlinear models are presented
in order to illustrate the methodology. In particular, it is demonstrated that
naively chosen equally spaced designs may lead to less accurate estimation.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS324 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Binary Systematic Network Coding for Progressive Packet Decoding
We consider binary systematic network codes and investigate their capability
of decoding a source message either in full or in part. We carry out a
probability analysis, derive closed-form expressions for the decoding
probability and show that systematic network coding outperforms conventional
network coding. We also develop an algorithm based on Gaussian elimination that
allows progressive decoding of source packets. Simulation results show that the
proposed decoding algorithm can achieve the theoretical optimal performance.
Furthermore, we demonstrate that systematic network codes equipped with the
proposed algorithm are good candidates for progressive packet recovery owing to
their overall decoding delay characteristics.Comment: Proc. of IEEE ICC 2015 - Communication Theory Symposium, to appea
Convex Hulls, Oracles, and Homology
This paper presents a new algorithm for the convex hull problem, which is
based on a reduction to a combinatorial decision problem
POLYTOPE-COMPLETENESS-COMBINATORIAL, which in turn can be solved by a
simplicial homology computation. Like other convex hull algorithms, our
algorithm is polynomial (in the size of input plus output) for simplicial or
simple input. We show that the ``no''-case of
POLYTOPE-COMPLETENESS-COMBINATORIAL has a certificate that can be checked in
polynomial time (if integrity of the input is guaranteed).Comment: 11 pages, 2 figure
Tropical Cramer Determinants Revisited
We prove general Cramer type theorems for linear systems over various
extensions of the tropical semiring, in which tropical numbers are enriched
with an information of multiplicity, sign, or argument. We obtain existence or
uniqueness results, which extend or refine earlier results of Gondran and
Minoux (1978), Plus (1990), Gaubert (1992), Richter-Gebert, Sturmfels and
Theobald (2005) and Izhakian and Rowen (2009). Computational issues are also
discussed; in particular, some of our proofs lead to Jacobi and Gauss-Seidel
type algorithms to solve linear systems in suitably extended tropical
semirings.Comment: 41 pages, 5 Figure
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