62-XX STATISTICS
Refine
Document Type
- ZIB-Report (11)
- Doctoral Thesis (1)
Language
- English (12)
Is part of the Bibliography
- no (12)
Keywords
- Bayesian inference (2)
- DS-MLE (2)
- EM algorithm (2)
- Jeffreys prior (2)
- MPLE (2)
- NPMLE (2)
- Optimal Experimental Design (2)
- hyperparameter (2)
- hyperprior (2)
- principle of maximum entropy (2)
Institute
- Numerical Mathematics (6)
- Mathematical Optimization (5)
- Computational Systems Biology (3)
- Visual and Data-centric Computing (2)
- Computational Molecular Design (1)
- Geometric Data Analysis and Processing (1)
- Mathematical Optimization Methods (1)
- Mathematics of Transportation and Logistics (1)
- Therapy Planning (1)
- Uncertainty Quantification (1)
In the past few years several applications of optimal
experimental designs have emerged to optimize the measurements
in communication networks. The optimal design problems arising from
this kind of applications share three interesting properties:
(i) measurements are only available at a small number of locations of the network;
(ii) each monitor can simultaneously measure several quantities, which
can be modeled by ``multiresponse experiments";
(iii) the observation matrices depend on the topology of the network.
In this paper, we give an overview of these experimental design
problems and recall recent results for the computation of optimal
designs by Second Order Cone Programming (SOCP). New results for the
network-monitoring of a discrete time process are presented. In particular, we show
that the optimal design problem for the monitoring of an AR1 process can be reduced
to the standard form and we give experimental results.
We show that a class of semidefinite programs (SDP) admits a solution that is a positive semidefinite
matrix of rank at most $r$, where $r$ is the rank of the matrix involved in the objective function of the SDP.
The optimization problems of this class are semidefinite packing problems,
which are the SDP analogs to vector packing problems.
Of particular interest is the case in which our result guarantees the existence of a solution
of rank one: we show that the computation of this solution actually reduces to a
Second Order Cone Program (SOCP).
We point out an application in statistics, in the optimal design of experiments.