# Estimation of parameters in a network reliability model with spatial dependence

ESAIM: Probability and Statistics (2005)

- Volume: 9, page 241-253
- ISSN: 1292-8100

## Access Full Article

top## Abstract

top## How to cite

topDinwoodie, Ian Hepburn. "Estimation of parameters in a network reliability model with spatial dependence." ESAIM: Probability and Statistics 9 (2005): 241-253. <http://eudml.org/doc/245601>.

@article{Dinwoodie2005,

abstract = {An iterative method based on a fixed-point property is proposed for finding maximum likelihood estimators for parameters in a model of network reliability with spatial dependence. The method is shown to converge at a geometric rate under natural conditions on data.},

author = {Dinwoodie, Ian Hepburn},

journal = {ESAIM: Probability and Statistics},

keywords = {Curie-Weiss; EM-algorithm; iterative proportional scaling; maximum likelihood; network tomography},

language = {eng},

pages = {241-253},

publisher = {EDP-Sciences},

title = {Estimation of parameters in a network reliability model with spatial dependence},

url = {http://eudml.org/doc/245601},

volume = {9},

year = {2005},

}

TY - JOUR

AU - Dinwoodie, Ian Hepburn

TI - Estimation of parameters in a network reliability model with spatial dependence

JO - ESAIM: Probability and Statistics

PY - 2005

PB - EDP-Sciences

VL - 9

SP - 241

EP - 253

AB - An iterative method based on a fixed-point property is proposed for finding maximum likelihood estimators for parameters in a model of network reliability with spatial dependence. The method is shown to converge at a geometric rate under natural conditions on data.

LA - eng

KW - Curie-Weiss; EM-algorithm; iterative proportional scaling; maximum likelihood; network tomography

UR - http://eudml.org/doc/245601

ER -

## References

top- [1] O. Barndorff-Nielsen, Information and Exponential Families. Wiley, New York (1978). Zbl0387.62011MR489333
- [2] T. Bu, N. Duffield, F. Lo Presti and D. Towsley, Network tomography on general topologies. Proc. ACM Sigmetrics 2002, Marina Del Ray, June 15–19 (2002).
- [3] R. Cáceres, N.G. Duffield, J. Horowitz, D. Towsley and T. Bu, Multicast-based inference of network internal characteristics: accuracy of packet loss estimation. IEEE Trans. Inform. Theory 45 (2000) 2462–2480. Zbl0961.94002
- [4] M. Coates, A.O. Hero, R. Nowak and B. Yu, Internet tomography. IEEE Signal Processing Magazine 19 (2002) 47–65.
- [5] J.N. Darroch and D. Ratcliff, Generalized iterative scaling for log-linear models. Ann. Math. Stat. 43 (1972) 1470–1480. Zbl0251.62020
- [6] A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B 39 (1997) 1–38. Zbl0364.62022
- [7] I.H. Dinwoodie and E. Mosteig, Statistical inference for network reliability with spatial dependence. SIAM J. Discrete Math. 16 (2003) 663–674. Zbl1047.62094
- [8] N. Duffield, J. Horowitz, D. Towsley, W. Wei and T. Friedman, Multicast-based loss inference with missing data. IEEE J. Selected Areas Communications 20 (2002) 700–713.
- [9] C. Ji and A. Elwalid, Measurement-based network monitoring and inference: scalability and missing information. IEEE J. Selected Areas Communications 20 (2002) 714–725.
- [10] G. Liang and B. Yu, Maximum pseudo-likelihood estimation in network tomography. IEEE Trans. Signal Process. 51 (2003) 2043–2053.
- [11] M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Boston (1964). Zbl0126.02404MR162808
- [12] P. Parrilo and B. Sturmfels, Minimizing polynomial functions. http://xyz.lanl.gov/abs/math.OC/0103170 (2002). Zbl1099.13516MR1995016
- [13] Y. Tsang, M. Coates and R. Nowak, Passive network tomography using EM algorithms. Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, Utah 3 (May 2001) 1469–1472.
- [14] C.F. Jeff Wu, On the convergence of the EM algorithm. Ann. Statist. 11 (1983) 95–103. Zbl0517.62035
- [15] B. Xi, G. Michailidis and V.N. Nair, Estimating network internal losses using a new class of probing experiments. University of Michigan Department of Statistics Technical Report 397 (2003).

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.