Searching for a trail of evidence in a maze

Annals of Statistics

Volumn 36, Issue 4, 2008, Pages 1726-1757

  Arias Castro, Ery ^a   Candès, Emmanuel J ^b   Helgason, Hannes ^b   Zeitouni, Ofer ^c,d,e  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

^d WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^e University of Minnesota   (United States)

Author keywords

Bayesian detection; Detecting a chain of nodes in a network; Exponential families of random variables; Martingales; Minimax detection; Predictability profile of a stochastic process

Indexed keywords

EID: 51049103448     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-AOS526     Document Type: Article

References (24)

1. AHUJA, R. K., MAGNANTI, T. L. and ORLIN, J. B. (1993). Network Flows. Theory, Algorithms and Applications. Prentice Hall, Englewood Cliffs, NJ. MR1205775
2. ARIAS-CASTRO, E., DONOHO, D. and HUO, X. (2005). Near-optimal detection of geometric objects by fast multiscale methods. IEEE Trans. Inform. Theory 51 2402-2425. MR2246369
3. ARIAS-CASTRO, E., DONOHO, D. and HUO, X. (2006). Adaptive multiscale detection of filamentary structures in a background of uniform random, points. Ann. Statist. 34 326-349. MR2275244
4. BAHADUR, R. and RANGA RAO, R. (1960). On deviations of the sample mean. Ann. Math. Statis. 31 1015-1027. MR0117775
5. BAIK, J. and RAINS, E. M. (2001a). The asymptotics of monotone subsequences of involutions. Duke Math. J. 109 205-281. MR1845180
6. BAIK, J. and RAINS, E. M. (2001b). Symmetrized random permutations. In Random Matrix Models and Their Applications (P. Bleher and A. Its, eds.) 1-19. Cambridge Univ. Press. MR1842780
7. BENJAMINI, I., PEMANTLE, R. and PERES, Y. (1998). Unpredictable paths and percolation. Ann. Probab. 26 1198-1211. MR1634419
8. BIGGINS, J. D. (1977). Martingale convergence in the branching random walk. J. Appl. Probab. 14 25-37. MR0433619
9. BUFFET, E., PATRICK, A. and PULÉ, J. V. (1993). Directed polymers on trees: A martingale approach. J. Phys. A 26 1823-1834. MR1220795
10. CANDES, E. J., CHARLTON, P. R. and HELGASON, H. (2006). Detecting highly oscillatory signals by chirplet path pursuit. Technical report, California Institute of Technology.
11. COMETS, F., SHIGA, T. and YOSHIDA, N. (2004). Probabilistic analysis of directed polymers in random environments: A review. In Stochastic Analysis on Large Scale Interacting Systems 115-142. Math. Soc. Japan, Tokyo. MR2073332
12. DERRIDA, B. and SPOHN, H. (1988). Polymers on disordered trees, spin glasses, and traveling waves. J. Statist. Phys. 51 817-840. MR0971033
13. DONOHO, D. L. and HUO, X. (2002). Beamlets and multiscale image analysis. In Multiscale and Multiresolution Methods. Lecture Notes in Comput. Sci. Eng. 20 149-196. Springer, Berlin. MR1928566
14. FELLER, W. (1957). The numbers of zeros and of changes of sign in a symmetric random walk. Enseignement Math. (2) 3 229-235. MR0097864
15. FELLER, W. (1968). An Introduction to Probability Theory and Its Applications I, 3rd ed. Wiley, New York. MR0228020
16. GLAZ, J., NAUS, J. and WALLENSTEIN, S. (2001). Scan Statistics. Springer, New York. MR1869112
17. HÄGGSTRÖM, O. and MOSSEL, E. (1998). Nearest-neighbor walks with low predictability profile and percolation in 2 + ε dimensions. Ann. Probab. 26 1212-1231. MR1640343
18. HOFFMAN, C. (1998). Unpredictable nearest neighbor processes. Ann. Probab. 26 1781-1787. MR1675075
19. INGSTER, Y. I. and SUSLINA, I. A. (2003). Nonparametric Goodness-of-fit Testing under Gaussian Models. Springer, New York. MR 1991446
20. KULLDORFF, M. (1997). A spatial scan statistic. Comm. Statist. Theory Methods 26 1481-1496. MR 1456844
21. LYONS, R. (1997). A simple path to Biggins' martingale convergence for branching random walk. In Classical and Modern Branching Processes (K. B. Athreya and P. Jagers, eds.) 217-221. Springer, New York. MR1601749
22. PATIL, G. P., BALBUS, J., BIGING, G., JAJA, J., MYERS, W. L. and TAILLIE, C. (2004). Multiscale advanced raster map analysis system.: Definition, design and development. Environ. Ecol. Stat. 11 113-138. MR2086391
23. PEMANTLE, R. (1995). Tree-indexed processes. Statist. Sci. 10 200-213. MR1368099
24. ZHONG, Y., JAIN, A. and DUBUISSON-J OLLY, M.-P. (2000). Object tracking using deformable templates. IEEE Trans. Pattern Anal. Mach. Intell. 2 544-549.