Estimation and model selection for an IDE-based spatio-temporal model

IEEE Transactions on Signal Processing

Volumn 57, Issue 2, 2009, Pages 482-492

  Scerri, Kenneth ^a   Dewar, Michael ^b,c   Kadirkamanathan, Visakan ^b  

^a UNIVERSITY OF MALTA   (Malta)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

^c UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Bayes factor; Data augmentation (DA) algorithm; Dynamic spatio temporal modeling; Integro difference equations; State space models

Indexed keywords

BAYESIAN NETWORKS; BRAIN; DIFFERENCE EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; MODEL STRUCTURES; TELECOMMUNICATION SYSTEMS; THREE TERM CONTROL SYSTEMS;

BAYES FACTOR; BAYESIAN MODEL SELECTIONS; DATA AUGMENTATION (DA) ALGORITHM; DATA AUGMENTATION ALGORITHMS; IMPORTANCE SAMPLINGS; INTEGRO-DIFFERENCE EQUATIONS; MAXIMUM A-POSTERIORI; MODEL SELECTIONS; MULTIDIMENSIONAL SAMPLINGS; NUMBER OF STATE; PARAMETER SPACES; SPATIAL BANDWIDTHS; SPATIO TEMPORALS; SPATIO-TEMPORAL MODELS; STATE SPACES; STATE-SPACE MODELS;

STOCHASTIC MODELS;

EID: 60549113753     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2008.2008550     Document Type: Article

References (46)

1. A. Matani, Y. Masuda, H. Okubo, and K. Chihara, "Hierarchical clustering and filtering in half-inverse space for MEG and/or EEG hypothesis-free analysis," IEEE Trans. Signal Process., vol. 51, no. 2, pp. 350-361, 2003.
2. J. de Munck, H. Huizenga, L. Waldorp, and R. Heethaar, "Estimating stationary dipoles from MEG/EEG data contaminated with spatially and temporally correlated background noise," IEEE Trans. Signal Process. vol. 50, no. 7, pp. 1565-1572, 2002.
3. V. Parthasarathy, M. Stone, and J. Prince, R. Galloway, Ed., "Spatiotemporal visualization of the tongue surface using ultrasound and kriging," Med. Imag. 2003: Visualization, Image-Guided Procedures and Display, vol. 5029, pp. 239-248, 2003.
4. A. Kokaram and S. Godsill, "MCMC for joint noise reduction and missing data treatment in degraded video," IEEE Trans. Signal Process., vol. 50, no. 2, pp. 189-205, 2002.
5. M. Kot and W. Schaffer, "Discrete-time growth-dispersal models," Math. Biosci., vol. 80, pp. 109-136, 1986.
6. M. Kot, M. Lewis, and P. van den Driessche, "Dispersal data and the spread of invading organisms," Ecology, vol. 77, pp. 2027-2042, 1996.
7. M. Neubert and H. Caswell, "Demography and dispersal: Calculation and sensitivity analysis of invasion speed for structured populations," Ecology, vol. 81, no. 6, pp. 1613-1628, 2000.
8. J. Medlock and M. Kot, "Spreading disease: Integro-differential equations old and new," Math. Biosci., vol. 184, pp. 201-222, 2003.
9. M. Neubert and I. Parker, "Projecting rates of spread for invasive species," Risk Analysis, vol. 24, no. 4, 2004.
10. R. Garrido, "Spatial interaction between the truck flows through the Mexico-Texas border," Transport. Res. Part A, vol. 34, no. 23-33, 2000.
11. J. Stroud, P. Muller, and B. Sanso, "Dynamic models for spatiotemporal data," J. Royal Statist. Soc. B, vol. 63, pp. 673-689, 2001.
12. K. Xu, C. Wikle, and N. Fox, "A kernel-based spatio-temporal dynamical model for nowcasting weather radar reflectivities," J. Amer. Statist. Assoc., vol. 100, no. 472, 2005.
13. C. Wikle, "A kernel-based spectral model for non-Gaussian spatio-temporal processes," Statist. Model.: An Int. J., 2002.
14. M. de Lemos and M. Pedras, "Recent mathematical models for turbulent flow in saturated rigid porous media," J. Fluids Eng., vol. 123, pp. 925-940, 2001.
15. M. Kot, "Dicrete-time travelling waves: Ecological examples," Journal of Math. Biol., vol. 30, pp. 413-436, 1992.
16. M. Dewar, K. Scerri, and V. Kadirkamanathan, "Data driven spatiotemporal modeling using the integro-difference eqaution," IEEE Trans. Signal Process., 2008, to appear in.
17. M. Unser, "Sampling - 50 years after Shannon," Proc. IEEE, vol. 88, no. 4, pp. 569-587, 2000.
18. Y. Edlar and M. Unser, "Nonideal sampling and interpolation from noisy observations in shift-invariant spaces," IEEE Trans. Signal Process. vol. 54, no. 7, pp. 2636-2651, 2006.
19. S. Ramani, D. V. D. Ville, T. Blu, and M. Unser, "Nonideal sampling and regularization theory," IEEE Trans. Signal Process., vol. 56, no. 3, pp. 1055-1070, 2002.
20. R. Veit and M. Lewis, "Dispersal, population growth, and the Allee effect: Dynamics of the house finch invasion of eastern north America," The Amer. Naturalist, vol. 148, no. 2, pp. 255-274, 1996.
21. G. Storvik, A. Frigessi, and D. Hirst, "Stationary space time Gaussian fields and their time autoregressive representation," Statist. Model., vol. 2, pp. 139-161, 2002.
22. S. D. Iaco, D. Myers, and D. Posa, "Space-time variograms and a functional form for total air pollution measurements," Computat. Statist. Data Anal., vol. 41, pp. 311-328, 2002.
23. M. Stein, "Statistical methods for regular monitoring data," J. Royal Statist. Soc. B, vol. 67, pp. 667-687, 2005.
24. D. Peterson and D. Middleton, "Sampling and reconstruction of wave-number-limited functions in n-dimensional Euclidean spaces," Inf. Control, vol. 5, pp. 279-323, 1962.
25. A. Jerri, "The Shannon sampling theorem - Its various extensions and applications: A tutorial review," Proc. IEEE, vol. 65, no. 11, pp. 1565-1596, 1977.
26. J. Arsac, Fourier Transforms and the Theory of Distributions. Englewood Cliffs, NJ: Prentice-Hall, 1966.
27. I. Sandberg, J. Lo, C. Fancourt, J. Principe, S. Katagiri, and S. Haykin, Nonlinear Dynamical Systems: Feedforward Neural Network Perspectives. New York: Wiley, 2001.
28. R. Sanner and J.-J. E. Slotine, "Gaussian networks for direct adaptive control," IEEE Trans. Neural Netw., vol. 3, no. 6, 1992.
29. A. Dempster, N. Laird, and D. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Royal Statist. Soc. B, vol. 39, pp. 1-38, 1977.
30. S. Gibson and B. Ninness, "Robust maximum-likelihood estimation of multivariable dynamic systems," Automatica, vol. 41, pp. 1667-1682, 2005.
31. L. Ljung, "Asymptotic behaviour of the extended Kalman filter as a parameter estimator for linear systems," IEEE Trans. Autom. Control vol. 24, pp. 36-50, 1979.
32. E. Wan, R. van der Merwe, and A. Nelson, "Dual estimation and the unscented transformation," in Proc. Neural Inf. Process. Syst. Conf. 1999.
33. R. van der Merwe, E. Wan, and S. Julier, "Sigma-point Kalman filters for nonlinear estimation and sensor-fusion - Applications to integrated navigation," in Proc. AIAAA Guid., Navigat. Contr. Conf., 2004.
34. C. Robert and G. Casella, Monte Carlo Statistical Methods. New York: Springer, 2004.
35. W. Gilks, S. Richardson, and D. Spiegelhalter, Markov Chain Monte Carlo in Practice. New York: Chapman and Hall, 1996.
36. K. Burnham and D. Anderson, Model Selection and Multimodel Inference 2nd ed. New York: Springer, 2002.
37. R. Kass and A. Raftery, "Bayes factor," J. Amer. Statist. Assoc. vol. 90, no. 430, 1995.
38. A. Raftery, "Hypothesis testing and model selection," in Markov Chain Monte Carlo in Practice, W. Gilks, S. Richardson, and D. Spiegelhalter, Eds. New York: Chapman and Hall, 1996, ch. 10.
39. S. Chib, "Marginal likelihood from the Gibbs output," J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1313-1321, 1995.
40. S. Chib and I. Jeliazkov, "Marginal likelihood from the Metropolis-Hastings output," J. Amer. Statist. Assoc., vol. 96, no. 453, pp. 270-281, 2001.
41. S. Fruhwirth-Schnatter, "Data augmentation and dynamic linear models," J. Time Series Anal., vol. 15, no. 183-202, 1992.
42. S. Fruhwirth-Schnatter, "Bayesian model discrimination and Bayes factor for linear Gaussian state space models," J. Royal Statist. Soc. B vol. 57, no. 1, pp. 237-246, 1995.
43. A. Raftery, "Bayesian model selection in social reasearch," in Socialog. Methodol., P. Marsden, Ed. New York: Blackwells, 1995.
44. M. Tanner and W. Wong, "The calculation of posterior distributions by data augmentation," J. Amer. Statist. Assoc., vol. 82, no. 398, pp. 528-540, 1987.
45. J. Park and I. Sandberg, "Universal approximation using radial-basis-function networks," Neural Computat., vol. 3, pp. 246-257, 1991.
46. T. Poggio and F. Girosi, "Networks for approximation and learning," Proc. IEEE, vol. 78, no. 9, 1990.