Ecological Prediction With Nonlinear Multivariate Time-Frequency Functional Data Models
Time-frequency analysis has become a fundamental component of many scientific inquiries. Due to improvements in technology, the amount of high-frequency signals that are collected for ecological and other scientific processes is increasing at a dramatic rate. In order to facilitate the use of these data in ecological prediction, we introduce a class of nonlinear multivariate time-frequency functional models that can identify important features of each signal as well as the interaction of signals corresponding to the response variable of interest. Our methodology is of independent interest and utilizes stochastic search variable selection to improve model selection and performs model averaging to enhance prediction. We illustrate the effectiveness of our approach through simulation and by application to predicting spawning success of shovelnose sturgeon in the Lower Missouri River.
Key WordsBayesian model averaging Dimension reduction Empirical orthogonal functions Nonlinearity Shovelnose sturgeon Spectrogram Stochastic search variable selection
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- DeLonay, A. J., Papoulias, D. M., Wildhaber, M. L., Annis, M., Bryan, J. L., Griffith, S. A., Holan, S. H., and Tillit, D. E. (2007), “Use of Behavioral and Physiological Indicators to Evaluate Scaphirhynchus Sturgeon Spawning Success,” Journal of Applied Ichthyology, 23, 428–435. CrossRefGoogle Scholar
- Funk, J. L., and Robinson, J. W. (1974), Changes in the Channel of the Lower Missouri River and Effects on Fish and Wildlife, Jefferson City: Missouri Department of Conservation. Google Scholar
- Geweke, J. (1992), “Variable Selection and Model Comparison in Regression,” in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford: Oxford Press, pp. 609–620. Google Scholar
- Holan, S. H., Davis, G. M., Wildhaber, M. L., DeLonay, A. J., and Papoulias, D. M. (2009), “Hierarchical Bayesian Markov Switching Models With Application to Predicting Spawning Success of Shovelnose Sturgeon,” Journal of the Royal Statistical Society. Series C. Applied Statistics, 58 (1), 47–64. MathSciNetCrossRefGoogle Scholar
- Jolliffe, I. T. (2010), Principal Component Analysis, Berlin: Springer. Google Scholar
- Martinez, J. G., Bohn, K. M., Carroll, R. J., and Morris, J. S. (2013), “A Study of Mexican Free-Tailed Bat Chirp Syllables: Bayesian Functional Mixed Models for Nonstationary Acoustic Time Series,” UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series, Working Paper 79. Google Scholar
- Morris, J. S., Baladandayuthapani, V., Herrick, R. C., Sanna, P., and Gutstein, H. B. (2011), “Automated Analysis of Quantitative Image Data Using Isomorphic Functional Mixed Models, With Application to Proteomics Data,” Annals of Applied Statistics, 5 (2A). Google Scholar
- Oppenheim, A. V., and Schafer, R. W. (2009), Discrete-Time Signal Processing, Prentice Hall Signal Processing. Google Scholar
- U.S. Fish and Wildlife Service (2000), Biological Opinion on the Operation of the Missouri River Main Stem Reservoir System, Operation and Maintenance of the Missouri River Bank Stabilization and Navigation Project, and Operation of the Kansas River Reservoir System, Bismarck: US Fish and Wildlife Service. Google Scholar
- Vannucci, M., and Stingo, F. C. (2010), “Bayesian Models for Variable Selection That Incorporate Biological Information,” in Bayesian Statistics 9, eds. J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith, and M. West, Oxford: Oxford University Press. Google Scholar
- Wildhaber, M. L., DeLonay, A. J., Papoulias, D. M., Galat, D. L., Jacobson, R. B., Simpkins, D. G., Braaten, P. J., Korschegen, C. E., and Mac, M. J. (2007), “A Conceptual Life-History Model for Pallid and Shovelnose Sturgeon,” Tech. rep., USGS Circular 1315. Google Scholar
- Wildhaber, M. L., Holan, C. H., Davis, G. M., Gladish, D. W., DeLonay, A. J., Papoulias, D. M., and Sommerhauser, D. K. (2011b), “Evaluating Spawning Migration Patterns and Predicting Spawning Success of Shovelnose Sturgeon in the Lower Missouri River,” Journal of Applied Ichthyology, 27, 301–308. CrossRefGoogle Scholar