- Volume 25 Issue 4
Spatial time series data can be viewed as a set of time series simultaneously collected at a number of spatial locations. This paper studies Bayesian inferences in a spatial time bilinear model with a Gibbs sampling algorithm to overcome problems in the numerical analysis techniques of a spatial time series model. For illustration, the data set of mumps cases reported from the Korea Center for Disease Control and Prevention monthly over the years 2001~2009 are selected for analysis.
Spatial time series data;STARMA;STBL;Bayesian;MCMC;Gibbs sampling;Mumps data
- Sanso, B. and Guenni, L. (1999). Venezuelan rainfall data analysed by using a Bayesian space-time model, Applied Statistics, 48, 345-362. https://doi.org/10.1111/1467-9876.00157
- Chen, C. W. S. (1992). Bayesian analysis of bilinear time series models: A Gibbs sampling approach, Communications in Statistics - Theory and Methods, 21, 3407-3425. https://doi.org/10.1080/03610929208830987
- Gelfand, A. and Smith, A. F. M. (1990). Sampling based approaches to calculating marginal densities, Journal of the American Statistical Association, 85, 398-409. https://doi.org/10.1080/01621459.1990.10476213
- Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457-472. https://doi.org/10.1214/ss/1177011136
- Pfeifer, P. E. and Deutsch, S. J. (1980). Identification and Interpretation of First order space-time ARMA Models, Technometrics, 22, 397-408. https://doi.org/10.1080/00401706.1980.10486172
- Raftery, A. L. and Lewis, S. (1992). One long run with diagnostics: Implementation strategies for Markov chain Monte Carlo, Statistical Science, 7, 493-507. https://doi.org/10.1214/ss/1177011143
- Ritter, C. and Tanner, M. A. (1992). Facilitating the Gibbs sampler: The Gibbs stopper and the griddy Gibbs sampler, Journal of the American Statistical Association, 85, 398-409.
- Geman, S. and Geman, D. (1984). stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741. https://doi.org/10.1109/TPAMI.1984.4767596
- Tanner, M. A. and Wong, W. H. (1987). The calculation of posterior distributions by data augmentation, Journal of the American Statistical Association, 82, 528-550. https://doi.org/10.1080/01621459.1987.10478458
- Tierney, L. and Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities, Journal of American Statistical Association, 81, 82-86. https://doi.org/10.1080/01621459.1986.10478240
Supported by : National Research Foundation of Korea(NRF)