Modeling of Spatio-Temporal Data with Non-Ignorable Missing

Document Type : Original Paper


Department of Statistics, Tarbiat Modares University


Often, due to conditions under which measurements are made, spatio-temporal data contain missing values. Missing data in spatial or temporal vicinity may include useful information. Using this information, we can provide more accurate results, so missing data should be carefully examined. By modeling the missing process and spatio-temporal measurement process jointly, some lost information could be recovered. In this paper, we implement joint modeling in a Bayesian framework using the "shared parameter model" technique, so that the bad effects of missing values will be moderated. Also, we will associate these two processes via a latent spatio-temporal random field. To estimate the model parameters and for predictions, the Bayesian method INLA using SPDE approach is applied. Also, the lake surface water temperature data for Caspian sea is used to evaluate the performance of the joint model.


Main Subjects

1. Rubin, D. B. (1976). Inference and missing data,
, 581-592.
2. Smith, R. L., Kolenikov, S. and Cox, L. H. (2003). Spatio-temporal
modeling of PM2.5 data with missing values,
Journal of Geophysical
Research: Atmospheres
, 108(D24).
3. Kondrashov, D. and Ghil, M. (2006). Spatio-temporal filling of missing
points in geophysical data sets,
Nonlinear Processes in
4.Cheng, S. and Lu, F. (2017). A two-step method for missing spatio-
temporal data reconstruction,
ISPRS International Geo-Information
[5] Bae, B., Kim, H., Lim, H., Liu, Y., Han, L. D. and Freeze, P. B.
(2018).Missing data imputation for traffic flow speed using spatio-
temporal cokriging,
Emerging Technologies
, 124-139.
[6] Yang, H., Yang, J., Han, L. D., Liu, X., Pu, L., Chin, S. M. and Hwang, H.
L. (2018). A Kriging based spatio-temporal approach for traffic volume
data imputation,
PloS one
, e0195957.
[7] Gerber, F., de Jong, R., Schaepman, M., Schaepman-Strub, G. and Furrer,
R. (2018). Predicting missing values in spatio-temporal remote sensing