Change of spatiotemporal scale in dynamic models

Spatiotemporal processes show complicated and different patterns across different space-time scales. Each process that we attempt to model must be considered in the context of its own spatial and temporal resolution. Both scientific understanding and observed data vary in form and content across scale. Such information sources can be combined through Bayesian hierarchical framework. This approach restricts a few essential scales. However, it is common in the trade-off view between simple modeling and analysis strategy with complicate modeling. Wikle and Berliner (2005) suggested a specialized, though useful, approach to the change of support (COS) problem within hierarchical framework. We extended their strategy by adding temporal modeling in their style and allowing discretized time-varying parameters. We apply a Bayesian inference based on combining information across spatiotemporal scale to some climate temperature data, which are point-referenced data and areal unit data. The inference focuses on the temperature process on specific prediction grid scale and maybe different time scale.

[1]  Christopher K. Wikle,et al.  Space-time Kalman filter , 2014 .

[2]  Noel A Cressie,et al.  Change of support and the modifiable areal unit problem , 1996 .

[3]  C. Gotway,et al.  Combining Incompatible Spatial Data , 2002 .

[4]  Arnaud Gloter,et al.  Parameter estimation for a discrete sampling of an intergrated Ornstein-Uhlenbeck process , 2001 .

[5]  L. Mark Berliner,et al.  Spatiotemporal Hierarchical Bayesian Modeling Tropical Ocean Surface Winds , 2001 .

[6]  A E Gelfand,et al.  On the change of support problem for spatio-temporal data. , 2001, Biostatistics.

[7]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[8]  Bradley P. Carlin,et al.  Fully Model-Based Approaches for Spatially Misaligned Data , 2000 .

[9]  Emilio Porcu,et al.  Space-time covariance functions with compact support , 2009 .

[10]  N. Cressie,et al.  Classes of nonseparable, spatio-temporal stationary covariance functions , 1999 .

[11]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[12]  N. Cressie,et al.  Spatio-temporal prediction of snow water equivalent using the Kalman filter , 1996 .

[13]  Paul G. Blackwell,et al.  Bayesian inference for Markov processes with diffusion and discrete components , 2003 .

[14]  T. Hassard,et al.  Applied Linear Regression , 2005 .

[15]  Gardar Johannesson,et al.  Dynamic multi-resolution spatial models , 2007, Environmental and Ecological Statistics.

[16]  Alan E. Gelfand,et al.  Spatio-Temporal Modeling of Residential Sales Data , 1998 .

[17]  L. M. Berliner,et al.  Hierarchical Bayesian space-time models , 1998, Environmental and Ecological Statistics.

[18]  J. R. Wallis,et al.  An Approach to Statistical Spatial-Temporal Modeling of Meteorological Fields , 1994 .

[19]  J. Holton.  An introduction to dynamic meteorology , 2004 .

[20]  Noel A Cressie,et al.  Fast, Resolution-Consistent Spatial Prediction of Global Processes From Satellite Data , 2002 .

[21]  Christian P. Robert,et al.  Monte Carlo Statistical Methods (Springer Texts in Statistics) , 2005 .

[22]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[23]  P. Brown,et al.  Blur‐generated non‐separable space–time models , 2000 .

[24]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition) , 1999 .

[25]  M. Parlange,et al.  Mixtures of stochastic processes: application to statistical downscaling , 1996 .

[26]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[27]  L. Mark Berliner,et al.  Combining Information Across Spatial Scales , 2005, Technometrics.

[28]  Noel A Cressie,et al.  Long-Lead Prediction of Pacific SSTs via Bayesian Dynamic Modeling , 2000 .

[29]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[30]  L. Mark Berliner,et al.  Bayesian hierarchical modeling of air-sea interaction , 2003 .

[31]  Noel A Cressie,et al.  Multiscale Graphical Modeling in Space: Applications to Command and Control , 2001 .

[32]  Richard H. Jones,et al.  Models for Continuous Stationary Space-Time Processes , 1997 .

[33]  W. T. Grandy,et al.  Maximum Entropy and Bayesian Methods , 1991 .