by Geir Storvik, Arnoldo Frigessi, David Hirst
http://www.math.uio.no/~geirs/publ/blurdjh_sent_020800.ps
Add To MetaCart
Abstract:
We compare two dierent modeling strategies for continuous space discrete time data. The rst strategy is in the spirit of Gaussian kriging. The model is a general space-time Gaussian eld where the key point is the choice of a parametric form for the covariance function. Mostly, covariance functions which are used are separable in space and time. Non-separable covariance functions are useful in many applications, but construction of such is not easy. The second strategy is to model the time-evolution of the process more directly. We consider models of the autoregressive type where the process at time t is obtained by convolving the process at time t 1 and adding some noise which are spatially correlated. Under specic conditions, the two strategies describe two dierent formulations of the same stochastic process. We show how the two representations look in dierent cases. Furthermore, by transforming time-dynamic convolution models to Gaussian elds we can obtain new covariance functions and by writing a Gaussian eld as a time-dynamic convolution model, interesting properties are discovered. 1
Citations
|
493
|
Statistics for Spatial Data
– Cressie
- 1991
|
|
403
|
Numerical recipes
– Press, Flannery, et al.
- 1986
|
|
122
|
Constrained monte carlo maximum likelihood for dependent data
– Geyer, Thompson
- 1992
|
|
58
|
The simulation smoother for time series models
– JONG, SHEPHARD
- 1995
|
|
22
|
Model-based Geostatistics
– Diggle, Ribeiro
- 2006
|
|
22
|
Modelling risk from a disease in time and space
– Knorr-Held, Besag
- 1998
|
|
21
|
Non-Stationary Spatial Modeling
– Higdon, Swall, et al.
- 1999
|
|
17
|
Bayesian Variogram Modeling for an Isotropic Spatial Process
– Ecker, Gelfand
- 1997
|
|
14
|
Classes of nonseparable, spatio-temporal stationary covariance functions
– Cressie, Huang
- 1999
|
|
14
|
Local prediction of a spatio-temporal process with an application to wet sulfate deposition
– Haas
- 1995
|
|
13
|
Bayesian forecasting and dynamic models. Springer Series in Statistics
– West, Harrison
- 1997
|
|
11
|
Ozone exposure and population density in Harris County, Texas
– Carroll, Chen, et al.
- 1997
|
|
9
|
Fourier transforms of distributions and their inverses; a collection of tables
– Oberhettinger
- 1973
|
|
8
|
Hierarchical bayesian space-time models. Environmental and Ecological Statistics
– Wikle, Berliner, et al.
- 1998
|
|
7
|
Spatial interpolation errors for monitoring data
– Host, Omre, et al.
- 1995
|
|
6
|
Blur-generated non-separable space-time models
– Brown, Karesen, et al.
- 2000
|
|
5
|
Models for continuous stationary space-time processes
– Jones, Zhang
- 1997
|
|
4
|
Numerical methods for stochastic processes. Wiley series in Probability and mathematical statistics
– Bouleau, Lepingle
- 1994
|
|
4
|
Spatial Variation. Number 36
– Matern
- 1986
|
|
4
|
A dimension-reduced approach to space-time Kalman
– Wikle, Cressie
- 1999
|
|
2
|
Modelling risk from a disease in time and space. Statistics in medicine
– KnorrHeld, Besag
- 1998
|
|
2
|
A general class of models for stationary two-dimensional random processes
– Vecchia
- 1985
|
|
1
|
A hierarchical modelling approach to combining environmental data at dierent scales. Submitted for publication
– Hirst, Storvik, et al.
- 2001
|
|
1
|
Nonparametric-estimation of nonstationary spatial covariance structure
– Sampson, Guttorp
- 1992
|
|
1
|
Time trend estimation for a geographic region
– Slna, Switzer
- 1996
|
|
1
|
D.and Guttorp. Nonparametric-estimation of nonstationary spatial covariance structure
– Sampson, P
- 1992
|
|
1
|
Statistical assesment of spatio-temporal pollutant trends and meteorogical transport models', Atmospheric Environment
– Haas
- 1998
|
|
1
|
Fitting continous arma model to unequally spaced spatial data
– Jones
- 1993
|
|
1
|
Spatial Statistics, Wiley series in probability and mathematical statistics
– Ripley
- 1981
|
|
1
|
A dimension-reducecd approach to space-time Kalman ltering
– Wikle
- 1999
|
