Name
Abstract | ||
|---|---|---|
Models based on Markov random fields are now widely used to model spatial processes. Key components of any statistical analysis using such models are the choice of an appropriate model as the prior distribution and the estimation of prior model parameters. In this paper, we shall investigate spatial behavior of auto models, concentrating on the first-order neighborhood system in a rectangular lattice, but also considering the second-order neighborhood system in a rectangular lattice and first-order neighborhood system in a hexagonal lattice. We present a simple deterministic model based on a univariate iterative scheme which appears to emulate the behavior of auto models and allows us to make predictions regarding the behavior of the spatial models. For well-defined regions in the parameter space this iterative scheme is unstable leading to catastrophic and 2-cycle behavior. We claim that this instability coincides with structural changes in the corresponding spatial model and that the critical boundaries for the iterative scheme coincide with those for the spatial model. We use the Gibbs sampler to produce realizations illustrating the wide range of possible models, and to reinforce the predictions made using the simple iterative scheme. |
Year | DOI | Venue |
|---|---|---|
1996 | 10.1006/gmip.1996.0037 | CVGIP: Graphical Model and Image Processing |
Keywords | Field | DocType |
unexpected spatial pattern,exponential family auto model,statistical analysis,parameter space,second order,structural change,gibbs sampler,first order,exponential family,prior distribution,spatial pattern | Statistical physics,Random field,Markov model,Markov chain,Exponential family,Statistical model,Deterministic system,Prior probability,Calculus,Gibbs sampling,Mathematics | Journal |
Volume | Issue | ISSN |
58 | 5 | Graphical Models and Image Processing |
Citations | PageRank | References |
1 | 0.68 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| R. G. Aykroyd | 1 | 3 | 2.15 |
| J. G. B. Haigh | 2 | 11 | 1.79 |
| Stelios Zimeras | 3 | 12 | 7.07 |