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Some Theory on Random Fields
| Content Provider | Scilit |
|---|---|
| Author | Schabenberger, Oliver Gotway, Carol A. |
| Copyright Year | 2017 |
| Description | A stochastic process is a family or collection of random variables, the members of which can be identified or located (indexed) according to some metric. For example, a time series Y (t), t = t$ _{1}$, ···, $t_{n}$ , is indexed by the time points t$ _{1}$, ···, $t_{n}$ at which the series is observed. Similarly, a spatial process is a collection of random variables that are indexed by some set D ⊂ $ℝ^{ d }$ containing spatial coordinates s = [s$ _{1}$, s$ _{2}$, ···, $s_{d}$ ]′. For a process in the plane, d = 2, and the longitude and latitude coordinates are often identified as s = [x, y]′. If the dimension d of the index set of the stochastic process is greater than one, the stochastic process is often referred to as a random field. In this text we are mostly concerned with spatial processes in $ℝ^{2}$, although higher-dimensional spaces are implicit in many derivations; spatio-temporal processes are addressed in Chapter 9. The name random “field” should not connote a two-dimensional plane or even an agricultural application. It is much more general. Book Name: Statistical Methods for Spatial Data Analysis |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2009-0-03703-3&isbn=9781315275086&doi=10.1201/9781315275086-2&format=pdf |
| Ending Page | 80 |
| Page Count | 40 |
| Starting Page | 41 |
| DOI | 10.1201/9781315275086-2 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2017-01-27 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Statistical Methods for Spatial Data Analysis Stochastic Process Random Variables Random Fields Coordinates Longitude Spatial Process Connote |
| Content Type | Text |
| Resource Type | Chapter |
