The NOAA IR serves as an archival repository of NOAA-published products including scientific findings, journal articles, guidelines, recommendations, or other information authored or co-authored by NOAA or funded partners.
As a repository, the NOAA IR retains documents in their original published format to ensure public access to scientific information.
i
On the relationship between conditional (CAR) and simultaneous (SAR) autoregressive models
-
2018
-
Source: Spatial Statistics, 25, 68-85
[PDF-674.45 KB]
Details:
-
Journal Title:Spatial Statistics
-
Personal Author:
-
NOAA Program & Office:
-
Description:We clarify relationships between conditional (CAR) and simultaneous (SAR) autoregressive models. We review the literature on this topic and find that it is mostly incomplete. Our main result is that a SAR model can be written as a unique CAR model, and while a CAR model can be written as a SAR model, it is not unique. In fact, we show how any multivariate Gaussian distribution on a finite set of points with a positive-definite covariance matrix can be written as either a CAR or a SAR model. We illustrate how to obtain any number of SAR covariance matrices from a single CAR covariance matrix by using Givens rotation matrices on a simulated example. We also discuss sparseness in the original CAR construction, and for the resulting SAR weights matrix. For a real example, we use crime data in 49 neighborhoods from Columbus, Ohio, and show that a geostatistical model optimizes the likelihood much better than typical first-order CAR models. We then use the implied weights from the geostatistical model to estimate CAR model parameters that provides the best overall optimization.
-
Keywords:
-
Source:Spatial Statistics, 25, 68-85
-
DOI:
-
ISSN:2211-6753
-
Format:
-
Publisher:
-
Document Type:
-
Rights Information:Accepted Manuscript
-
Compliance:Library
-
Main Document Checksum:
-
Download URL:
-
File Type:
