English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

I consider the use of Markov random fields (MRFs) on a fine grid to representlatent spatial processes when modeling point-level and areal data, includingsituations with spatial misalignment. Point observations are related to thegrid cell in which they reside, while areal observations are related to the(approximate) integral over the latent process within the area of interest. Ireview several approaches to specifying the neighborhood structure forconstructing the MRF precision matrix, presenting results comparing these MRFrepresentations analytically, in simulations, and in two examples. The resultsprovide practical guidance for choosing a spatial process representation andhighlight the importance of this choice. In particular, the results demonstratethat, and explain why, standard CAR models can behave strangely for point-leveldata. They show that various neighborhood weighting approaches based onhigher-order neighbors that have been suggested for MRF models do not producesmooth fields, which raises doubts about their utility. Finally, they indicatethat an MRF that approximates a thin plate spline compares favorably tostandard CAR models and to kriging under many circumstances.

Spatial models for point and areal data using Markov random fields on a fine grid