Project Details
Description
Traditional models for area data assume a hierarchical structure where one of the components is the random effects that spatially correlate areas.
The conditional autoregressive (CAR) model is the most popular distribution to jointly model the prior uncertainty about these spatial random effects.
A limitation of the CAR distribution is the inability to produce high correlations between neighboring areas.
We propose a robust model for area data that alleviates this problem. We represent the map using an undirected graph where the nodes are the areas and the randomly weighted edges connect the nodes that are neighbors.
The model is based on a multivariate, spatially structured Student distribution, in which the precision matrix is constructed indirectly by assuming a multivariate distribution for the random edges.
The joint distribution of the weights is a spatial multivariate Student that induces another distribution for the spatial effects of the areas that inherit their ability to accommodate outliers and heavy-tailed behavior.
More importantly, it can produce a higher marginal correlation between spatial effects than the CAR model, overcoming one of the main limitations of this model.
We fine-tuned the proposed model to analyze real cancer maps and compared its performance with several state-of-the-art competitors.
Our proposed model provides a better fit in almost all cases.
The conditional autoregressive (CAR) model is the most popular distribution to jointly model the prior uncertainty about these spatial random effects.
A limitation of the CAR distribution is the inability to produce high correlations between neighboring areas.
We propose a robust model for area data that alleviates this problem. We represent the map using an undirected graph where the nodes are the areas and the randomly weighted edges connect the nodes that are neighbors.
The model is based on a multivariate, spatially structured Student distribution, in which the precision matrix is constructed indirectly by assuming a multivariate distribution for the random edges.
The joint distribution of the weights is a spatial multivariate Student that induces another distribution for the spatial effects of the areas that inherit their ability to accommodate outliers and heavy-tailed behavior.
More importantly, it can produce a higher marginal correlation between spatial effects than the CAR model, overcoming one of the main limitations of this model.
We fine-tuned the proposed model to analyze real cancer maps and compared its performance with several state-of-the-art competitors.
Our proposed model provides a better fit in almost all cases.
| Status | Finished |
|---|---|
| Effective start/end date | 7/1/22 → 12/20/22 |
UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):
Main Funding Source
- Installed Capacity (Academic Unit)
Location
- Bogotá D.C.
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