# Statistical Modeling
This section of the dataset contains sparse matrices related to statistical modeling. More specifically, this contain precision matrices as used within the integrated nested Laplace approximation (INLA) framework.

## temp_prior_st1
Domain: Prior precision matrix from spatio-temporal statistical modeling applied to temperature prediction

### Caracteristics
- Type: positive-definite symmetric
- Size: 1000506x1000506, 50870502 nnz
- Used in: Linear system solving

|                | Initial  | Cholesky | Fill-in | Depth |
|----------------|----------|----------|---------|-------|
| temp_prior_st1 | 50870502 |          |         |       |
| RCM            |          |          |         |       |
| AMD            |          |          |         |       |
| ND             |          |          |         |       |

### References
- [Integrated Nested Laplace Approximations for Large-Scale Spatiotemporal Bayesian Modeling](https://epubs.siam.org/doi/full/10.1137/23M1561531)

## temp_conditional_st1
Domain: Conditional precision matrix from spatio-temporal statistical modeling applied to temperature prediction

### Caracteristics
- Type: positive-definite symmetric
- Size: 1000506x1000506, 62837532 nnz
- Used in: Linear system solving, Selected linear system solving

|                      | Initial  | Cholesky | Fill-in | Depth |
|----------------------|----------|----------|---------|-------|
| temp_conditional_st1 | 62837532 |          |         |       |
| RCM                  |          |          |         |       |
| AMD                  |          |          |         |       |
| ND                   |          |          |         |       |

### References
- [Integrated Nested Laplace Approximations for Large-Scale Spatiotemporal Bayesian Modeling](https://epubs.siam.org/doi/full/10.1137/23M1561531)



## airpoll_prior_st3
Domain: Prior precision matrix from a coregional (trivariate) spatio-temporal statistical modeling applied to air pollution

### Caracteristics
- Type: positive-definite symmetric
- Size: 8499x8499, 1205931 nnz
- Used in: Linear system solving
- 
|                   | Initial | Cholesky | Fill-in | Depth |
|-------------------|---------|----------|---------|-------|
| airpoll_prior_st3 | 1205931 |          |         |       |
| RCM               |         |          |         |       |
| AMD               |         |          |         |       |
| ND                |         |          |         |       |

### References
- []()
- [Multivariate disaggregation modeling of air pollutants: a case-study of PM2.5, PM10 and ozone prediction in Portugal and Italy](https://arxiv.org/abs/2503.12394)


## airpoll_conditional_st3
Domain: Conditional precision matrix from a coregional (trivariate) spatio-temporal statistical modeling applied to air pollution

### Caracteristics
- Type: positive-definite symmetric
- Size: 8499x8499, 1218651 nnz
- Used in: Linear system solving, Selected linear system solving

|                         | Initial | Cholesky | Fill-in | Depth |
|-------------------------|---------|----------|---------|-------|
| airpoll_conditional_st3 | 1218651 |          |         |       |
| RCM                     |         |          |         |       |
| AMD                     |         |          |         |       |
| ND                      |         |          |         |       |

### References
- []()
- [Multivariate disaggregation modeling of air pollutants: a case-study of PM2.5, PM10 and ozone prediction in Portugal and Italy](https://arxiv.org/abs/2503.12394)