Multivariate skew-normal distribution for modelling skewed spatial data.

Area of Science:

• Spatial statistics
• Statistical modeling
• Biostatistics

Background:

• Multivariate spatial data often use shared spatial component and multivariate intrinsic conditional autoregressive (MICAR) models.
• These models typically assume normally distributed spatial random variables, which may not always hold true.

Purpose of the Study:

• To introduce a novel multivariate skew-normal spatial distribution for modeling multivariate conditional autoregressive models.
• To address the limitations of normality assumptions in existing spatial models.

Main Methods:

• Developed a multivariate skew-normal spatial model.
• Employed Bayesian inference for parameter estimation.
• Utilized simulations and a real-world application (South African HIV rates) for validation.
• Compared the proposed model with the standard MICAR model using conditional predictive ordinate (CPO).

Main Results:

• The proposed multivariate skewed spatial model demonstrated improved predictive capabilities.
• CPO values indicated superior performance of the new model over the MICAR model for both simulated and HIV data.
• The model effectively handles non-normal spatial structures.

Conclusions:

• The multivariate skew-normal spatial model offers a more flexible and accurate approach for analyzing multivariate spatial data with potential non-normal components.
• This approach enhances prediction accuracy in epidemiological studies, such as estimating HIV rates.