On the Fernández–Steel distribution: Inference and application

Fernandez–Steel Skew Normal Conditional Autoregressive (FSSN CAR) Model in Stan for Spatial Data

In spatial data analysis, the prior conditional autoregressive (CAR) model is used to express the spatial dependence on random effects from adjacent regions. This paper provides a new proposed approach regarding the development of the existing normal CAR model into a more flexible, Fernandez–Steel skew normal (FSSN) CAR model. This approach is able to capture spatial random effects that have both symmetrical and asymmetrical patterns. The FSSN CAR model is built on the basis of the normal CAR with an additional skew parameter. The FSSN distribution is able to provide good estimates for symmetry with heavy- or light-tailed and skewed-right and skewed-left data. The effects of this approach are demonstrated by establishing the FSSN distribution and FSSN CAR model in spatial data using Stan language. On the basis of the plot of the estimation results and histogram of the model error, the FSSN CAR model was shown to behave better than both models without a spatial effect and with the normal CAR model. Moreover, the smallest widely applicable information criterion (WAIC) and leave-one-out (LOO) statistical values also validate the model, as FSSN CAR is shown to be the best model used.