Prior specification of spatio-temporal models

Abstract

Introduction: The population sample estimated parameters are key statistical point to make the population inference, predicting and forecasting the response of future subjects. In Bayesian Statistics, prior knowledge have a big impact in estimating parameters and predicting future values. The interest of this study was to investigate how the choice of prior affect the parameters’estimation for the spatio-temporal model which is constructed under the Bayesian Framework. The objective of this study is to investigate the effect of different prior specifications in a spatio-temporal model after simulating data of aborted cattle in different areas of Flanders. Methodology: A spatio-temporal model which assumed a space-time variation was used to conduct a simulation for 100 different datasets on 306 areas of Flanders for a period of 36 Months. Each dataset has 11016 observations, the response variable was the number of aborted cattle and there were four covariate variables. The same model was then fitted 11 times on these datasets by applying different priors each time, different criterion have been used to propose a better prior among the used priors. All the analysis was done in Bayesian framework using Integrated Nested Laplace Approximation (INLA) package. Results: Different combinations of priors have been used for hyperparameters compo- nents including the structured and unstructured spatial effect, first order autoregressive (AR1) precision and correlation and time space interaction. A model4 fitted using pe- nalised Complexity prior for both spatial effects in combination with default prior for other terms was proposed among 8 (Model1-Model8) models as good in terms of minimum mean bias, minimum mean squared error and a good coverage probability. Additional 3 models (Model9-Model11) were fitted, where PC priors were used for other components of the model. Likewise model4 still being preferable than others. Averaged DIC for all models were compared, the DIC of model4 was smaller than anyone else with a difference larger 10. Conclusion: It was concluded that Penalised Complexity (PC) prior in combination with default prior can be used while fitting a spatio-temporal model as they provided stability in hyperparameter estimates, and they can be used in real-world applied statistics as they are constructed by the user to avoid ”cut and paste” prior from other related research articles.