Malaysian Journal of Mathematical Sciences, December 2025, Vol. 19, No. 4
Bayesian Spatio-Temporal Modeling: Application to Development of Blue Economy Index and Its Influence to GRDP in Sumatera Island
Rinaldi, A., Christina, A., Rachmawati, R. N., and Muslim, A.
Corresponding Email: achi@radenintan.ac.id
Received date: 11 November 2024
Accepted date: 22 June 2025
Abstract:
Indonesia, as a maritime country, can utilize blue economy as a new economic opportunity for environmental sustainability that provides added value for socio-economic conditions of the community. So far, quantitative studies on the blue economy are still very minimal and studies on the influence of the blue economy spatio-temporally on Gross Regional Domestic Product (GRDP) do not exist. Therefore, this study aims to establish the Blue Economy Index (BEI) and determine the variables that significantly affect GRDP through spatial and temporal regression modeling in Sumatera. Using data from 2019 to 2022 across 154 regencies, BEI is organized by environmental, social, and economic pillars. This study uses parametric, nonparametric, and nonparametric Bayesian spatio-temporal models with 4 types of interactions. INLA uses a deterministic approach with a multilevel Laplace approximation involving numerical integration to integrate the latent fields and generate marginal posterior distributions for the model parameters. Findings of this study show that average BEI (ranging from 0 to 100) which is still below 20 means that the potential of blue economy has not been optimally utilized. Based on this value, only a few regions in Sumatera have high BEI values, including Medan, Palembang, and Musi Banyuasin. Model performance evaluation shows that four of six models tested can describe BEI characteristics in ten Sumateran provinces, namely parametric as well as nonparametric with interaction Types 1, 2, and 4. The global trend in spatio-temporal modeling shows a positive trajectory which means that blue economy has the potential to increase GRDP. Significant variables that influence GRDP include waste management and tourism in South and West Sumatera, electricity and freshwater seed farming in North Sumatera, education in South Sumatera, and freshwater pond farming in West Sumatera.
Keywords: Blue Economy Index (BEI); principal component analysis; GRDP; Bayesian regression; INLA
