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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Fachri Faisal
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Indonesia
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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THE UNINFORMATIVE PRIOR OF JEFFREYS’ DISTRIBUTION IN BAYESIAN GEOGRAPHICALLY WEIGHTED REGRESSION Fachri Faisal; Henny Pramoedyo; Suci Astutik; Achmad Efendi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp1229-1236

Abstract

When using the Bayesian method for estimating parameters in a geographically weighted regression model, the choice of the prior distribution directly impacts the posterior distribution. The distribution known as the Jeffreys prior is an uninformative type of prior distribution and is invariant to reparameterization. In cases where information about the parameter is not available, the Jeffreys' prior is utilized. The data was fitted with an uninformative Jeffreys' prior distribution, which yielded a posterior distribution that was utilized for estimating parameters. This study aims to derive the prior and marginal posterior distributions of the Jeffreys' and in Bayesian geographically weighted regression (BGWR). The marginal posterior distributions of and can be obtained by integrating the other parameters of a common posterior distribution. Based on the results and discussion, the Jeffreys prior in BGWR with the likelihood function is . On the other hand, the marginal posterior distribution of follows a normal multivariate distribution, that is, , while the marginal posterior distribution of follows an inverse gamma distribution, that is, . As further research, it is necessary to follow up on several limitations of the results of this research, namely numerical simulations and application to a particular case that related to the results of the analytical studies that we have carried out.
Co-Authors Achmad Efendi Henny Pramoedyo Suci Astutik