A Generalized Log Gamma Approach: Theoretical Contributions and an Application to Companies’ Life Expectancy

Dias Gonçalves, José H.; Ferreira Gomes, João J.; Rubio, Lihki; Ramos, Filipe R.

doi:10.3390/math11234792

Cited by 1 publication

(2 citation statements)

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“…To ensure comprehensive future investigations, it is imperative to examine the utilization of generalized logGamma [12], generalized Half-Cauchy [13], and generalized Uniform [14] distributions. These alternatives have the potential to be strong replacements for hyperpriors, potentially improving the accuracy of predictions and accounting for additional variability in the data.…”

Section: Discussionmentioning

confidence: 99%

“…Several alternative hyperpriors can be considered as substitutes, such as the Half-Cauchy [10], Penalized Complexity [11], Uniform, generalized logGamma [12], generalized Half-Cauchy [13], and generalized Uniform [14]. However, practitioners may encounter challenges when trying to implement the generalized distribution, as it is not currently supported in common Bayesian software such as R-INLA 2023 (https://www.r-inla.org/) (accessed on 25 December 2023).…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity Analysis on Hyperprior Distribution of the Variance Components of Hierarchical Bayesian Spatiotemporal Disease Mapping

Jaya,

Kristiani,

Andriyana

et al. 2024

Mathematics

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Spatiotemporal disease mapping modeling with count data is gaining increasing prominence. This approach serves as a benchmark in developing early warning systems for diverse disease types. Spatiotemporal modeling, characterized by its inherent complexity, integrates spatial and temporal dependency structures, as well as interactions between space and time. A Bayesian approach employing a hierarchical structure serves as a solution for spatial model inference, addressing the identifiability problem often encountered when utilizing classical approaches like the maximum likelihood method. However, the hierarchical Bayesian approach faces a significant challenge in determining the hyperprior distribution for the variance components of hierarchical Bayesian spatiotemporal models. Commonly used distributions include logGamma for log inverse variance, Half-Cauchy, Penalized Complexity, and Uniform distribution for hyperparameter standard deviation. While the logGamma approach is relatively straightforward with faster computing times, it is highly sensitive to changes in hyperparameter values, specifically scale and shape. This research aims to identify the most optimal hyperprior distribution and its parameters under various conditions of spatial and temporal autocorrelation, as well as observation units, through a Monte Carlo study. Real data on dengue cases in West Java are utilized alongside simulation results. The findings indicate that, across different conditions, the Uniform hyperprior distribution proves to be the optimal choice.

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Section: Discussionmentioning

confidence: 99%