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- Title
Bayesian Hierarchical Modeling in Linear Regression Settings.
- Authors
Sosa, Juan
- Abstract
Considering the flexibility and applicability of Bayesian modeling, main characteristics of a hierarchical model are revised and summarized under the usual assumption of exchangeability: We present the probabilistic structure of the model, all the levels involved in it, and the full conditional distribution of every parameter of the model. In this model, we allow the mean of the second stage of the model to have a linear dependency on a set of covariates by means of a regression approach. In addition, the Gibbs sampling algorithm used to obtain samples from this hierarchical model is fully described and derived. The case study is one in which we characterize in depth the average surface of the sea temperature register by 86 devices in the Mediterranean sea by the type of devise and the location describe by the latitude and the longitude. The hierarchical model fitted considerably well to this data set. Findings derived in this application include the description of the within and between means and variability of the registered temperatures, evidence of similar devise precision, differences among types of devise, and good qualities of prediction of the model. Finally, the prediction ability of the model for each type of devise is tested using data from the National Oceanic and Atmospheric Administration.
- Subjects
GIBBS sampling; PREDICTION models; REGRESSION analysis; LONGITUDE; LATITUDE
- Publication
Comunicaciones en Estadística, 2024, Vol 17, Issue 1, p98
- ISSN
2027-3355
- Publication type
Article