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Title: A Bayesian Analysis of Population Density Over Time: How Spatial Correlation Matters

Citation Type: Dissertation/Thesis

Publication Year: 2016

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Abstract: In this work we propose a dynamic Bayesian approach to modeling the population's density; predictors of different nature are used, e.g. economics and geographic indices. The model is applied to the evaluation of the location of population in the state of Massachusetts over a period of 50 years, from 1970 to 2010. The aim of this work is to introduce into the analysis both spatial and time correlation among data. We deal with AutoRegressive models, that provide the most common way to explore time dependence. In order to explore spatial correlation, we propose two different generalized regression mixed models: one with spatial independent random effects and one that includes spatial random effects evolving as a Conditionally AutoRegressive model (CAR). Both are compared with a baseline linear model. For the CAR model, we derive the analytical expression of the full conditional distributions necessary to build a MCMC algorithm efficiently coded in Julia language, and to sample from a posterior distribution. The implementation of the other two models were made in Stan.

Url: https://www.politesi.polimi.it/bitstream/10589/123912/5/2016_07_Ghiringhelli_Chiara.pdf

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Authors: Ghiringhelli, Chiara

Institution: Politecnico di Milano

Department: Scuola di Ingegneria Industriale E Dell

Advisor: Dr. Ilenia Epifani

Degree: Master of Science in Mathematical Engineering

Publisher Location: Milan, Italy

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Data Collections: IPUMS NHGIS

Topics: Other

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