Abstract
This study applies computationally intensive methods for Bayesian analysis of spatially distributed data. It is assumed that the space is divided in contiguous and disjoint regions or areas. The neighboring structure in a given problem may indicate a wide range of number of neighbors per area, ranging from very few neighbors to cases where all areas neighbor each other. The main aim of this work is to evaluate the influence of neighborhood on results of Markov Chain Monte Carlo (MCMC) methods. Proper and improper prior specifications for state parameters are compared. Three schemes, proposed in the literature, for sampling from the joint posterior distribution are also compared. The comparison criterion is based on the autocorrelation structure of the chains. Two classes of models are studied: the first one is characterized by a simple model without any explanatory variables and the second one is an extension with multiple regression components. Initially, sensitivity of the analysis to different prior distributions is addressed. Finally, extensive empirical analyses confront the outcomes obtained with different neighboring arrangements of the units. Results are shown to generalize those obtained with dynamic or state space models.
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Mayrink, V.D., Gamerman, D. On computational aspects of Bayesian spatial models: influence of the neighboring structure in the efficiency of MCMC algorithms. Comput Stat 24, 641–669 (2009). https://doi.org/10.1007/s00180-009-0153-0
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DOI: https://doi.org/10.1007/s00180-009-0153-0