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Multivariate Spatial Regression Models

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  • Dani Gamerman
  • Ajax R. B. Moreira

Abstract

This paper describes the inference procedures required to perform Bayesian inference to some multivariate econometric models. These models have a spatial component built into commonly used multivariate models. In particular, the seemingly unrelated regression and vector autoregressive models are addressed and extended to accommodate for spatial dependence. Inference procedures are based on a variety of simulation-based schemes designed to obtain samples from the posterior distribution of model parameters. They are also used to provide a basis to forecast new observations. Este artigo descreve os procedimentos para a inferência bayesiana de modelos multivariados. Esses modelos incluem uma componente espacial que é comumente utilizada em modelos econômicos. Em particular, os modelos de regressões aparentemente não-relacionadas Sure e vetores auto-regressivos são estendidos para acomodar a dependência espacial. Os procedimentos de inferência são baseados em uma variedade de esquemas de simulação desenhados para obter amostras da distribuição a posteriori dos parâmetros do modelo. Estes podem ser utilizados para prover também estimativas da previsão de novas observações.

Suggested Citation

  • Dani Gamerman & Ajax R. B. Moreira, 2015. "Multivariate Spatial Regression Models," Discussion Papers 0116, Instituto de Pesquisa Econômica Aplicada - IPEA.
  • Handle: RePEc:ipe:ipetds:0116
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    References listed on IDEAS

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    1. Pace, R. Kelley & Barry, Ronald & Gilley, Otis W. & Sirmans, C. F., 2000. "A method for spatial-temporal forecasting with an application to real estate prices," International Journal of Forecasting, Elsevier, vol. 16(2), pages 229-246.
    2. Mardia, K. V., 1988. "Multi-dimensional multivariate Gaussian Markov random fields with application to image processing," Journal of Multivariate Analysis, Elsevier, vol. 24(2), pages 265-284, February.
    3. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    4. Gamerman, Dani & Moreira, Ajax R. B. & Rue, Havard, 2003. "Space-varying regression models: specifications and simulation," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 513-533, March.
    5. repec:sbe:breart:v:17:y:1997:i:1:a:2868 is not listed on IDEAS
    6. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344, April.
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