Bayesian MCMC Estimation

  • Jeffrey A. Mills
  • Olivier Parent
Reference work entry


This chapter provides a survey of the recent literature on Bayesian inference methods in regional science. This discussion is presented in the context of the Spatial Durbin Model (SDM) with heteroskedasticity as a canonical example. The overall performance of different hierarchical models is analyzed. We extend the benchmark specification to the dynamic panel data model with spatial dependence. An empirical illustration of the flexibility of the Bayesian approach is provided through the analysis of the role of knowledge production and spatiotemporal spillover effects using a space-time panel data set covering 49 US states over the period 1994–2005.


Markov Chain Markov Chain Monte Carlo Spatial Dependence Markov Chain Monte Carlo Method Transition Distribution 
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  1. Anselin L (1988) Spatial econometrics: methods and models. Kluwer, BostonCrossRefGoogle Scholar
  2. Autant-Bernard C, LeSage JP (2011) Quantifying knowledge spillovers using spatial econometric models. J Reg Sci 51(3):471–496CrossRefGoogle Scholar
  3. Banerjee S, Carlin B, Gelfand A (2004) Hierarchical modeling and analysis for spatial data. Chapman & Hall, Boca RatonGoogle Scholar
  4. Barry R, Pace RK (1999) Monte Carlo estimates of the log determinant of large sparse matrices. Linear Algebra Appl 289(1–3):41–54CrossRefGoogle Scholar
  5. Chib S (2008) Panel data modeling and inference: a Bayesian primer. In: Matyas L, Sevestre P (eds) The econometrics of panel data. Springer, Berlin/Heidelberg, pp 479–515CrossRefGoogle Scholar
  6. Chib S, Greenberg E (1995) Understanding the Metropolis-Hastings algorithm. Am Stat 49(4):327–335Google Scholar
  7. Debarsy N, Ertur C, LeSage JP (2012) Interpreting dynamic space-time panel data models. Stat Methodol 9(1–2):158–171CrossRefGoogle Scholar
  8. Ertur C, Koch W (2007) The role of human capital and technological interdependence in growth and convergence processes: international evidence. J Appl Econom 22(6):1033–1062CrossRefGoogle Scholar
  9. Gamerman D, Lopes HF (2006) Markov chain Monte Carlo. Chapman & HallGoogle Scholar
  10. Gelfand AE, Smith AFM (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85(410):98–409Google Scholar
  11. Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis, 2nd edn. Chapman & Hall, LondonGoogle Scholar
  12. Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6(6):721–741CrossRefGoogle Scholar
  13. Geweke J (1993) Bayesian treatment of the independent Student-t linear model. J Appl Econom 8(1):519–540Google Scholar
  14. Geyer C (2011) Introduction to Markov chain Monte Carlo. In: Brooks SP, Gelman A, Jones G, Meng X-L (eds) Handbook of Markov chain Monte Carlo. Chapman and Hall/CRC Press, Boca RatonGoogle Scholar
  15. Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97–109CrossRefGoogle Scholar
  16. Jones CI (2002) Sources of U.S. economic growth in a world of ideas. Am Econ Rev 92(1):220–239CrossRefGoogle Scholar
  17. Kakamu KW, Polasek W, Wago H (2012) Production technology and agglomeration for Japanese prefectures during 1991–2000. Paper Reg Sci 91(1):29–41CrossRefGoogle Scholar
  18. Lee LF, Yu J (2010) Some recent developments in spatial panel data models. Reg Sci Urban Econ 40(5):255–271CrossRefGoogle Scholar
  19. LeSage JP, Fischer MM (2008) Spatial growth regressions: model specification, estimation and interpretation. Spatial Econ Anal 3(3):275–304CrossRefGoogle Scholar
  20. LeSage JP, Pace RK (2009) An introduction to spatial econometrics. CRC Press, Boca RatonCrossRefGoogle Scholar
  21. Meng XL, van Dyk DA (1999) Seeking efficient data augmentation schemes via conditional and marginal augmentation. Biometrika 86(2):301–320CrossRefGoogle Scholar
  22. Metropolis N, Ulam S (1949) The Monte Carlo method. J Am Stat Assoc 44(247):335–341CrossRefGoogle Scholar
  23. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machine. J Chem Phys 21:1087–1092CrossRefGoogle Scholar
  24. Parent O (2012) A space-time analysis of knowledge production. J Geogr Syst 14(1):49–73CrossRefGoogle Scholar
  25. Parent O, LeSage JP (2008) Using the variance structure of the conditional autoregressive spatial specification to model knowledge spillovers. J Appl Econom 23(2):235–256CrossRefGoogle Scholar
  26. Parent O, LeSage JP (2012) Spatial dynamic panel data models with random effects. Reg Sci Urban Econ 42(4):727–738CrossRefGoogle Scholar
  27. Tanner MA, Wong W (1987) The calculation of posterior distributions by data augmentation (with discussion). J Am Stat Assoc 82(398):528–550CrossRefGoogle Scholar
  28. Tierney L (1994) Markov chains for exploring posterior distributions (with discussion). Ann Stat 22(4):1701–1762CrossRefGoogle Scholar
  29. Wang X, Kockelman K, Lemp J (2012) The dynamic spatial multinomial Probit model: analysis of land use change using parcel-level data. J Transp geogr 24:77–88CrossRefGoogle Scholar
  30. Yu J, de Jong R, Lee LF (2008) Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large. J Econom 146(1):118–134CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of CincinnatiCincinnatiUSA

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