A random walk Metropolis-Hastings algorithm has been widely used in sampling the parameter of spatial interaction in spatial autoregressive model from a Bayesian point of view. In addition, as an alternative approach, the griddy Gibbs sampler is proposed by  and utilized by . This paper proposes an acceptance-rejection Metropolis-Hastings algorithm as a third approach, and compares these three algorithms through Monte Carlo experiments. The experimental results show that the griddy Gibbs sampler is the most efficient algorithm among the algorithms whether the number of observations is small or not in terms of the computation time and the inefficiency factors. Moreover, it seems to work well when the size of grid is 100.
Ritter, C. and Tanner, M. (1992) Facilitating the Gibbs Sampler: The Gibbs Stopper and the Griddy-Gibbs Sampler. Journal of the American Statistical Association, 87, 861-868. http://dx.doi.org/10.1080/01621459.1992.10475289
Ohtsuka, Y. and Kakamu, K. (2009) Estimation of Electric Demand in Japan: A Bayesian Spatial Autoregressive AR(p) Approach. In: Schwartz, L.V., Ed., Inflation: Causes and Effects, Nova Science Publisher, New York, 156-178.
Gelfand, A.E., Banerjee, S., Sirmans, C.F., Tu, Y. and Ong, S.E. (2007) Multilevel Modeling Using Spatial Processes: Application to the Singapore Housing Market. Computational Statistics and Data Analysis, 51, 3567-3579.
Kelejian, H.H. and Prucha, I.R. (1999) A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review, 40, 509-533. http://dx.doi.org/10.1111/1468-2354.00027
Kakamu, K. and Wago, H. (2008) Small-Sample Properties of Panel Spatial Autoregressive Models: Comparison of the Bayesian and Maximum Likelihood Methods. Spatial Economic Analysis, 3, 305-319.
Holloway, G., Shankar, B. and Rahman, S. (2002) Bayesian Spatial Probit Estimation: A Primer and an Application to HYV Rice Adoption. Agricultural Economics, 27, 383-402. http://dx.doi.org/10.1111/j.1574-0862.2002.tb00127.x
Ohtsuka, Y., Oga, T. and Kakamu, K. (2010) Forecasting Electricity Demand in Japan: A Bayesian Spatial Autoregressive ARMA Approach. Computational Statistics & Data Analysis, 54, 2721-2735.
Stakhovych, S. and Bijmolt, T.H.A. (2009) Specification of Spatial Models: A Simulation Study on Weights Matrices. Papers in Regional Science, 88, 389-408. http://dx.doi.org/10.1111/j.1435-5957.2008.00213.x
Gelfand, A.E. and Smith, A.F.M. (1990) Sampling-Based Approaches to Calculating Marginal Densities. Journal of the American Statistical Association, 85, 398-409. http://dx.doi.org/10.1080/01621459.1990.10476213