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Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation

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  • Ming Gao Gu
  • Hong‐Tu Zhu

Abstract

We propose a two‐stage algorithm for computing maximum likelihood estimates for a class of spatial models. The algorithm combines Markov chain Monte Carlo methods such as the Metropolis–Hastings–Green algorithm and the Gibbs sampler, and stochastic approximation methods such as the off‐line average and adaptive search direction. A new criterion is built into the algorithm so stopping is automatic once the desired precision has been set. Simulation studies and applications to some real data sets have been conducted with three spatial models. We compared the algorithm proposed with a direct application of the classical Robbins–Monro algorithm using Wiebe's wheat data and found that our procedure is at least 15 times faster.

Suggested Citation

  • Ming Gao Gu & Hong‐Tu Zhu, 2001. "Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 339-355.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:2:p:339-355
    DOI: 10.1111/1467-9868.00289
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    1. Jin, Ick Hoon & Liang, Faming, 2014. "Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 402-416.
    2. R. Reeves, 2004. "Efficient recursions for general factorisable models," Biometrika, Biometrika Trust, vol. 91(3), pages 751-757, September.
    3. Chopin, Nicolas & Gadat, Sébastien & Guedj, Benjamin & Guyader, Arnaud & Vernet, Elodie, 2015. "On some recent advances in high dimensional Bayesian Statistics," TSE Working Papers 15-557, Toulouse School of Economics (TSE).
    4. Wanchuang Zhu & Yanan Fan, 2023. "A synthetic likelihood approach for intractable markov random fields," Computational Statistics, Springer, vol. 38(2), pages 749-777, June.
    5. Bee, Marco & Espa, Giuseppe & Giuliani, Diego, 2015. "Approximate maximum likelihood estimation of the autologistic model," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 14-26.
    6. Faming Liang & Ick Hoon Jin & Qifan Song & Jun S. Liu, 2016. "An Adaptive Exchange Algorithm for Sampling From Distributions With Intractable Normalizing Constants," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 377-393, March.
    7. Koutchadé, Philippe & Carpentier, Alain & Féménia, Fabienne, 2015. "Empirical modelling of production decisions of heterogeneous farmers with mixed models," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205098, Agricultural and Applied Economics Association.
    8. Koutchade, Philippe & Carpentier, Alain & Femenia, Fabienne, 2015. "Accounting for unobserved heterogeneity in micro-econometric agricultural production models: a random parameter approach," 2015 Conference, August 9-14, 2015, Milan, Italy 212015, International Association of Agricultural Economists.
    9. Koutchade, Philippe & Carpentier, Alain & Féménia, Fabienne, 2015. "Empirical modeling of production decisions of heterogeneous farmers with random parameter models," Working Papers 210097, Institut National de la recherche Agronomique (INRA), Departement Sciences Sociales, Agriculture et Alimentation, Espace et Environnement (SAE2).
    10. L. Sun & M. K. Clayton, 2008. "Bayesian Analysis of Crossclassified Spatial Data with Autocorrelation," Biometrics, The International Biometric Society, vol. 64(1), pages 74-84, March.
    11. Yao Chen & Qingyi Gao & Xiao Wang, 2022. "Inferential Wasserstein generative adversarial networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 83-113, February.
    12. Sy-Miin Chow & Zhaohua Lu & Andrew Sherwood & Hongtu Zhu, 2016. "Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 102-134, March.
    13. Nial Friel & Håvard Rue, 2007. "Recursive computing and simulation-free inference for general factorizable models," Biometrika, Biometrika Trust, vol. 94(3), pages 661-672.
    14. Lee, Sik-Yum & Xu, Liang, 2004. "Influence analyses of nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 321-341, March.
    15. Moon, Sangkil & Azizi, Kathryn, 2013. "Finding Donors by Relationship Fundraising," Journal of Interactive Marketing, Elsevier, vol. 27(2), pages 112-129.
    16. Tadić, Vladislav B., 2015. "Convergence and convergence rate of stochastic gradient search in the case of multiple and non-isolated extrema," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1715-1755.
    17. Li Cai, 2010. "High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 33-57, March.
    18. Matthias von Davier & Sandip Sinharay, 2010. "Stochastic Approximation Methods for Latent Regression Item Response Models," Journal of Educational and Behavioral Statistics, , vol. 35(2), pages 174-193, April.
    19. Qian, Zhiguang & Shapiro, Alexander, 2006. "Simulation-based approach to estimation of latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1243-1259, November.
    20. Gu, Minggao & Wu, Yueqin & Huang, Bin, 2014. "Partial marginal likelihood estimation for general transformation models," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 1-18.

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