TY - JOUR
T1 - Maximum likelihood from spatial random effects models via the stochastic approximation expectation maximization algorithm
AU - Zhu, Hongtu
AU - Gu, Minggao
AU - Peterson, Bradley
N1 - Funding Information:
Acknowledgments This work was supported in part by NSF grant SES-0643663 to Dr. Zhu, Hong Kong Research Grants Council competitive grant 216078 to Dr. Gu, NIDA grant DA017820, NIMH grants MH068318 and K0274677 to Dr. Peterson, by the Suzanne Crosby Murphy Endowment at Columbia University Medical Center, and by the Thomas D. Klingenstein and Nancy D. Perlman Family Fund. We thank the Editor, an Associate Editor, and three anonymous referees for valuable suggestions, which greatly helped improve our presentation. Thanks to Dr. Jason Royal for his invaluable editorial assistance.
PY - 2007/6
Y1 - 2007/6
N2 - We introduce a class of spatial random effects models that have Markov random fields (MRF) as latent processes. Calculating the maximum likelihood estimates of unknown parameters in SREs is extremely difficult, because the normalizing factors of MRFs and additional integrations from unobserved random effects are computationally prohibitive. We propose a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood functions of spatial random effects models. The SAEM algorithm integrates recent improvements in stochastic approximation algorithms; it also includes components of the Newton-Raphson algorithm and the expectation-maximization (EM) gradient algorithm. The convergence of the SAEM algorithm is guaranteed under some mild conditions. We apply the SAEM algorithm to three examples that are representative of real-world applications: a state space model, a noisy Ising model, and segmenting magnetic resonance images (MRI) of the human brain. The SAEM algorithm gives satisfactory results in finding the maximum likelihood estimate of spatial random effects models in each of these instances.
AB - We introduce a class of spatial random effects models that have Markov random fields (MRF) as latent processes. Calculating the maximum likelihood estimates of unknown parameters in SREs is extremely difficult, because the normalizing factors of MRFs and additional integrations from unobserved random effects are computationally prohibitive. We propose a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood functions of spatial random effects models. The SAEM algorithm integrates recent improvements in stochastic approximation algorithms; it also includes components of the Newton-Raphson algorithm and the expectation-maximization (EM) gradient algorithm. The convergence of the SAEM algorithm is guaranteed under some mild conditions. We apply the SAEM algorithm to three examples that are representative of real-world applications: a state space model, a noisy Ising model, and segmenting magnetic resonance images (MRI) of the human brain. The SAEM algorithm gives satisfactory results in finding the maximum likelihood estimate of spatial random effects models in each of these instances.
KW - Expectation maximization
KW - Markov chain Monte Carlo
KW - Markov random fields
KW - Spatial random effects models
KW - Stochastic approximation
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U2 - 10.1007/s11222-006-9012-9
DO - 10.1007/s11222-006-9012-9
M3 - Article
AN - SCOPUS:34249667588
SN - 0960-3174
VL - 17
SP - 163
EP - 177
JO - Statistics and Computing
JF - Statistics and Computing
IS - 2
ER -