Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptive algorithms and stochastic approximations
Adaptive algorithms and stochastic approximations
Acceleration of stochastic approximation by averaging
SIAM Journal on Control and Optimization
Markov random field modeling in image analysis
Markov random field modeling in image analysis
Hidden Markov Measure Field Models for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
ML parameter estimation for Markov random fields with applications to Bayesian tomography
IEEE Transactions on Image Processing
Expectation maximization enhancement with evolutionstrategy for stochastic ontology mapping
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Joint analysis of mixed Poisson and continuous longitudinal data with nonignorable missing values
Computational Statistics & Data Analysis
Incremental distributed identification of Markov random field models in wireless sensor networks
IEEE Transactions on Signal Processing
Approximate Bayesian inference in spatial GLMM with skew normal latent variables
Computational Statistics & Data Analysis
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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.