2007
DOI: 10.1007/s11222-006-9012-9
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Maximum likelihood from spatial random effects models via the stochastic approximation expectation maximization algorithm

Abstract: 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 in… Show more

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Cited by 31 publications
(18 citation statements)
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“…Determine the maximum likelihood function value, L, of the battery charge capacity over time using the experimental data and apply Equation (9) that has P Q ij , φ ij , representing the probability density function of the nonlinear battery charge decay [34].…”
Section: Estimation Of Future Battery Charge Capacitymentioning
confidence: 99%
“…Determine the maximum likelihood function value, L, of the battery charge capacity over time using the experimental data and apply Equation (9) that has P Q ij , φ ij , representing the probability density function of the nonlinear battery charge decay [34].…”
Section: Estimation Of Future Battery Charge Capacitymentioning
confidence: 99%
“…Our interest is in estimating the parameters in bold-italicθ=false(βT,θμT,θΛT,θεT,θbTfalse) via the SAEM algorithm (Zhu & Gu, 2007). Here, θ μ is a p μ × 1 (where p μ ≤ n y ) vector of freed parameters in μ , θ Λ is a p Λ × 1 vector containing all unknown factor loadings in Λ , θ ε is a p ε × 1 vector containing all the unknown parameters in Σ ε , and θ b is a p b × 1 vector containing all the unknown parameters in Σ b .…”
Section: Nonlinear Ordinary Differential Equation (Ode) Models Witmentioning
confidence: 99%
“…Under the Bayesian framework, spatial correlations in imaging data have been modeled through various spatial priors, such as conditional autoregressive (CAR), Gaussian process, or Markov random field (MRF), to spatial component of the signal or the noise process (Groves et al, 2009; Penny et al, 2005; Brezger et al, 2007). Such spatial priors are commonly characterized by several tuning parameters, but it can be computationally prohibitive in calculating these tuning parameters (Zhu et al, 2007). Moreover, it can be restrictive to assume a specific type of correlation structure such as CAR and MRF, since such correlation structure may not accurately approximate the global and local spatial dependence structure of imaging data.…”
Section: Introductionmentioning
confidence: 99%