Coupling a stochastic approximation version of EM with an MCMC procedure

Kuhn, Estelle; Lavielle, Marc

doi:10.1051/ps:2004007

Cited by 205 publications

(278 citation statements)

References 13 publications

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“…Gradient search algorithms such as the FOCE method can also be parallelized; however, to our knowledge the fraction of the computations of the FOCE method that can be parallelized (and therefore accelerated) is notably less than 99%. Among the parametric EM algorithms (1)(2)(3)(4)(5)(6)13,15,19,52,53), the MC-PEM method requires the fewest number of iterations (often 80-300, depending on the model complexity and data), since the MC-PEM algorithm spends most of its computation time on exploring potential parameter values for each subject per iteration. The MC-PEM algorithm typically uses 1,000-3,000 random samples per subject and iteration for the multidimensional integration to compute the conditional means and conditional var-cov matrices.…”

Section: Discussionmentioning

confidence: 99%

Performance and Robustness of the Monte Carlo Importance Sampling Algorithm Using Parallelized S-ADAPT for Basic and Complex Mechanistic Models

Bulitta

Landersdorfer

2011

AAPS J

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Abstract. The Monte Carlo Parametric Expectation Maximization (MC-PEM) algorithm can approximate the true log-likelihood as precisely as needed and is efficiently parallelizable. Our objectives were to evaluate an importance sampling version of the MC-PEM algorithm for mechanistic models and to qualify the default estimation settings in SADAPT-TRAN. We assessed bias, imprecision and robustness of this algorithm in S-ADAPT for mechanistic models with up to 45 simultaneously estimated structural parameters, 14 differential equations, and 10 dependent variables (one drug concentration and nine pharmacodynamic effects). Simpler models comprising 15 parameters were estimated using three of the ten dependent variables. We set initial estimates to 0.1 or 10 times the true value and evaluated 30 bootstrap replicates with frequent or sparse sampling. Datasets comprised three dose levels with 16 subjects each. Parallelized estimation was 23-fold (6.9-fold) faster using 48 threads (eight threads) relative to one thread. The MC-PEM algorithm was robust and provided unbiased and adequately precise means and variances during simultaneous estimation of complex, mechanistic models in a 45 dimensional parameter space with rich or sparse data using poor initial estimates.

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Section: Discussionmentioning

confidence: 99%

Performance and Robustness of the Monte Carlo Importance Sampling Algorithm Using Parallelized S-ADAPT for Basic and Complex Mechanistic Models

Bulitta

Landersdorfer

2011

AAPS J

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“…By deriving it with respect to each of the parameters, it follows that: where φ [k] and u [k] are simulated according to the conditional distribution p(.|y, θ [k−1] ) either directly or using a Metropolis-Hastings algorithm [14].…”

Section: Appendix Parameters Estimation With the Saem Algorithmmentioning

confidence: 99%

Genetic analysis of growth curves using the SAEM algorithm

Jaffrézic¹,

Meza

Lavielle

et al. 2006

Genet. Sel. Evol.

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-The analysis of nonlinear function-valued characters is very important in genetic studies, especially for growth traits of agricultural and laboratory species. Inference in nonlinear mixed effects models is, however, quite complex and is usually based on likelihood approximations or Bayesian methods. The aim of this paper was to present an efficient stochastic EM procedure, namely the SAEM algorithm, which is much faster to converge than the classical Monte Carlo EM algorithm and Bayesian estimation procedures, does not require specification of prior distributions and is quite robust to the choice of starting values. The key idea is to recycle the simulated values from one iteration to the next in the EM algorithm, which considerably accelerates the convergence. A simulation study is presented which confirms the advantages of this estimation procedure in the case of a genetic analysis. The SAEM algorithm was applied to real data sets on growth measurements in beef cattle and in chickens. The proposed estimation procedure, as the classical Monte Carlo EM algorithm, provides significance tests on the parameters and likelihood based model comparison criteria to compare the nonlinear models with other longitudinal methods. genetic analysis / growth curves / longitudinal data / stochastic approximation EM algorithm

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“…is proposed for the maximum likelihood inference in the multivariate SGLMMs. This algorithm combines boosting which is a very flexible and powerful tool, with stochastic approximation method (was originally introduced by [14] and extended by [10]) which is similar to the SAEM method ( [12]). Generally, the Robbins-Monro procedure is a stochastic root-finding method and the component-wise boosting approach makes the technique straightforward to implement.…”

Section: Introductionmentioning

confidence: 99%

Likelihood Inference in A Multivariate Spatial GLMM with Skew Gaussian Random Effects Using the Slice-SAB Algorithm

Rivaz¹,

Khaledi²

2017

JSTA

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This paper introduces a multivariate skew Gaussian process and uses it to extend the family of multivariate spatial generalized linear mixed models to include skew Gaussian random effects. In this setting, the parameter estimation encounters problems because the likelihood function involves high dimensional integrations which are computationally intensive. For estimating parameters of the complicated model structure, this article proposes an algorithm which is a combination of boosting with a variant of stochastic approximation. This algorithm which known as stochastic approximation boosting (SAB) algorithm, uses the Markov chain Monte Carlo method based on slice sampling to obtain simulations from full conditional distribution of random effects. A simulation study is conducted to assess the performance of our method. The proposed methodology is further illustrated through an application to a data set of soil pollution in a province of Iran.

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Coupling a stochastic approximation version of EM with an MCMC procedure

Cited by 205 publications

References 13 publications

Performance and Robustness of the Monte Carlo Importance Sampling Algorithm Using Parallelized S-ADAPT for Basic and Complex Mechanistic Models

Performance and Robustness of the Monte Carlo Importance Sampling Algorithm Using Parallelized S-ADAPT for Basic and Complex Mechanistic Models

Genetic analysis of growth curves using the SAEM algorithm

Likelihood Inference in A Multivariate Spatial GLMM with Skew Gaussian Random Effects Using the Slice-SAB Algorithm

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