On Implementation of the Markov Chain Monte Carlo Stochastic Approximation Algorithm
The Markov Chain Monte Carlo Stochastic Approximation Algorithm (MCMCSAA) was developed to compute estimates of parameters with incomplete data. In theory this algorithm guarantees convergence to the expected fixed points. However, due to its flexibility and complexity, care needs to be taken for implementation in practice. In this paper we show that the performance of MCMCSAA depends on many factors such as the Markov chain Monte Carlo sample size, the step-size of the parameter update, the initial values and the choice of an approximation to the Hessian matrix. Good choices of these factors are crucial to the practical performance and our results provide practical guidelines for these choices. We propose a new adaptive and hybrid procedure which is stable and faster while maintaining the same theoretical properties.
KeywordsMarkov Chain Monte Carlo Monte Carlo Generalize Linear Mixed Model Hybrid Algorithm Stat Assoc
Unable to display preview. Download preview PDF.
- 1.Benveniste A, Métivier M, Priouret B (1987) Adaptive algorithms and stochastic approximations: Theory and applications of signal detection and processing and pattern recognition (French). Masson, ParisGoogle Scholar
- 9.Kushner HJ, Yin GG (1997) Stochastic approximations algorithms and applications. Springer, New YorkGoogle Scholar
- 15.Zhu HT, Lee SY (2003) Analysis of generalized linear mixed models via a stochastic approximation algorithm with markov chain Monte–Carlo method. Stat Comput 391–406Google Scholar