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On Implementation of the Markov Chain Monte Carlo Stochastic Approximation Algorithm

In: Advances in Directional and Linear Statistics

Author

Listed:
  • Yihua Jiang

    (Capital One Financial Corp., 15000 Capital One Dr.)

  • Peter Karcher
  • Yuedong Wang

Abstract

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.

Suggested Citation

  • Yihua Jiang & Peter Karcher & Yuedong Wang, 2011. "On Implementation of the Markov Chain Monte Carlo Stochastic Approximation Algorithm," Springer Books, in: Martin T. Wells & Ashis SenGupta (ed.), Advances in Directional and Linear Statistics, chapter 0, pages 97-111, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2628-9_7
    DOI: 10.1007/978-3-7908-2628-9_7
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