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Transdimensional sequential Monte Carlo using variational Bayes — SMCVB

Author

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  • McGrory, C.A.
  • Pettitt, A.N.
  • Titterington, D.M.
  • Alston, C.L.
  • Kelly, M.

Abstract

A new transdimensional Sequential Monte Carlo (SMC) algorithm called SMCVB is proposed. In an SMC approach, a weighted sample of particles is generated from a sequence of probability distributions which ‘converge’ to the target distribution of interest, in this case a Bayesian posterior distribution. The approach is based on the use of variational Bayes to propose new particles at each iteration of the SMCVB algorithm in order to target the posterior more efficiently. The variational-Bayes-generated proposals are not limited to a fixed dimension. This means that the weighted particle sets that arise can have varying dimensions thereby allowing us the option to also estimate an appropriate dimension for the model. This novel algorithm is outlined within the context of finite mixture model estimation. This provides a less computationally demanding alternative to using reversible jump Markov chain Monte Carlo kernels within an SMC approach. We illustrate these ideas in a simulated data analysis and in applications.

Suggested Citation

  • McGrory, C.A. & Pettitt, A.N. & Titterington, D.M. & Alston, C.L. & Kelly, M., 2016. "Transdimensional sequential Monte Carlo using variational Bayes — SMCVB," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 246-254.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:246-254
    DOI: 10.1016/j.csda.2015.03.006
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    References listed on IDEAS

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    5. Jasra, Ajay & Doucet, Arnaud & Stephens, David A. & Holmes, Christopher C., 2008. "Interacting sequential Monte Carlo samplers for trans-dimensional simulation," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1765-1791, January.
    6. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
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    Cited by:

    1. Han, Ningren & Ram, Rajeev J., 2020. "Bayesian modeling and computation for analyte quantification in complex mixtures using Raman spectroscopy," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).

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