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Residual and stratified branching particle filters

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  • Kouritzin, Michael A.

Abstract

A class of discrete-time branching particle filters is introduced with individual resampling: If there are Nn particles alive at time n, N0=N, an≤1≤bn, L̂n+1i is the current unnormalized importance weight for particle i and An+1=1N∑i=1NnL̂n+1i, then weight is preserved when L̂n+1i∈(anAn+1,bnAn+1). Otherwise, ⌊L̂n+1iAn+1⌋+ρni offspring are produced and assigned weight An+1, where ρni is a Bernoulli of parameter L̂n+1iAn+1−⌊L̂n+1iAn+1⌋. The algorithms are shown to be stable with respect to the number of particles and perform better than the bootstrap algorithm as well as other popular resampled particle filters on both tracking problems considered here. Moreover, the new branching filters run significantly faster than these other particle filters on tracking and Bayesian model selection problems.

Suggested Citation

  • Kouritzin, Michael A., 2017. "Residual and stratified branching particle filters," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 145-165.
    • Handle: RePEc:eee:csdana:v:111:y:2017:i:c:p:145-165
    DOI: 10.1016/j.csda.2017.02.003
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    References listed on IDEAS

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    1. repec:wyi:journl:002173 is not listed on IDEAS
    2. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    3. Michael A. Kouritzin & Yong Zeng, 2005. "Bayesian Model Selection Via Filtering For A Class Of Micro-Movement Models Of Asset Price," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 97-121.
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    1. Tang, Xiaopeng & Zou, Changfu & Yao, Ke & Lu, Jingyi & Xia, Yongxiao & Gao, Furong, 2019. "Aging trajectory prediction for lithium-ion batteries via model migration and Bayesian Monte Carlo method," Applied Energy, Elsevier, vol. 254(C).
    2. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "Hyperbolastic Models from a Stochastic Differential Equation Point of View," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    3. Michael A. Kouritzin & Anne MacKay, 2017. "VIX-linked fees for GMWBs via Explicit Solution Simulation Methods," Papers 1708.06886, arXiv.org, revised Apr 2018.
    4. Kouritzin, Michael A. & MacKay, Anne, 2018. "VIX-linked fees for GMWBs via explicit solution simulation methods," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 1-17.
    5. Michael A. Kouritzin & Anne MacKay, 2019. "Branching Particle Pricers with Heston Examples," Papers 1907.00219, arXiv.org, revised Nov 2019.

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