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Reversed particle filtering for hidden markov models

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Abstract

We present an approach to selecting the distributions in sampling-resampling which improves the efficiency of the weighted bootstrap. To complement the standard scheme of sampling from the prior and reweighting with the likelihood, we introduce a reversed scheme, which samples from the (normalized) likelihood and reweights with the prior. We begin with some motivating examples, before developing the relevant theory. We then apply the approach to the particle filtering of time series, including nonlinear and non-Gaussian Bayesian state-space models, a task that demands efficiency, given the repeated application of the weighted bootstrap. Through simulation studies on a normal dynamic linear model, Poisson hidden Markov model, and stochastic volatility model, we demonstrate the gains in efficiency obtained by the approach, involving the choice of the standard or reversed filter. In addition, for the stochastic volatility model, we provide three real-data examples, including a comparison with importance sampling methods that attempt to incorporate information about the data indirectly into the standard filtering scheme and an extension to multivariate models. We determine that the reversed filtering scheme offers an advantage over such auxiliary methods owing to its ability to incorporate information about the data directly into the sampling, an ability that further facilitates its performance in higher-dimensional settings.

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References

  • Andrieu, C., Doucet, A., Holenstein, R.: Particle Markov chain Monte Carlo methods. J Royal Statist Soc Ser B Statist Methodol 72(3), 269–342 (2010)

    Article  MathSciNet  Google Scholar 

  • Briers, M., Doucet, A., Maskell, S.: Smoothing algorithms for state-space models. Ann Inst Statist Math 62, 61–89 (2010)

    Article  MathSciNet  Google Scholar 

  • Chib, S., Nardari, F., Shephard, N.: Analysis of high dimensional multivariate stochastic volatility models. J Econom 134(2), 341–371 (2006)

    Article  MathSciNet  Google Scholar 

  • Chib, S., Omori, Y., Asai, M.: Multivariate stochastic volatility, pp. 365–400. Springer, Berlin (2009)

    Google Scholar 

  • Choy, S., Smith, A.: On robust analysis of a normal location parameter. J Royal Statist Soc Ser B 59, 463–474 (1997)

    Article  MathSciNet  Google Scholar 

  • Doucet, A., Godsill, S., Andrieu, C.: On sequential Monte Carlo sampling methods for Bayesian filtering. Statist Comput 10, 197–208 (2000)

    Article  Google Scholar 

  • Efron, B.: Bayesian inference and the parametric bootstrap. Ann Appl Statist 6, 1971–1997 (2012)

    Article  MathSciNet  Google Scholar 

  • Fearnhead, P.: Using random quasi-Monte-Carlo within particle filters, with application to financial time series. J Computat Graph Statist 14(4), 751–769 (2005)

    Article  MathSciNet  Google Scholar 

  • Fearnhead, P., Wyncoll, D., Tawn, J.: A sequential smoothing algorithm with linear computational cost. Biometrika 97(2), 447–464 (2010)

    Article  MathSciNet  Google Scholar 

  • French, K.R.: Data library (2024). Available from World Wide Web: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french

  • Godsill, S.J., Doucet, A., West, M.: Monte Carlo smoothing for nonlinear time series. J Am Statist Assoc 99(465), 156–168 (2004)

    Article  MathSciNet  Google Scholar 

  • Gordon, N.J., Salmond, D.J., Smith, A.F.: Novel approach to nonlinear/non-Gaussian Bayesian state estimation. Proc F (Radar Signal Process) 140, 107–113 (1993)

    Article  Google Scholar 

  • Harvey, A., Ruiz, E., Shephard, N.: Multivariate stochastic variance models. Rev Econom Stud 61(2), 247–264 (1994)

    Article  Google Scholar 

  • Jacquier, E., Polson, N.G., Rossi, P.E.: Bayesian analysis of stochastic volatility models. J Bus Econom Statist 20(1), 69–87 (2002)

  • Johannes, M.S., Polson, N.G., Stroud, J.R.: Optimal filtering of jump diffusions: extracting latent states from asset prices. Rev Financ Stud 22(7), 2759–2799 (2009)

    Article  Google Scholar 

  • Kastner, G., Frühwirth-Schnatter, S., Lopes, H.F.: Efficient Bayesian inference for multivariate factor stochastic volatility models. J Computat Graph Statist 26(4), 905–917 (2017)

    Article  MathSciNet  Google Scholar 

  • Kitagawa, G.: A Monte Carlo filtering and smoothing method for non-Gaussian nonlinear state space models. Proc Joint Sem Statist Time Ser Anal 2, 110–131 (1993)

    Google Scholar 

  • Kitagawa, G.: Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J Computat Graph Statist 5(1), 1–25 (1996)

    Article  MathSciNet  Google Scholar 

  • Kong, A., Liu, J.S., Wong, W.H.: Sequential imputations and Bayesian missing data problems. J Am Statist Assoc 89(425), 278–288 (1994)

    Article  Google Scholar 

  • Li, Y., Ghosh, S.K.: Efficient sampling methods for truncated multivariate normal and student-t distributions subject to linear inequality constraints. J Statist Theory Pract 9, 712–732 (2015)

    Article  MathSciNet  Google Scholar 

  • Liu, J., West, M.: Combined parameter and state estimation in simulation-based filtering. In: sequential monte carlo methods in practice, pp. 197–223. Springer, London (2001)

    Chapter  Google Scholar 

  • Liu, J.S.: Metropolized independent sampling with comparisons to rejection sampling and importance sampling. Statist Comput 6, 113–119 (1996)

    Article  Google Scholar 

  • Liu, J.S., Chen, R.: Sequential Monte Carlo methods for dynamic systems. J Am Statist Assoc 93(443), 1032–1044 (1998)

    Article  MathSciNet  Google Scholar 

  • Lopes, H.F., Tsay, R.S.: Particle filters and Bayesian inference in financial econometrics. J Forecast 30(1), 168–209 (2011)

    Article  MathSciNet  Google Scholar 

  • Malik, S., Pitt, M.K.: Particle filters for continuous likelihood evaluation and maximisation. J Econom 165(2), 190–209 (2011)

    Article  MathSciNet  Google Scholar 

  • Martin, G.M., McCabe, B.P., Frazier, D.T., Maneesoonthorn, W., Robert, C.P.: Auxiliary likelihood-based approximate Bayesian computation in state space models. J Computat Graph Stat 28(3), 508–522 (2019)

    Article  MathSciNet  Google Scholar 

  • Neal, R.M.: Slice sampling. Ann Statist 31(3), 705–767 (2003)

    Article  MathSciNet  Google Scholar 

  • Pitt, M.K., Malik, S., Doucet, A.: Simulated likelihood inference for stochastic volatility models using continuous particle filtering. Ann Instit Statist Math 66, 527–552 (2014)

    Article  MathSciNet  Google Scholar 

  • Pitt, M.K., Shephard, N.: Filtering via simulation: auxiliary particle filters. J Am Statist Assoc 94(446), 590–599 (1999)

    Article  MathSciNet  Google Scholar 

  • Smith, A.F., Gelfand, A.E.: Bayesian statistics without tears: a sampling-resampling perspective. Am Statist 46(2), 84–88 (1992)

    MathSciNet  Google Scholar 

  • Stan Development Team (2023). Stan modeling language users guide and reference manual. Version 2.33. https://mc-stan.org

  • Tsay, R.S.: Analysis of Financial Time Series, p. 12. Wiley, New York (2005)

    Book  Google Scholar 

  • Yamauchi, Y., Omori, Y.: Multivariate stochastic volatility model with realized volatilities and pairwise realized correlations. J Bus Econom Statist 38(4), 839–855 (2020)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank an anonymous referee for their constructive comments that inspired the multivariate extension.

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Authors and Affiliations

  1. Department of Statistics and Data Sciences, The University of Texas at Austin, Austin, Texas, USA

    Frank Rotiroti

  2. Department of Mathematics, The University of Texas at Austin, Austin, Texas, USA

    Stephen G. Walker

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  1. Frank Rotiroti
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  2. Stephen G. Walker
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Correspondence to Stephen G. Walker.

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Rotiroti, F., Walker, S.G. Reversed particle filtering for hidden markov models. Stat Comput 34, 111 (2024). https://doi.org/10.1007/s11222-024-10426-4

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