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Particle efficient importance sampling

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  • Scharth, Marcel
  • Kohn, Robert

Abstract

The efficient importance sampling (EIS) method is a general principle for the numerical evaluation of high-dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers. Despite a number of successful applications in high dimensions, it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases. We solve this problem by recognising that the EIS framework has an offline sequential Monte Carlo interpretation. The particle EIS method is based on non-standard resampling weights that take into account the construction of the importance sampler as a sequential approximation to the state smoothing density. We apply the method for a range of univariate and bivariate stochastic volatility specifications. We also develop a new application of the EIS approach to state space models with Student’s t state innovations. Our results show that the particle EIS method strongly outperforms both the standard EIS method and particle filters for likelihood evaluation in high dimensions. We illustrate the efficiency of the method for Bayesian inference using the particle marginal Metropolis–Hastings and importance sampling squared algorithms.

Suggested Citation

  • Scharth, Marcel & Kohn, Robert, 2016. "Particle efficient importance sampling," Journal of Econometrics, Elsevier, vol. 190(1), pages 133-147.
    • Handle: RePEc:eee:econom:v:190:y:2016:i:1:p:133-147
    DOI: 10.1016/j.jeconom.2015.03.047
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    2. Sergei Seleznev, 2016. "Solving DSGE models with stochastic trends," Bank of Russia Working Paper Series wps15, Bank of Russia.
    3. Rub'en Loaiza-Maya & Didier Nibbering, 2022. "Efficient variational approximations for state space models," Papers 2210.11010, arXiv.org, revised Jun 2023.
    4. Smith, Michael Stanley & Maneesoonthorn, Worapree, 2018. "Inversion copulas from nonlinear state space models with an application to inflation forecasting," International Journal of Forecasting, Elsevier, vol. 34(3), pages 389-407.
    5. Mengheng Li & Marcel Scharth, 2022. "Leverage, Asymmetry, and Heavy Tails in the High-Dimensional Factor Stochastic Volatility Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 285-301, January.
    6. Andras Fulop & Jeremy Heng & Junye Li, 2022. "Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models," Papers 2201.01094, arXiv.org.

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