Particle Ecient Importance Sampling

The ecient 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 oine sequential Monte Carlo interpretation. The particle EIS method is based on non-standard resampling weights that take into account the look-ahead construction of the importance sampler. We apply the method for a range of univariate and bivariate stochastic volatility specications. 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 lters for likelihood evaluation in high dimensions. Moreover, the ratio between the variances of the particle EIS and particle lter methods remains stable as the time series dimension increases. We illustrate the eciency of the method

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