Abstract
In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms—also known as particle filters—relying on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the quality of the estimates. Thus, we show how the long-used coefficient of variation (suggested by Kong et al. in J. Am. Stat. Assoc. 89(278–288):590–599, 1994) of the weights can be used for estimating the chi-square distance between the target and instrumental distributions of the auxiliary particle filter. As a by-product of this analysis we obtain an auxiliary adjustment multiplier weight type for which this chi-square distance is minimal. Moreover, we establish an empirical estimate of linear complexity of the Kullback-Leibler divergence between the involved distributions. Guided by these results, we discuss adaptive designing of the particle filter proposal distribution and illustrate the methods on a numerical example.
Original language | English |
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Pages (from-to) | 461-480 |
Journal | Statistics and Computing |
Volume | 18 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2008 |
Subject classification (UKÄ)
- Probability Theory and Statistics
Free keywords
- Adaptive Monte Carlo
- Auxiliary particle filter
- Coefficient of variation
- Kullback-Leibler divergence
- Cross-entropy method
- Sequential Monte Carlo
- State space models