access icon free Importance sampling with transformed weights

The importance sampling (IS) method lies at the core of many Monte Carlo-based techniques. IS allows the approximation of a target probability distribution by drawing samples from a proposal (or importance) distribution, different from the target, and computing importance weights (IWs) that account for the discrepancy between these two distributions. The main drawback of IS schemes is the degeneracy of the IWs, which significantly reduces the efficiency of the method. It has been recently proposed to use transformed IWs (TIWs) to alleviate the degeneracy problem in the context of population Monte Carlo, which is an iterative version of IS. However, the effectiveness of this technique for standard IS is yet to be investigated. The performance of IS when using TIWs is numerically assessed, and showed that the method can attain robustness to weight degeneracy thanks to a bias/variance trade-off.

Inspec keywords: importance sampling; statistical distributions

Other keywords: transformed weights; Importance sampling; probability distribution; transformed IW; importance weights; Monte Carlo-based techniques

Subjects: Statistics; Monte Carlo methods; Monte Carlo methods; Probability theory, stochastic processes, and statistics

References

    1. 1)
      • 1. Robert, C.P., Casella, G.: ‘Monte Carlo statistical methods’ (Springer, 2004).
    2. 2)
    3. 3)
    4. 4)
      • 2. Bengtsson, T., Bickel, P., Li, B., et al: ‘Curse-of-dimensionality revisited: collapse of the particle filter in very large scale systems’, in: Freedman, D.A. (Ed.): ‘Probability and statistics’ (Institute of Mathematical Statistics, 2008), pp. 316334.
http://iet.metastore.ingenta.com/content/journals/10.1049/el.2016.3462
Loading

Related content

content/journals/10.1049/el.2016.3462
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading