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Improved Sampling‐Importance Resampling and Reduced Bias Importance Sampling

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  • Øivind Skare
  • Erik Bølviken
  • Lars Holden

Abstract

. The sampling‐importance resampling (SIR) algorithm aims at drawing a random sample from a target distribution π. First, a sample is drawn from a proposal distribution q, and then from this a smaller sample is drawn with sample probabilities proportional to the importance ratios π/q. We propose here a simple adjustment of the sample probabilities and show that this gives faster convergence. The results indicate that our version converges better also for small sample sizes. The SIR algorithms are compared with the Metropolis–Hastings (MH) algorithm with independent proposals. Although MH converges asymptotically faster, the results indicate that our improved SIR version is better than MH for small sample sizes. We also establish a connection between the SIR algorithms and importance sampling with normalized weights. We show that the use of adjusted SIR sample probabilities as importance weights reduces the bias of the importance sampling estimate.

Suggested Citation

  • Øivind Skare & Erik Bølviken & Lars Holden, 2003. "Improved Sampling‐Importance Resampling and Reduced Bias Importance Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 719-737, December.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:4:p:719-737
    DOI: 10.1111/1467-9469.00360
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    Cited by:

    1. Boyang Shang & Daniel W. Apley & Sanjay Mehrotra, 2023. "Diversity Subsampling: Custom Subsamples from Large Data Sets," INFORMS Joural on Data Science, INFORMS, vol. 2(2), pages 161-182, October.
    2. Runhuan Feng & Peng Li, 2021. "Sample Recycling Method -- A New Approach to Efficient Nested Monte Carlo Simulations," Papers 2106.06028, arXiv.org.
    3. Tan, Ming & Tian, Guo-Liang & Wang Ng, Kai, 2006. "Hierarchical models for repeated binary data using the IBF sampler," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1272-1286, March.

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