Improved sampling-importance resampling and reduced bias importance sampling

The sampling-importance resampling (SIR) algorithm aims at drawing a random sample from a target distribution pi. 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 pi/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 Metropotis-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.