Compute the effective sample size (ESS) of the particles.

The ESS is a "rule of thumb" for assessing the degeneracy of the importance distribution: $$ESS = \frac{(\sum_{q=1}^Q w_q)^2}{\sum_{q=1}^Q w_q^2}$$

Usage

effectiveSampleSize(log_weights)

Arguments

log_weights

logarithms of the importance weights of each particle.

Value

the effective sample size, a scalar between 0 and Q

References

Liu, JS (2001) "Monte Carlo Strategies in Scientific Computing." Springer, NY, pp. 34–36.

Examples

x <- runif(100)
effectiveSampleSize(log(x))
#> [1] 74.85258