ImportanceSamplingResult

ImportanceSamplingResult(log_weights: Tensor, log_norm: Tensor, ess: Tensor)

An object containing the results of importance sampling.

Attributes

log_weights : Tensor

An \(n\)-dimensional vector containing the unnormalised importance weights associated with a set of samples.

log_norm : Tensor

An estimate of the logarithm of the normalising constant associated with the target density.

ess : Tensor

An estimate of the effective sample size.

Notes

The effective sample size is computed using the formula \[ N_{\mathrm{eff}} = \frac{(\sum_{i=1}^{n}w_{i})^{2}}{\sum_{i=1}^{n}w_{i}^{2}}, \] where \(w_{i}\) denotes the importance weight associated with particle \(i\) (Owen, 2013).

References

Owen, AB (2013, Chapter 6). Monte Carlo theory, methods and examples.