pyPDAF.PDAF.diag_effsample

pyPDAF.PDAF.diag_effsample()

Calculating the effective sample size of a particle filter.

Based on [1], it is defined as the inverse of the sum of the squared particle filter weights: \(N_{eff} = \frac{1}{\sum_{i=1}^{N} w_i^2}\) where \(w_i\) is the weight of particle with index i. and \(N\) is the number of particles.

If the \(N_{eff}=N\), all weights are identical, and the filter has no influence on the analysis. If \(N_{eff}=0\), the filter is collapsed.

This is typically called during the analysis step of a particle filter, e.g. in the analysis step of NETF and LNETF.

References

[1]

Doucet, A., de Freitas, N., Gordon, N. (2001). An Introduction to Sequential Monte Carlo Methods. In: Doucet, A., de Freitas, N., Gordon, N. (eds) Sequential Monte Carlo Methods in Practice. Statistics for Engineering and Information Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3437-9_1

Parameters:

• dim_sample (int) – Sample size

• weights (ndarray[np.float64, ndim=1]) – Weights of the samples Array shape: (dim_sample)

Returns:

n_eff – Effecfive sample size

Return type:

double