# Weighted statistics¶

Functions performing statistical operations on weighted points generated via importance sampling.

pyabc.weighted_statistics.effective_sample_size(weights)[source]

Compute the effective sample size of weighted points sampled via importance sampling according to the formula

$n_\text{eff} = \frac{(\sum_{i=1}^nw_i)^2}{\sum_{i=1}^nw_i^2}$
pyabc.weighted_statistics.resample(points, weights, n)[source]

Resample from weighted samples.

Parameters
• points – The random samples.

• weights – Weights of each sample point.

• n – Number of samples to resample.

Returns

A total of n points sampled from points with putting back according to weights.

Return type

resampled

pyabc.weighted_statistics.resample_deterministic(points, weights, n, enforce_n=False)[source]

Resample from weighted samples in a deterministic manner. Essentially, multiplicities are picked as follows: The weights are multiplied by the target number n and rounded to the nearest integer, potentially with correction if enforce_n.

Parameters
• points – The random samples.

• weights – Weights of each sample point.

• n – Number of samples to resample.

• enforce_n – Whether to enforce the returned array to have length n. If not, its length can be slightly off, but it may be more representative.

Returns

A total of (roughly) n points resampled from points deterministically using a rational representation of the weights.

Return type

resampled

pyabc.weighted_statistics.weight_checked(function)[source]

Function decorator to check normalization of weights.

pyabc.weighted_statistics.weighted_mean(points, weights=None, **kwargs)[source]

Compute the weighted mean.

pyabc.weighted_statistics.weighted_median(points, weights=None, **kwargs)[source]

Compute the weighted median (i.e. 0.5 quantile).

pyabc.weighted_statistics.weighted_quantile(points, weights=None, **kwargs)[source]

Compute the weighted alpha-quantile. E.g. alpha = 0.5 -> median.

pyabc.weighted_statistics.weighted_std(points, weights=None, **kwargs)[source]

Compute the weighted standard deviation from the weighted mean.