# pyabc.weighted_statistics

## Weighted statistics

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

pyabc.weighted_statistics.effective_sample_size(weights)[source]

Effective sample size.

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

$n_\text{eff} = \frac{(\sum_{i=1}^nw_i)^2}{\sum_{i=1}^nw_i^2}$
Parameters:

weights (Importance sampling weights.) –

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.weighted_mean(points: ndarray, weights: ndarray)[source]

Compute the weighted mean.

Parameters:
• points (Parameter samples, shape (n_sample,) or (n_sample, n_par).) –

• weights (Weights, shape (n_sample,) or (n_sample, 1).) –

Returns:

mean

Return type:

The mean, shape () or (n_par,).

pyabc.weighted_statistics.weighted_median(points, weights)[source]

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

pyabc.weighted_statistics.weighted_mse(points, weights, refval)[source]

Compute the weighted mean square error.

pyabc.weighted_statistics.weighted_quantile(points, weights=None, alpha=0.5)[source]

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

pyabc.weighted_statistics.weighted_rmse(points, weights, refval)[source]

Compute the weighted root mean square error.

pyabc.weighted_statistics.weighted_std(points, weights)[source]

Compute the weighted standard deviation.

See weighted_mean for docs.

pyabc.weighted_statistics.weighted_var(points, weights)[source]

Compute the weighted variance.

See weighted_mean for docs.