variance module¶
The variance-based pilot for the MLMC algorithm.
- class gemseo_umdo.statistics.multilevel.mlmc.pilots.variance.Variance(sampling_ratios, costs)[source]¶
Bases:
MLMCPilotThe variance-based pilot for the MLMC algorithm.
See also
El Amri et al., Algo. 1, Multilevel Surrogate-based Control Variates, 2023.
- Parameters:
sampling_ratios (NDArray[float]) – The sampling ratios $r_0,ldots,r_L$; the sampling ratio $r_ell$ is the factor by which $n_ell$ is increased between two sampling steps on the level $ell$.
costs (NDArray[float]) – The unit sampling costs of each level of the telescopic sum. Namely, $(mathcal{C}_{ell-1}+mathcal{C}_ell)_{ellin{0,ldots,L}}$ with $mathcal{C}_{-1}=0$.
- compute_next_level_and_statistic(levels, total_n_samples, samples, *pilot_parameters)¶
Compute the next level $ell^*$ to sample and estimate the statistic.
- Parameters:
levels (Iterable[int]) – The levels that have just been sampled.
total_n_samples (ndarray[Any, dtype[int]]) – The total number of samples of each level.
samples (Sequence[ndarray[Any, dtype[float]]]) – The samples of the different quantities of each level.
*pilot_parameters (Any) – The parameters of the pilot.
- Returns:
The next level $ell^*$ to sample and an estimation of the statistic.
- Return type:
tuple[int, numpy.ndarray[Any, numpy.dtype[float]]]