ProductMeasure currently combines multiple independent true-measure marginals for sampling, but it does not expose combined summary statistics such as the mean, variance, standard deviation, or covariance.
It would be useful for ProductMeasure to derive these quantities directly from its marginals when the corresponding statistics are available.
For independent marginal blocks:
mean should concatenate the marginal means.
variance should concatenate the marginal variances.
standard_deviation should concatenate the marginal standard deviations.
covariance should form a block-diagonal matrix from the marginal covariance matrices.
For example, if two marginals have dimensions 1 and 2, their means should combine into a length-3 vector, while their covariance matrices should be placed along the diagonal of a 3 × 3 covariance matrix with zero covariance between the independent marginal blocks.
The implementation should follow the existing statistic attribute names and conventions used by QMCPy TrueMeasure classes.
Expected Behavior
product_measure.mean
product_measure.variance
product_measure.standard_deviation
product_measure.covariance
ProductMeasurecurrently combines multiple independent true-measure marginals for sampling, but it does not expose combined summary statistics such as the mean, variance, standard deviation, or covariance.It would be useful for
ProductMeasureto derive these quantities directly from its marginals when the corresponding statistics are available.For independent marginal blocks:
meanshould concatenate the marginal means.varianceshould concatenate the marginal variances.standard_deviationshould concatenate the marginal standard deviations.covarianceshould form a block-diagonal matrix from the marginal covariance matrices.For example, if two marginals have dimensions 1 and 2, their means should combine into a length-3 vector, while their covariance matrices should be placed along the diagonal of a 3 × 3 covariance matrix with zero covariance between the independent marginal blocks.
The implementation should follow the existing statistic attribute names and conventions used by QMCPy
TrueMeasureclasses.Expected Behavior