ReferenceMeasure: Reference measures: the geometry of a Bayes space

In DistributionalDDA: Distributional Data Analysis in Bayes Spaces

Reference measures: the geometry of a Bayes space

Description

A reference measure is the probability distribution that defines a [BayesSpace]: it plays the role of the origin, and all modelled distributions are expressed relative to it. Choosing it fixes the support and the geometry of the analysis.

Details

# Choosing a reference measure Pick a measure whose support matches your data, and ideally whose mass is distributed similarly:

[ReferenceMeasureUniform]

uniform on an interval '(a, b)'; the simplest choice for data on a bounded interval (predefined: 'B2Unif01').

[ReferenceMeasureTransformed]

a transformed support, e.g. a Gaussian reference via its CDF (predefined: 'B2N01'); useful for data on the real line or with a known reference shape.

[ReferenceMeasureDiscrete]

a finite set of categories with given probabilities.

A poor choice (e.g. a uniform reference for strongly skewed data) still works but gives a less informative geometry. Inspect a measure with [getReferenceMeasure] and the resulting metric with [getMetricTensor].

See Also

[BayesSpace], [BayesSpaceBasis], [BData]

DistributionalDDA documentation built on Oct. 20, 2026, 5:06 p.m.