Bayes Hilbert Spaces

DOI10.1111/anzs.12074zbMath1335.62025OpenAlexW2019317784WikidataQ60182761 ScholiaQ60182761MaRDI QIDQ2802870

Juan José Egozcue, Vera Pawlowsky-Glahn, Karl Gerald van den Boogaart

Publication date: 27 April 2016

Published in: Australian & New Zealand Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/anzs.12074

zbMATH Keywords

perturbationnormal distributionFourier coefficientsprobability measuresinfinite measuresAitchison geometry of the simplexdistance between measures

Mathematics Subject Classification ID

Bayesian problems; characterization of Bayes procedures (62C10) Probability theory on linear topological spaces (60B11)

Related Items (24)

Kriging for Hilbert-space valued random fields: the operatorial point of view ⋮ Bias reduction by projection on parametric models in Hilbertian nonparametric regression ⋮ Outlier Detection for Pandemic-Related Data Using Compositional Functional Data Analysis ⋮ Hotelling's \(T^2\) in separable Hilbert spaces ⋮ Compositional regression with functional response ⋮ Extending compositional data analysis from a graph signal processing perspective ⋮ Orthogonal decomposition of multivariate densities in Bayes spaces and relation with their copula-based representation ⋮ Weighting of parts in compositional data analysis: advances and applications ⋮ Bivariate densities in Bayes spaces: orthogonal decomposition and spline representation ⋮ Nonparametric Estimation of Repeated Densities with Heterogeneous Sample Sizes ⋮ Additive regression with Hilbertian responses ⋮ Preprocessing of centred logratio transformed density functions using smoothing splines ⋮ Cointegrated linear processes in Bayes Hilbert space ⋮ O2S2 for the Geodata Deluge ⋮ Spatial prediction and spatial dependence monitoring on georeferenced data streams ⋮ Statistical analysis of complex and spatially dependent data: a review of object oriented spatial statistics ⋮ Simplicial principal component analysis for density functions in Bayes spaces ⋮ Compositional data: the sample space and its structure ⋮ A Class-Kriging predictor for functional compositions with application to particle-size curves in heterogeneous aquifers ⋮ Compositional splines for representation of density functions ⋮ Additive regression for predictors of various natures and possibly incomplete Hilbertian responses ⋮ Compositional scalar-on-function regression with application to sediment particle size distributions ⋮ Quantum Aitchison geometry ⋮ Logratio Approach to Distributional Modeling

Uses Software

• sm

Cites Work

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• Bayes spaces: use of improper distributions and exponential families
• Isometric logratio transformations for compositional data analysis
• Groups of parts and their balances in compositional data analysis
• On some global measures of the deviations of density function estimates
• Hilbert space of probability density functions based on Aitchison geometry
• Remarks on Some Nonparametric Estimates of a Density Function
• On the Foundations of Statistical Inference
• Statistical Interpretation of Species Composition
• On Estimation of a Probability Density Function and Mode
• On Information and Sufficiency
• Geometric approach to statistical analysis on the simplex

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