Bayesian Analysis

Reduced rank regression models with latent variables in Bayesian functional data analysis

Angelika van der Linde

Full-text: Open access

Abstract

In functional data analysis (FDA) it is of interest to generalize techniques of multivariate analysis like canonical correlation analysis or regression to functions which are often observed with noise. In the proposed Bayesian approach to FDA two tools are combined: (i) a special Demmler-Reinsch like basis of interpolation splines to represent functions parsimoniously and flexibly; (ii) latent variable models initially introduced for probabilistic principal components analysis or canonical correlation analysis of the corresponding coefficients. In this way partial curves and non-Gaussian measurement error schemes can be handled. Bayesian inference is based on a variational algorithm such that computations are straight forward and fast corresponding to an idea of FDA as a toolbox for explorative data analysis. The performance of the approach is illustrated with synthetic and real data sets.

Article information

Source
Bayesian Anal. Volume 6, Number 1 (2011), 77-126.

Dates
First available in Project Euclid: 13 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1339611942

Digital Object Identifier
doi:10.1214/11-BA603

Mathematical Reviews number (MathSciNet)
MR2781809

Zentralblatt MATH identifier
1330.62163

Subjects
Primary: 62F15: Bayesian inference
Secondary: 62G99: None of the above, but in this section 62H20: Measures of association (correlation, canonical correlation, etc.) 62H25: Factor analysis and principal components; correspondence analysis 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Keywords
Functional data analysis Functional canonical correlation analysis Functional regression Functional prediction Functional discriminant analysis

Citation

van der Linde, Angelika. Reduced rank regression models with latent variables in Bayesian functional data analysis. Bayesian Anal. 6 (2011), no. 1, 77--126. doi:10.1214/11-BA603. https://projecteuclid.org/euclid.ba/1339611942


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