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Enriched Stick Breaking Processes for Functional Data.

Bruno Scarpa1, David B Dunson2

  • 1Department of Statistical Sciences, University of Padua, Padua, Italy.

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|July 1, 2014
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Summary
This summary is machine-generated.

We introduce novel stick-breaking priors for functional data analysis, allowing incorporation of prior knowledge about curve attributes. This method enhances functional Dirichlet process (FDP) models for better analysis of common curve characteristics.

Keywords:
Functional Dirichlet processFunctional data analysisNonparametric BayesPrior elicitationRandom curvesRandom probability measure

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Bayesian Inference

Background:

  • Prior information on curve attributes is often available but difficult to integrate into functional data analysis.
  • Existing methods like the functional Dirichlet process (FDP) do not easily accommodate such specific prior knowledge.

Purpose of the Study:

  • To propose a new class of stick-breaking priors for functional data distributions.
  • To enable the incorporation of user-specified prior probabilities for curve attributes.
  • To generalize the functional Dirichlet process (FDP) for enriched analysis of common curve patterns.

Main Methods:

  • Developed a generalized functional Dirichlet process (FDP) using stick-breaking priors.
  • Incorporated functional atoms from constrained stochastic processes.
  • Specified stick-breaking weights with user-defined prior probabilities and hyperpriors for uncertainty.

Main Results:

  • The proposed priors enrich the random distribution for curves with common attributes.
  • Theoretical properties of the new priors were investigated.
  • Methods for posterior computation were developed and validated.

Conclusions:

  • The novel stick-breaking priors offer a flexible framework for functional data analysis incorporating prior attribute information.
  • The approach provides a more enriched representation of data with known common characteristics.
  • Demonstrated utility through an application to menstrual cycle temperature curve data.