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Latent Stick-Breaking Processes.

Abel Rodríguez1, David B Dunson, Alan E Gelfand

  • 1Abel Rodriguez is Assistant Professor, Department of Applied Mathematics and Statistics, University of California, Mailstop SOE2, Santa Cruz, CA 95064 ( abel@soe.ucsc.edu ). David B. Dunson is Professor ( dunson@stat.duke.edu ) and Alan E. Gelfand is Professor ( alan@stat.duke.edu ), Department of Statistical Sciences, Duke University, Box 90251, Durham, NC 27708.

Journal of the American Statistical Association
|April 6, 2013
PubMed
Summary
This summary is machine-generated.

We introduce a novel latent stick-breaking process (LaSBP) for modeling stochastic processes with random distributions. This method partitions data, clustering nearby points effectively for diverse applications.

Keywords:
Nonparametric BayesOption pricingPoint-referenced countsRandom probability measureRandom stochastic processes

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Area of Science:

  • Statistics
  • Probability Theory
  • Data Science

Background:

  • Stochastic processes often assume fixed marginal distributions, limiting their applicability.
  • Modeling dependence structures in random distributions is computationally challenging.
  • Existing methods struggle to capture complex spatial correlations in random processes.

Purpose of the Study:

  • To develop a flexible model for stochastic processes with random marginal distributions.
  • To introduce a novel method for inducing dependence across locations in such processes.
  • To provide an efficient computational algorithm for the proposed model.

Main Methods:

  • Utilized a stick-breaking construction for defining random marginal distributions.
  • Employed a latent Gaussian copula model to introduce dependence across locations.
  • Developed a Markov chain Monte Carlo (MCMC) algorithm for efficient computation.

Main Results:

  • The proposed latent stick-breaking process (LaSBP) effectively models stochastic processes with random marginals.
  • LaSBP induces a random partition of the index space, clustering nearby points.
  • An efficient MCMC algorithm facilitates practical implementation and analysis.

Conclusions:

  • The LaSBP offers a powerful and flexible framework for stochastic modeling with random distributions.
  • The model demonstrates potential for applications in financial econometrics and ecology.
  • The developed MCMC algorithm ensures computational feasibility for complex datasets.