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Smoothness properties and gradient analysis under spatial Dirichlet process models

Publication ,  Journal Article
Guindani, M; Gelfand, AE
Published in: Methodology and Computing in Applied Probability
June 1, 2006

When analyzing point-referenced spatial data, interest will be in the first order or global behavior of associated surfaces. However, in order to better understand these surfaces, we may also be interested in second order or local behavior, e.g., in the rate of change of a spatial surface at a given location in a given direction. In a Bayesian parametric setting, such smoothness analysis has been pursued by Banerjee and Gelfand (2003) and Banerjee et al. (2003). We study continuity and differentiability of random surfaces in the Bayesian nonparametric setting proposed by Gelfand et al. (2005), which is based on the formulation of a spatial Dirichlet process (SDP). We provide conditions under which the random surfaces sampled from a SDP are smooth. We also obtain complete distributional theory for the directional finite difference and derivative processes associated with those random surfaces. We present inference under a Bayesian framework and illustrate our methodology with a simulated dataset. © Springer Science + Business Media, LLC 2006.

Duke Scholars

Published In

Methodology and Computing in Applied Probability

DOI

EISSN

1573-7713

ISSN

1387-5841

Publication Date

June 1, 2006

Volume

8

Issue

2

Start / End Page

159 / 189

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

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Guindani, M., & Gelfand, A. E. (2006). Smoothness properties and gradient analysis under spatial Dirichlet process models. Methodology and Computing in Applied Probability, 8(2), 159–189. https://doi.org/10.1007/s11009-006-8547-8
Guindani, M., and A. E. Gelfand. “Smoothness properties and gradient analysis under spatial Dirichlet process models.” Methodology and Computing in Applied Probability 8, no. 2 (June 1, 2006): 159–89. https://doi.org/10.1007/s11009-006-8547-8.
Guindani M, Gelfand AE. Smoothness properties and gradient analysis under spatial Dirichlet process models. Methodology and Computing in Applied Probability. 2006 Jun 1;8(2):159–89.
Guindani, M., and A. E. Gelfand. “Smoothness properties and gradient analysis under spatial Dirichlet process models.” Methodology and Computing in Applied Probability, vol. 8, no. 2, June 2006, pp. 159–89. Scopus, doi:10.1007/s11009-006-8547-8.
Guindani M, Gelfand AE. Smoothness properties and gradient analysis under spatial Dirichlet process models. Methodology and Computing in Applied Probability. 2006 Jun 1;8(2):159–189.
Journal cover image

Published In

Methodology and Computing in Applied Probability

DOI

EISSN

1573-7713

ISSN

1387-5841

Publication Date

June 1, 2006

Volume

8

Issue

2

Start / End Page

159 / 189

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics