Generalized spatial dynamic factor models

Hedibert Freitas Lopes, Dani Gamerman, Esther Salazar

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

This paper introduces a new class of spatio-temporal models for measurements belonging to the exponential family of distributions. In this new class, the spatial and temporal components are conditionally independently modeled via a latent factor analysis structure for the (canonical) transformation of the measurements mean function. The factor loadings matrix is responsible for modeling spatial variation, while the common factors are responsible for modeling the temporal variation. One of the main advantages of our model with spatially structured loadings is the possibility of detecting similar regions associated to distinct dynamic factors. We also show that the new class outperforms a large class of spatial-temporal models that are commonly used in the literature. Posterior inference for fixed parameters and dynamic latent factors is performed via a custom tailored Markov chain Monte Carlo scheme for multivariate dynamic systems that combines extended Kalman filter-based MetropolisHastings proposal densities with block-sampling schemes. Factor model uncertainty is also fully addressed by a reversible jump Markov chain Monte Carlo algorithm designed to learn about the number of common factors. Three applications, two based on synthetic Gamma and Bernoulli data and one based on real Bernoulli data, are presented in order to illustrate the flexibility and generality of the new class of models, as well as to discuss features of the proposed MCMC algorithm.

Original languageEnglish (US)
Pages (from-to)1319-1330
Number of pages12
JournalComputational Statistics and Data Analysis
Volume55
Issue number3
DOIs
StatePublished - Mar 1 2011
Externally publishedYes

Keywords

  • Exponential family
  • Factor model
  • Gaussian process
  • Markov chain Monte Carlo
  • Reversible jump
  • Sampling schemes

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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