Bayesian Analysis

Spatial dynamic factor analysis

Dani Gamerman, Hedibert Freitas Lopes, and Esther Salazar

Full-text: Open access

Abstract

A new class of space-time models derived from standard dynamic factor models is proposed. The temporal dependence is modeled by latent factors while the spatial dependence is modeled by the factor loadings. Factor analytic arguments are used to help identify temporal components that summarize most of the spatial variation of a given region. The temporal evolution of the factors is described in a number of forms to account for different aspects of time variation such as trend and seasonality. The spatial dependence is incorporated into the factor loadings by a combination of deterministic and stochastic elements thus giving them more flexibility and generalizing previous approaches. The new structure implies nonseparable space-time variation to observables, despite its conditionally independent nature, while reducing the overall dimensionality, and hence complexity, of the problem. The number of factors is treated as another unknown parameter and fully Bayesian inference is performed via a reversible jump Markov Chain Monte Carlo algorithm. The new class of models is tested against one synthetic dataset and applied to pollution data obtained from the Clean Air Status and Trends Network (CASTNet). Our factor model exhibited better predictive performance when compared to benchmark models, while capturing important aspects of spatial and temporal behavior of the data.

Article information

Source
Bayesian Anal., Volume 3, Number 4 (2008), 759-792.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1340370408

Digital Object Identifier
doi:10.1214/08-BA329

Mathematical Reviews number (MathSciNet)
MR2469799

Zentralblatt MATH identifier
1330.62356

Keywords
Bayesian inference forecasting Gaussian process spatial interpolation reversible jump Markov chain Monte Carlo random fields

Citation

Lopes, Hedibert Freitas; Salazar, Esther; Gamerman, Dani. Spatial dynamic factor analysis. Bayesian Anal. 3 (2008), no. 4, 759--792. doi:10.1214/08-BA329. https://projecteuclid.org/euclid.ba/1340370408


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