Generalized spatial dynamic factor models

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...

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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 55; no. 3; pp. 1319 - 1330
Main Authors: Lopes, Hedibert Freitas, Gamerman, Dani, Salazar, Esther
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.03.2011
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
Algorithms
Computer simulation
Density
Dynamical systems
Dynamics
Exact sciences and technology
Exponential family
Exponential family Factor model Gaussian process Markov chain Monte Carlo Reversible jump Sampling schemes
Factor model
Gaussian process
General topics
Markov chain Monte Carlo
Markov chains
Markov processes
Mathematical models
Mathematics
Monte Carlo methods
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Probability theory and stochastic processes
Reversible jump
Sampling schemes
Sciences and techniques of general use
Statistics
Temporal logic
Exponential family
Factor model
Gaussian process
Reversible jump
Sampling schemes
Markov chain Monte Carlo
Density estimation
Statistical distribution
Exponential distribution
Kalman filter
Multivariate analysis
Stochastic method
Spatial variation
Markov chain
Canonical analysis
Correspondence analysis
Approximation theory
Sampling
Dynamic model
Posterior distribution
Monte Carlo method
Data analysis
Factor analysis
Metropolis Hastings algorithm
Statistical estimation
Mean estimation
Numerical analysis
Statistical computation
Experimental design
Gaussian processes
Principal component analysis
ISSN:0167-9473, 1872-7352
Online Access:Get full text
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Summary: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 Metropolis–Hastings 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.
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2010.09.020