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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Vydané v:	Computational statistics & data analysis Ročník 55; číslo 3; s. 1319 - 1330
Hlavní autori:	Lopes, Hedibert Freitas, Gamerman, Dani, Salazar, Esther
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.03.2011 Elsevier
Edícia:	Computational Statistics & Data Analysis
Predmet:	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
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Popis
Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0167-9473 1872-7352
DOI:	10.1016/j.csda.2010.09.020