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Spatial Dynamic Factor Analysis

Spatial Dynamic Factor Analysis . Hedibert Freitas Lopes, Esther Salazar, Dani Gamerman Presented by Zhengming Xing Jan 29 ,2010. * tables and figures are directly copied from the original paper. . Outline.

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Spatial Dynamic Factor Analysis

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  1. Spatial Dynamic Factor Analysis Hedibert Freitas Lopes, Esther Salazar, Dani Gamerman Presented by Zhengming Xing Jan 29 ,2010 * tables and figures are directly copied from the original paper.

  2. Outline • Introduction • Spatial Dynamic Factor Analysis Model • Inference and Application • Experiment • Future direction

  3. Basic factor analysis introduction observations Factor loading matrix Factor score Spatial dynamic FA model Locations: Times: key idea: Temporal dependence is modeled by latent factor score and spatial dependence is modeled by the factor loadings

  4. Spatial Dynamic Factor Analysis Model:

  5. Covariate effects Mean level of Gaussian process Mean level of the spatio-time process 1.Constant mean 2.Regression model 3.Dynamic coefficient model 1. 2. 3.

  6. Prior information Recall: Priors:

  7. Seasonal dynamic factors Goal: capture the periodicor cyclical behavior Example : p=52 for weekly data and annual cycle

  8. Spatio-temporal separability Assume Random process indexed by space and time if then separable Choose for convenience rather than for the ability to fit the data SDFA model m=1 m>1

  9. MCMC Inference Assume: Model in matrix notation Posterior distribution: Full conditional distribution of all parameters can be found in appendix

  10. Number of factors Reverse jump MCMC Collect samples Proposal distribution: accept With probability

  11. Applications Prediction Interpolation

  12. Experiment Data description Sulfur dioxide concentration in eastern US 24 stations 342 observations (from the first week of 1998 to the 30th week of 2004) 2 station left out for interpolation and the last 30 weeks left out for prediction Dataset available online: http://www.epa.gov/castnet/data.html

  13. Experiment Spatial dynamic factor models Benchmark model

  14. Experiment

  15. Experiment

  16. Experiment

  17. Experiment

  18. Experiment

  19. Future direction • Time varying factor loadings • Allow binomial and Poisson response • Non-diagonal covariance matrix and more general dynamic structure.

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