Parameter Estimation in the Spatio-Temporal Mixed Effects Model – Analysis of Massive Spatio-Temporal Data Sets Matthias Katzfuß Advisor: Dr. Noel Cressie Department of Statistics The Ohio State University September 17, 2010 Matthias Katzfuß (OSU Statistics) STME Parameter Estimation September 17, 2010 1 / 23
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Parameter Estimation in the Spatio-Temporal Mixed Effects ...€¦ · Parameter Estimation in the Spatio-Temporal Mixed Effects Model – Analysis of Massive Spatio-Temporal Data
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Parameter Estimation in the Spatio-TemporalMixed Effects Model –
• Many ad-hoc methods used outside the statistics literature(non-optimal, no measures of uncertainty)
• Other statistical spatio-temporal dimension-reduction models are lessgeneral (e.g., Nychka et al., 2002)
• STME model: Parameter estimation via binned-method-of-moments(Kang et al., 2010):• Many arbitrary choices have to be made• Estimates have to be modified to be valid• Does not fully exploit temporal dependence in the data
• Covariance matrices K0 and U: Multiresolutional Givens-angle prior(Kang & Cressie, 2009)• Control extreme eigenvalues• Shrink off-diagonal elements toward zero
• Propagator matrix H: Shrink off-diagonal elements depending on howfar corresponding basis functions are apart
Posterior distribution:
• Samples of posterior distribution obtained using MCMC
• Cressie, N., Shi, T., & Kang, E. L. (2010). Fixed rank filtering for spatio-temporaldata. Journal of Computational and Graphical Statistics. Forthcoming.
• Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum Likelihood fromIncomplete Data via the EM Algorithm. Journal of the Royal Statistical Society,Series B, 39(1), 1–38.
• Kalman, R. (1960). A new approach to linear filtering and prediction problems.Journal of Basic Engineering, 82(1), 35–45.
• Kang, E. L., & Cressie, N. (2009). Bayesian inference for the spatial randomeffects model. Department of Statistics Technical Report No. 830. The OhioState University.
• Kang, E. L., Cressie, N., & Shi, T. (2010). Using temporal variability to improvespatial mapping with application to satellite data. Canadian Journal of Statistics.Forthcoming.
• Katzfuss, M., & Cressie, N. (2010). Spatio-Temporal Smoothing and EMEstimation for Massive Remote-Sensing Data Sets. Department of StatisticsTechnical Report No. 840. The Ohio State University.
• Nychka, D. W., Wikle, C., & Royle, J. (2002). Multiresolution models fornonstationary spatial covariance functions. Statistical Modelling, 2, 315-331.