Ãw t w t u i n vec ã n nc ² d w t n nc w t u i n n

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Ãw t ± w t U § I N   vec à   ¡ N Nc ² d  ¢ W ± t ± N Nc   w t U § I N   N d   X ± t ¡ Nc ² d   1 ¢ * ± ± Nc 1   vec à   d 1   c y ± t ± W ± t * ± ² / t / t L N 0 , @ / 2 I N  
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17 prior: a ± vec A   a | @ / 2 , C L N m A , @ 2 M A   à ± I N " C B   A ã ± vec à   ± Qa Q ± I c § I N " C B   a | @ / 2 , C L N m A , @ 2 M A   ã ± Qa ã | @ / 2 , C L N m à , @ / 2 M à   m à ± Qm A M à ± QM A Q U prior: ã | @ / 2 , C c | @ / 2 , C L N m à m c , @ / 2 M à 0 0 @ / 2 M c * ± | @ / 2 , C L N m * µ , @ / 2 M * µ  
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18 prior: * ± | @ / 2 , C L N m * µ , @ / 2 M * µ   data: y ± t ± W ± t * ± ² / t / t L N 0 , @ / 2 I N   posterior: * ± | @ / 2 , C , y , q ,... L N m * µ ' , @ / 2 M * µ '   M * µ ' ± M * µ " 1 ² ! t ± 1 T W ± t U W ± t " 1 m * µ ' ± M * µ ' M * µ " 1 m * µ ² ! t ± 1 T W ± t U y ± t Gibbs sampler blocks: (5) C , @ / 2   prior: @ / " 2 L ³ N / , 5 /   C | @ / 2 L N m C , @ / 2 M C  
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19 data: u t ± y t " Aw t " X t c " q t " a t u t | C , @ / 2 L N 0 , @ / 2 I N " C B   " 1 I N " C B U   " 1   posterior: @ / 2 , C | u - | I N " C B | " T exp " ! t ± 1 T u t " C Bu t   U u t " C Bu t   2 @ / 2 @ / " 2   N / /2   " 1 exp " 5 / @ / " 2 /2   @ / 2   " 1/2 exp " C " m C   2 2 @ / 2 M C Could generate with Metropolis- Hastings. Candidate density could be the Normal-Gamma posterior if we ignored the Jacobian.
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20 q @ / " 2 | u   L ³ N / ' , 5 / '   N / ' ± N / ² NT 5 / ' ± 5 / ² ! t ± 1 T u t " § C Bu t   U u t " § C Bu t   ² § C " m C   2 / Q § C ± S xx " 1 S xy S xx ± ! t ± 1 T u t U B U Bu t S xy ± ! t ± 1 T u t U B U u t Q ± M C " 1 S xx / M C " 1 ² S xx   C | @ / 2 , u L N m C ' , @ / 2 M C '   M C ' ± M C " 1 ² S xx   " 1 m C ' ± M C ' M C " 1 ² S xy   VI. Spatiotemporal models A. Introduction B. Modeling spatial correlation C. Modeling spatiotemporal correlation D. Summary of model E. Wikle, Berliner, and Cressie results
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21 y t ± Aw t ² q t ² u t w t ± 1, cos 2 = t /12   , sin 2 = t /12    U A ± 6 0 f g spatial trend: j s   ± longitude of site s k s   ± latitude of site s 6 0 s   ± 6 0 ¡ 1 ¢ ² 6 0 ¡ 2 ¢ j s   ² 6 0 ¡ 3 ¢ k s   f s   ± f ¡ 1 ¢ ² f ¡ 2 ¢ j s   ² f ¡ 3 ¢ k s   priors: 6 0 ¡ r ¢ L N 6 µ 0 ¡ r ¢ @ µ u 0 2 ¡ r ¢  f ¡ r ¢ L N f µ ¡ r ¢ , @ µ f 2 ¡ r ¢ 
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22 q t ± Hq t " 1 ² 1 t h ss ± a ¡ j s   , k s  ¢ a j , k   ± a 0 j , k   ² ã j , k   a 0 j , k   ± a 0 ¡ 1 ¢ ² a 0 ¡ 2 ¢ j ² a 0 ¡ 3 ¢ k ã j , k   ± ) a ¡ ã j " 1, k   ² ã j ² 1, k  ¢ ² * a ¡ ã j , k " 1   ² ã j , k ² 1  ¢
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  • Winter '09
  • JamesHamilton
  • Unemployment, Trigraph, Yt, Qt, VI. Spatiotemporal models

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