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QUERY: sampling from the fcd in Dynamic Linear Models

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Tue, 10 Nov 2009 14:03:13 +0100

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 ```Dear list users, here there is a question about Dynamic Linear Models. Let me consider the usual DLM. For simplicity let me consider only the seasonal component, with 4 seasonal data per year. The sum of the seasonal components must sum to zero, and therefore the last component can be ignored: transpose(theta_t) = (s_t, s_t-1, s_t-2) The rotation matrix G becomes          -1 -1 -1 G = 1 0 0           0 1 0 (It is also reasonable suppose that the system variance adds an error only in the first variable):                     omega 0 0 V[omega]= 0 0 0                             0 0 0 The full conditional distribution (fcd) for theta_t is f(theta_t | theta_t-1,theta_t+1,y_t) which is a multivariate normal distribution. If I want to sample theta_t from its fcd, it happens that its variance, is zero. This independently from the variance matrix which is used. This means that given theta_t-1 and theta_t+1, theta_t is fully determined. The impossibility of sampling theta_t is for me totally unreasonable. These problems are avoided if the notations of West&Harrison (Bayesian Forecasting and DLM, 1997) are used: transpose(theta_t) = (s_t, s_t+1, s_t+2, s_t+3) and         0 1 0 0 G = 0 0 1 0         0 0 0 1         1 0 0 0 Why in this second case the variance of the fcd of theta_t is not zero and a value for theta_t can be sampled? Why in the first case sampling is not permitted? Which is the difference? Any help will be highly appreciated, really. Stefano AVVISO IMPORTANTE: Questo messaggio di posta elettronica pu? contenere informazioni confidenziali, pertanto ? destinato solo a persone autorizzate alla ricezione. I messaggi di posta elettronica per i client di Regione Marche possono contenere informazioni confidenziali e con privilegi legali. Se non si ? il destinatario specificato, non leggere, copiare, inoltrare o archiviare questo messaggio. Se si ? ricevuto questo messaggio per errore, inoltrarlo al mittente ed eliminarlo completamente dal sistema del proprio computer. Ai sensi dell'art. 6 della DGR n. 1394/2008 si segnala che, in caso di necessit? ed urgenza, la risposta al presente messaggio di posta elettronica pu? essere visionata da persone estranee al destinatario. IMPORTANT NOTICE: This e-mail message is intended to be received only by persons entitled to receive the confidential information it may contain. E-mail messages to clients of Regione Marche may contain information that is confidential and legally privileged. Please do not read, copy, forward, or store this message unless you are an intended recipient of it. If you have received this message in error, please forward it to the sender and delete it completely from your computer system. ```

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