close Warning: Can't synchronize with repository "(default)" (/var/svn/tolp does not appear to be a Subversion repository.). Look in the Trac log for more information.

Changes between Version 3 and Version 4 of Ticket #664


Ignore:
Timestamp:
Mar 23, 2009, 2:42:18 PM (16 years ago)
Author:
Víctor de Buen Remiro
Comment:

Legend:

Unmodified
Added
Removed
Modified

  • Ticket #664 – Description

    v3 v4  
    66[[LatexEquation(e \sim N\left(0,\sigma^{2} I\right) $$)]][[BR]]
    77
    8 ARMA and variance parameters are changing in each iteration of BSR, and, if there are missing values or non linear filters matrices [[LatexEquation(Y $$)]] and [[LatexEquation(X $$)]] could also change in each iteration. So, an ARIMA decomposition and filter and a Cholesky decomposition is needed in order to simulate linear block. Even if [[LatexEquation(X $$)]] is very sparse, after applying ARIMA filter it could become dense and process will be too slow.
     8ARMA and variance parameters are changing in each iteration of BSR, and, if there are missing values or non linear filters matrices [[LatexEquation(Y $$)]] and [[LatexEquation(X $$)]] could also change in each iteration. Only constraining inequations remain invariant in any case.
     9
     10So, an ARIMA decomposition and filter and a Cholesky decomposition are needed in order to simulate linear block. Even if [[LatexEquation(X $$)]] is very sparse, after applying ARIMA filter it could become dense and process will be too slow.
    911
    1012I propose a preconditioning method to save a lot of time calculating and storing all blocks of a simulation only for one of a lot of iterations and using them to generate aproximations that will be refinated inside an internal Metropolis-Hastings chain.
    … …  
    2830 1. ARIMA noise for current system becomes simply [[BR]][[LatexEquation(z_t = \frac{\theta\left(B\right)}{\phi\left(B\right)} e_t $$)]]
    2931 1. Then, we can solve sparse linear system [[BR]][[LatexEquation(Y = X \beta + z $$)]]
    30  1. If resulting vector doesn' match constraining inequations [[BR]] [[LatexEquation(A \beta <= a $$)]][[BR]] density will be toggled to [[LatexEquation(-\infty $$)]] in order to force rejection.
     32 1. If resulting vector doesn't match constraining inequations [[BR]] [[LatexEquation(A \beta <= a $$)]][[BR]] density will be toggled to [[LatexEquation(-\infty $$)]] in order to force rejection.
    3133
    32 The number of internal Metropolis-Hastings non rejected iterations must be a parameter of user configuration.
    33 
    34 When number of rejected iterations growns is the moment of remake full calculations and store a new preconditioner regression.
     34The number of internal Metropolis-Hastings non rejected iterations must be a parameter of user configuration and should not be more than 10 or 20 iterations. When number of rejected iterations growns is the moment of remake full calculations and store a new preconditioner regression. If this happens after a large number of iterations, then a lot of time will be saved.