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The '''auxiliary particle filter''' is a [[particle filter]]ing algorithm introduced by Pitt and Shephard in 1999 to improve some deficiencies of the [[particle filter#Sequential importance resampling .28SIR.29|sequential importance resampling]] (SIR) algorithm when dealing with tailed observation densities.


Assume that the filtered [[Posterior probability|posterior]] is described by the following ''M'' weighted samples:
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: <math>
p(x_t|z_{1:t}) \approx \sum_{i=1}^M \omega^{(i)}_t \delta \left( x_t - x^{(i)}_t \right).
</math>
 
Then, each step in the algorithm consists of first drawing a sample of the particle index <math>k</math> which will be propagated from <math>t-1</math> into the new step <math>t</math>. These indexes are auxiliary variables only used as an intermediary step, hence the name of the algorithm. The indexes are drawn according to the likelihood of some reference point <math>\mu^{(i)}_t</math> which in some way is related to the transition model <math>x_t|x_{t-1}</math> (for example, the mean, a sample, etc.):
 
: <math>
k^{(i)} \sim P(i=k|z_t) \propto \omega^{(i)}_t p( z_t | \mu^{(i)}_t )
</math>
 
This is repeated for <math>i=1,2,\dots,M</math>, and using these indexes we can now draw the conditional samples:
 
: <math>
x_t^{(i)} \sim p( x | x^{k^{(i)}}_{t-1}).
</math>
 
Finally, the weights are updated to account for the mismatch between the likelihood at the actual sample and the predicted point <math>\mu_t^{k^{(i)}}</math>:
 
: <math>
\omega_t^{(i)} \propto \frac{p( z_t | x^{(i)}_t) } { p( z_t | \mu^{k^{(i)}}_t) }.
</math>
 
==References==
* {{cite journal
| author = Pitt, M.K.
| coauthors = Shephard, N.
| year = 1999
| title = Filtering Via Simulation: Auxiliary Particle Filters
| journal = Journal of the American Statistical Association
| volume = 94
| issue = 446
| pages = 590&ndash;591
| url = http://www.questia.com/PM.qst?a=o&se=gglsc&d=5002321997
| accessdate = 2008-05-06
| doi = 10.2307/2670179
| jstor = 2670179
| publisher = American Statistical Association
}}
 
[[Category:Estimation theory]]
[[Category:Monte Carlo methods]]
[[Category:Computational statistics]]
[[Category:Nonlinear filters]]
 
 
{{Mathapplied-stub}}
{{statistics-stub}}

Latest revision as of 15:07, 6 December 2014


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You just download ready made templates to a separate directory and then choose a favorite one in the admin panel. When you write a new post, you'll see a small bar that goes across the text input area. This plugin is a must have for anyone who is serious about using Word - Press. You can up your site's rank with the search engines by simply taking a bit of time with your site. That's a total of 180$ for each Wordpress theme if you sell 3 links and keep the designer link for your own website, or 240$ if you sell all links.

Usually, Wordpress owners selling the ad space on monthly basis and this means a residual income source. Note: at a first glance WP Mobile Pro themes do not appear to be glamorous or fancy. I've applied numerous Search engine optimization-ready Word - Press themes and I can say from knowledge that I consider the Genesis Search engine marketing panel one particular of the simplest to use. The first thing you need to do is to choose the right web hosting plan. If you have any type of questions relating to where and how you can use wordpress backup plugin, you can call us at our own site. After that the developer adds the unordered list for navigations.

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