- For k = 1 . . . K

- For i = 1 . . . N i s = 1 . . . S
Compute φ i s l i ) from φ i
, using Eq.32.

z(sli) × p(yk = s; yi;k-1)
- For : = 1 . . . N
Select a tuple (s | j ) ~ qk

$\downarrow$ . 
) 1 k - 1 : ) k  =  s )
Note that the procedure has a "built-in" resampling schema for eliminating particles with small importance weight. Sampling jointly on ( s | i ) is equivalent to sampling a single s for each i and then resampling i according to the weights w ( i ). One can also check that, since we are using the optimal proposal distribution of Eq.27, the weight at each step is given by w ( i ) = p ( i )

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