Abstract
[17] recently introduced Sequential quasiMonte Carlo (SQMC) algorithms as an efficient way to perform filtering in statespace models. The basic idea is to replace random variables with lowdiscrepancy point sets, so as to obtain faster convergence than with standard particle filtering. [17] describe briefly several ways to extend SQMC to smoothing, but do not provide supporting theory for this extension. We discuss more thoroughly how smoothing may be performed within SQMC, and derive convergence results for the soobtained smoothing algorithms. We consider in particular SQMC equivalents of forward smoothing and forward filtering backward sampling, which are the most wellknown smoothing techniques.
As a preliminary step, we provide a generalization of the classical result of [22] on the transformation of QMC point sets into low discrepancy point sets with respect to non uniform distributions. As a corollary of the latter, we note that we can slightly weaken the assumptions to prove the consistency of SQMC.
As a preliminary step, we provide a generalization of the classical result of [22] on the transformation of QMC point sets into low discrepancy point sets with respect to non uniform distributions. As a corollary of the latter, we note that we can slightly weaken the assumptions to prove the consistency of SQMC.
Original language  English 

Pages (fromto)  29512987 
Number of pages  37 
Journal  Bernoulli 
Volume  23 
Issue number  4B 
Early online date  23 May 2017 
DOIs  
Publication status  Published  Nov 2017 
Keywords
 Hidden Markov models
 Low discrepancy
 Particle filtering
 QuasiMonte Carlo
 Sequential quasiMonte Carlo
 Smoothing
 Statespace models
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Dr Mathieu Gerber
 School of Mathematics  Senior Lecturer in Statistical Science
 Statistical Science
Person: Academic