Imperial College London
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ProfessorDanCrisan

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8489d.crisan Website

 
 
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Location

 

670Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Crisan:2018:10.3150/17-BEJ954,
author = {Crisan, DO and Miguez, J},
doi = {10.3150/17-BEJ954},
journal = {Bernoulli},
pages = {3039--3086},
title = {Nested particle filters for online parameter estimation in discrete-time state-space Markov models},
url = {http://dx.doi.org/10.3150/17-BEJ954},
volume = {24},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We  address  the  problem  of  approximating  the  posterior  probability  distribution  of  the  fixedparameters  of  a  state-space  dynamical  system  using  a  sequential  Monte  Carlo  method.  Theproposed  approach  relies  on  a  nested  structure  that  employs  two  layers  of  particle  filters  toapproximate the posterior probability measure of the static parameters and the dynamic statevariables  of  the  system  of  interest,  in  a  vein  similar  to  the  recent  “sequential  Monte  Carlosquare” (SMC2) algorithm. However, unlike the SMC2scheme, the proposed technique operatesin a purely recursive manner. In particular, the computational complexity of the recursive stepsof the method introduced herein is constant over time. We analyse the approximation of integralsof real bounded functions with respect to the posterior distribution of the system parameterscomputed via the proposed scheme. As a result, we prove, under regularity assumptions, that theapproximation errors vanish asymptotically inLp(p≥1) with convergence rate proportional to1√N+1√M, whereNis the number of Monte Carlo samples in the parameter space andN×Mis the number of samples in the state space. This result also holds for the approximation of thejoint posterior distribution of the parameters and the state variables. We discuss the relationshipbetween the SMC2algorithm and the new recursive method and present a simple example inorder to illustrate some of the theoretical findings with computer simulations.Keywords:particle filtering, parameter estimation, model inference, state space models, recursivealgorithms, Monte Carlo, error bounds.
AU  - Crisan,DO
AU  - Miguez,J
DO  - 10.3150/17-BEJ954
EP  - 3086
PY  - 2018///
SN  - 1350-7265
SP  - 3039
TI  - Nested particle filters for online parameter estimation in discrete-time state-space Markov models
T2  - Bernoulli
UR  - http://dx.doi.org/10.3150/17-BEJ954
UR  - http://hdl.handle.net/10044/1/48492
VL  - 24
ER  -
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