Efficient Online Smoothing in General Hidden Markov Models
(2012) FMS820 20122Mathematical Statistics
 Abstract
 This thesis discusses the problem of estimating smoothed expectations of sums of additive functionals of sequences of hidden states in general hidden Markov models. To compute expectations of this sort, the smoothing distribution, i.e. the conditional distribution of the hidden states given the corresponding observations, needs to be approximated. This thesis proposes a new algorithm to achieve this in an efficient way. The method is based on an algorithm proposed by Del Moral et al. (2009) and contains as a key ingredient an acceptreject sampling step or a MetropolisHastings algorithm (depending on wether the transition density of the state sequence is bounded or not).
The proposed algorithm, which replaces certain expectations occur... (More)  This thesis discusses the problem of estimating smoothed expectations of sums of additive functionals of sequences of hidden states in general hidden Markov models. To compute expectations of this sort, the smoothing distribution, i.e. the conditional distribution of the hidden states given the corresponding observations, needs to be approximated. This thesis proposes a new algorithm to achieve this in an efficient way. The method is based on an algorithm proposed by Del Moral et al. (2009) and contains as a key ingredient an acceptreject sampling step or a MetropolisHastings algorithm (depending on wether the transition density of the state sequence is bounded or not).
The proposed algorithm, which replaces certain expectations occur ring in the original algorithm by Monte Carlo estimates, allows for on line computation of these expectations. When a single Monte Carlo draw is used in these estimates a degeneracy problem occurs, which can be avoided completely by simply using two or more draws. The new algorithm is tested on three different models: a linear and Gaus sian statespace model, a stochastic volatility model, and a model with nonbounded transition density. For the same input the new algorithm produces an output similar to the method proposed by Del Moral et al. (2009), but at a fraction of the computation time. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/3294794
 author
 Westerborn, Johan ^{LU}
 supervisor

 Jimmy Olsson ^{LU}
 organization
 course
 FMS820 20122
 year
 2012
 type
 H2  Master's Degree (Two Years)
 subject
 language
 English
 id
 3294794
 date added to LUP
 20121221 10:21:50
 date last changed
 20121221 10:21:50
@misc{3294794, abstract = {This thesis discusses the problem of estimating smoothed expectations of sums of additive functionals of sequences of hidden states in general hidden Markov models. To compute expectations of this sort, the smoothing distribution, i.e. the conditional distribution of the hidden states given the corresponding observations, needs to be approximated. This thesis proposes a new algorithm to achieve this in an efficient way. The method is based on an algorithm proposed by Del Moral et al. (2009) and contains as a key ingredient an acceptreject sampling step or a MetropolisHastings algorithm (depending on wether the transition density of the state sequence is bounded or not). The proposed algorithm, which replaces certain expectations occur ring in the original algorithm by Monte Carlo estimates, allows for on line computation of these expectations. When a single Monte Carlo draw is used in these estimates a degeneracy problem occurs, which can be avoided completely by simply using two or more draws. The new algorithm is tested on three different models: a linear and Gaus sian statespace model, a stochastic volatility model, and a model with nonbounded transition density. For the same input the new algorithm produces an output similar to the method proposed by Del Moral et al. (2009), but at a fraction of the computation time.}, author = {Westerborn, Johan}, language = {eng}, note = {Student Paper}, title = {Efficient Online Smoothing in General Hidden Markov Models}, year = {2012}, }