Advanced

Efficient Online Smoothing in General Hidden Markov Models

Westerborn, Johan LU (2012) FMS820 20122
Mathematical 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 accept-reject sampling step or a Metropolis-Hastings 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 accept-reject sampling step or a Metropolis-Hastings 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 state-space model, a stochastic volatility model, and a model with non-bounded 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:
author
Westerborn, Johan LU
supervisor
organization
course
FMS820 20122
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
3294794
date added to LUP
2012-12-21 10:21:50
date last changed
2012-12-21 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 accept-reject sampling step or a Metropolis-Hastings 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 state-space model, a stochastic volatility model, and a model with non-bounded 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},
}