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Coupling stochastic EM and Approximate Bayesian Computation for parameter inference in state-space models

Picchini, Umberto LU and Samson, Adeline (2015)
Abstract
We study the class of state-space models (or hidden Markov models) and perform maximum likelihood inference on the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system and this is achieved using ABC-SMC, that is we used an approximate sequential Monte Carlo (SMC) sampler for the hidden state. Three simulation studies are presented, first a nonlinear Gaussian state-space model then a state-space model having dynamics expressed by a stochastic differential equation, finally a stochastic volatility model.... (More)
We study the class of state-space models (or hidden Markov models) and perform maximum likelihood inference on the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system and this is achieved using ABC-SMC, that is we used an approximate sequential Monte Carlo (SMC) sampler for the hidden state. Three simulation studies are presented, first a nonlinear Gaussian state-space model then a state-space model having dynamics expressed by a stochastic differential equation, finally a stochastic volatility model. In our examples, ten iterations of our SAEM-ABC-SMC strategy were enough to return sensible parameter estimates. Comparisons with results using SAEM coupled with a standard, non-ABC, SMC sampler show that the ABC algorithm can be calibrated to return accurate solutions. (Less)
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author
organization
publishing date
type
Working Paper
publication status
submitted
subject
pages
24 pages
language
English
LU publication?
yes
id
103fe344-dd1f-4e48-b483-92d69523bb85 (old id 8410639)
alternative location
http://arxiv.org/abs/1512.04831
date added to LUP
2016-02-29 16:19:02
date last changed
2016-09-15 18:43:58
@misc{103fe344-dd1f-4e48-b483-92d69523bb85,
  abstract     = {We study the class of state-space models (or hidden Markov models) and perform maximum likelihood inference on the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system and this is achieved using ABC-SMC, that is we used an approximate sequential Monte Carlo (SMC) sampler for the hidden state. Three simulation studies are presented, first a nonlinear Gaussian state-space model then a state-space model having dynamics expressed by a stochastic differential equation, finally a stochastic volatility model. In our examples, ten iterations of our SAEM-ABC-SMC strategy were enough to return sensible parameter estimates. Comparisons with results using SAEM coupled with a standard, non-ABC, SMC sampler show that the ABC algorithm can be calibrated to return accurate solutions.},
  author       = {Picchini, Umberto and Samson, Adeline},
  language     = {eng},
  pages        = {24},
  title        = {Coupling stochastic EM and Approximate Bayesian Computation for parameter inference in state-space models},
  year         = {2015},
}