Coupling stochastic EM and Approximate Bayesian Computation for parameter inference in state-space models
(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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/8410639
- author
- Picchini, Umberto ^{LU} and Samson, Adeline
- organization
- publishing date
- 2015
- 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}, }