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Likelihood-free stochastic approximation EM for inference in complex models

Picchini, Umberto LU (2016)
Abstract
A new approximate maximum likelihood methodology for the parameters of incomplete data models is introduced. We consider a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function of model parameters, with the novelty of using synthetic likelihoods within SAEM. While SAEM is best suited for models having a tractable complete likelihood function, its application to moderately complex models is a difficult task, which results impossible for models having so-called intractable likelihoods. The latter are models typically treated using approximate Bayesian computation (ABC) algorithms or synthetic likelihoods, where information from the data is carried by a set of... (More)
A new approximate maximum likelihood methodology for the parameters of incomplete data models is introduced. We consider a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function of model parameters, with the novelty of using synthetic likelihoods within SAEM. While SAEM is best suited for models having a tractable complete likelihood function, its application to moderately complex models is a difficult task, which results impossible for models having so-called intractable likelihoods. The latter are models typically treated using approximate Bayesian computation (ABC) algorithms or synthetic likelihoods, where information from the data is carried by a set of summary statistics. While ABC is considered the state-of-art methodology for intractable likelihoods, its algorithms are often difficult to tune. On the other hand, synthetic likelihoods (SL) is a more recent methodology which is less general than ABC, it requires stronger assumptions but also less tuning. By exploiting the Gaussian assumption set by SL on data summaries, we can construct a likelihood-free version of SAEM where sufficient statistics for the "synthetic complete likelihood" are automatically obtained via simulation. Our method is completely plug-and-play and available for both static and dynamic models, the ability to simulate realizations from the model being the only requirement. 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 and finally noisy realizations from g-and-k distributions. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working Paper
publication status
submitted
subject
keywords
maximum likelihood, SAEM, sequential Monte Carlo, synthetic likelihood;, state space model, Stochastic differential equation
pages
26 pages
language
English
LU publication?
yes
id
b4e72775-a092-4b85-9ccc-cc3694998fab
alternative location
https://arxiv.org/abs/1609.03508
date added to LUP
2016-09-13 10:51:54
date last changed
2016-09-15 18:40:48
@misc{b4e72775-a092-4b85-9ccc-cc3694998fab,
  abstract     = {A new approximate maximum likelihood methodology for the parameters of incomplete data models is introduced. We consider a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function of model parameters, with the novelty of using synthetic likelihoods within SAEM. While SAEM is best suited for models having a tractable complete likelihood function, its application to moderately complex models is a difficult task, which results impossible for models having so-called intractable likelihoods. The latter are models typically treated using approximate Bayesian computation (ABC) algorithms or synthetic likelihoods, where information from the data is carried by a set of summary statistics. While ABC is considered the state-of-art methodology for intractable likelihoods, its algorithms are often difficult to tune. On the other hand, synthetic likelihoods (SL) is a more recent methodology which is less general than ABC, it requires stronger assumptions but also less tuning. By exploiting the Gaussian assumption set by SL on data summaries, we can construct a likelihood-free version of SAEM where sufficient statistics for the "synthetic complete likelihood" are automatically obtained via simulation. Our method is completely plug-and-play and available for both static and dynamic models, the ability to simulate realizations from the model being the only requirement. 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 and finally noisy realizations from g-and-k distributions. },
  author       = {Picchini, Umberto},
  keyword      = {maximum likelihood,SAEM,sequential Monte Carlo,synthetic likelihood;,state space model,Stochastic differential equation},
  language     = {eng},
  pages        = {26},
  title        = {Likelihood-free stochastic approximation EM for inference in complex models},
  year         = {2016},
}