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

Umberto Picchini (1) , Adeline Samson (2)

1 Skane University Hospital [Lund]
2 SVH - Statistique pour le Vivant et l’Homme

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.

Mots clés: hidden Markov model; maximum likelihood; particle filter; SAEM; sequential Monte Carlo; stochastic differential equation

Domaines: Statistiques [math.ST]

Umberto Picchini, Adeline Samson. Coupling stochastic EM and Approximate Bayesian computation for parameter inference in state-space models. Computational Statistics, 2018, 33 (1), pp.179-212. ⟨10.1007/s00180-017-0770-y⟩. ⟨hal-01623737v2⟩