caa a22 4500 60552002X CHVBK 20210128100733.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s11009-013-9357-4 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9357-4 Gradient Free Parameter Estimation for Hidden Markov Models with Intractable Likelihoods [Elektronische Daten] [Elena Ehrlich, Ajay Jasra, Nikolas Kantas] In this article we focus on Maximum Likelihood estimation (MLE) for the static model parameters of hidden Markov models (HMMs). We will consider the case where one cannot or does not want to compute the conditional likelihood density of the observation given the hidden state because of increased computational complexity or analytical intractability. Instead we will assume that one may obtain samples from this conditional likelihood and hence use approximate Bayesian computation (ABC) approximations of the original HMM. Although these ABC approximations will induce a bias, this can be controlled to arbitrary precision via a positive parameter ϵ, so that the bias decreases with decreasing ϵ. We first establish that when using an ABC approximation of the HMM for a fixed batch of data, then the bias of the resulting log- marginal likelihood and its gradient is no worse than $\mathcal{O}(n\epsilon)$ , where n is the total number of data-points. Therefore, when using gradient methods to perform MLE for the ABC approximation of the HMM, one may expect parameter estimates of reasonable accuracy. To compute an estimate of the unknown and fixed model parameters, we propose a gradient approach based on simultaneous perturbation stochastic approximation (SPSA) and Sequential Monte Carlo (SMC) for the ABC approximation of the HMM. The performance of this method is illustrated using two numerical examples. Springer Science+Business Media New York, 2013 Approximate Bayesian computation nationallicence Hidden Markov models nationallicence Parameter estimation nationallicence Sequential Monte Carlo nationallicence Ehrlich Elena Department of Mathematics, Imperial College London, SW7 2AZ, London, UK aut Jasra Ajay Department of Statistics & Applied Probability, National University of Singapore, 117546, Singapore, Singapore aut Kantas Nikolas Department of Statistics & Applied Probability, National University of Singapore, 117546, Singapore, Singapore aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 315-349 1387-5841 17:2<315 2015 17 11009 https://doi.org/10.1007/s11009-013-9357-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9357-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ehrlich Elena Department of Mathematics, Imperial College London, SW7 2AZ, London, UK aut NATIONALLICENCE 700 1- Jasra Ajay Department of Statistics & Applied Probability, National University of Singapore, 117546, Singapore, Singapore aut NATIONALLICENCE 700 1- Kantas Nikolas Department of Statistics & Applied Probability, National University of Singapore, 117546, Singapore, Singapore aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 315-349 1387-5841 17:2<315 2015 17 11009