Bacri, Timothee and Berentsen, Geir D. and Bulla, Jan and Stove, Bard (2023) Computational issues in parameter estimation for hidden Markov models with template model builder. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 93 (18). pp. 3421-3457. ISSN 0094-9655, 1563-5163
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A popular way to estimate the parameters of a hidden Markov model (HMM) is direct numerical maximization (DNM) of the (log-)likelihood function. The advantages of employing the TMB [Kristensen K, Nielsen A, Berg C, et al. TMB: automatic differentiation and Laplace approximation. J Stat Softw Articles. 2016;70(5):1-21] framework in R for this purpose were illustrated recently [Bacri T, Berentsen GD, Bulla J, et al. A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using template model builder. Biom J. 2022 Oct;64(7):1260-1288]. In this paper, we present extensions of these results in two directions. First, we present a practical way to obtain uncertainty estimates in form of confidence intervals (CIs) for the so-called smoothing probabilities at moderate computational and programming effort via TMB. Our approach thus permits to avoid computer-intensive bootstrap methods. By means of several examples, we illustrate patterns present for the derived CIs. Secondly, we investigate the performance of popular optimizers available in R when estimating HMMs via DNM. Hereby, our focus lies on the potential benefits of employing TMB. Investigated criteria via a number of simulation studies are convergence speed, accuracy, and the impact of (poor) initial values. Our findings suggest that all optimizers considered benefit in terms of speed from using the gradient supplied by TMB. When supplying both gradient and Hessian from TMB, the number of iterations reduces, suggesting a more efficient convergence to the maximum of the log-likelihood. Last, we briefly point out potential advantages of a hybrid approach.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | QUASI-NEWTON METHODS; MAXIMUM-LIKELIHOOD; PROBABILISTIC FUNCTIONS; STOCK; MAXIMIZATION; SERIES; BULL; HMM; Hidden Markov model; template model builder; smoothing probabilities; confidence intervals; maximum likelihood estimation; robustness; initial conditions |
| Subjects: | 000 Computer science, information & general works > 004 Computer science 600 Technology > 610 Medical sciences Medicine |
| Divisions: | Medicine > Lehrstuhl für Psychiatrie und Psychotherapie |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Mar 2024 13:56 |
| Last Modified: | 14 Mar 2024 13:57 |
| URI: | https://pred.uni-regensburg.de/id/eprint/60117 |
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