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Bayesian inference for discretely observed continuous time multi-state models.

Statistics in medicine·2022
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Approximate Bayesian inference for discretely observed continuous-time multi-state models.

Andrea Tancredi1

  • 1Department of Methods and Models for Economics Territory and Finance, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161, Rome, Italy.

Biometrics
|January 17, 2019
PubMed
Summary
This summary is machine-generated.

Approximate Bayesian Computation (ABC) methods offer a computational solution for complex multi-state models, enabling parameter inference and model comparison even with limited data. This approach addresses challenges in continuous-time models observed discretely.

Keywords:
Markov modelModel choiceSemi-MarkovWeibullsequential Monte-Carlo

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Area of Science:

  • Computational Statistics
  • Statistical Modeling
  • Biostatistics

Background:

  • Continuous-time multi-state models are computationally challenging, especially when observed only at discrete time points.
  • Standard Markov models require intensive numerical approximations for likelihood evaluation.
  • Semi-Markov models are necessary for state transitions dependent on time since entry, but lack closed-form likelihoods.

Purpose of the Study:

  • To investigate the utility of Approximate Bayesian Computation (ABC) for multi-state models.
  • To enable posterior distribution estimation of model parameters.
  • To facilitate comparison between Markov and semi-Markov models, including hidden variants with classification errors.

Main Methods:

  • Utilized Approximate Bayesian Computation (ABC) techniques to circumvent intractable likelihood calculations.
  • Employed ABC for parameter inference in multi-state models.
  • Applied ABC for model comparison (Markov vs. semi-Markov) and analysis of hidden models with classification errors.

Main Results:

  • Demonstrated the effectiveness of ABC in obtaining posterior distributions for model parameters.
  • Showcased ABC's capability in comparing Markov and semi-Markov models.
  • Validated the ABC methodology using both simulated and real-world data examples.

Conclusions:

  • ABC methods provide a viable computational solution for complex multi-state models with intractable likelihoods.
  • ABC facilitates robust parameter estimation and model comparison in both standard and hidden multi-state scenarios.
  • The study confirms the practical applicability and performance of ABC in analyzing discrete-time observations of continuous-time processes.