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

Rosario Barone1, Andrea Tancredi1

  • 1Department of Methods and Models for Economics, Territory and Finance, Sapienza University of Rome, Rome, Italy.

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|May 31, 2022
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Summary
This summary is machine-generated.

This study introduces a new Bayesian inference method for complex multi-state models, specifically semi-Markov and inhomogeneous Markov models. The approach reconstructs unobserved state transitions, overcoming computational challenges in discrete time observations.

Keywords:
Metropolis-Hastingsinhomogeneous Markov modelspanel datasemi-Markov models

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Area of Science:

  • Statistics
  • Computational Statistics
  • Biostatistics

Background:

  • Multi-state models are essential for analyzing processes with discrete states.
  • Semi-Markov and inhomogeneous Markov models present inference challenges due to time-dependent transitions.
  • Computational difficulties arise when processes are observed only at discrete time points.

Purpose of the Study:

  • To develop a robust Bayesian inference framework for semi-Markov and inhomogeneous Markov models.
  • To address the lack of closed-form likelihood functions in these models.
  • To reconstruct unobserved state trajectories from discrete observations.

Main Methods:

  • Utilized a Metropolis-Hastings algorithm to reconstruct unobserved state trajectories.
  • Employed nested Markov models with uniformization technique for proposal density.
  • Applied Bayesian inference to handle computational difficulties in discrete-time observations.

Main Results:

  • Successfully reconstructed complete state trajectories conditioned on observed data.
  • Demonstrated the feasibility of the proposed Bayesian inference method through simulation studies.
  • Validated the approach using two benchmark multi-state model datasets.

Conclusions:

  • The proposed method provides a viable solution for Bayesian inference in complex multi-state models.
  • Reconstruction of unobserved trajectories via Metropolis-Hastings algorithm is effective.
  • The approach enhances the analysis of processes with discrete state transitions observed at discrete times.