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Under-reported data analysis with INAR-hidden Markov chains.

Amanda Fernández-Fontelo1, Alejandra Cabaña2, Pedro Puig2

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Summary

This study introduces flexible INAR(1)-hidden Markov chain models for analyzing correlated under-reported data. These models offer a simple autocorrelation function and are applied to public health examples.

Keywords:
discrete time seriesemission probabilitiesinteger-autoregressive modelsthinning operatorunder-recorded data

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Biostatistics

Background:

  • Under-reported data presents challenges in statistical analysis due to correlation.
  • Hidden Markov models (HMMs) offer a framework for modeling unobserved states influencing observed data.
  • Autoregressive models are commonly used for time series data.

Purpose of the Study:

  • To develop and evaluate flexible models for correlated under-reported data.
  • To introduce the INAR(1)-hidden Markov chain model for analyzing such data.
  • To demonstrate the utility of these models in public health applications.

Main Methods:

  • Utilizing Integer Autoregressive (INAR(1)) processes within a hidden Markov chain framework.
  • Proposing a naïve parameter estimation method alongside maximum likelihood estimation.
  • Employing a revised forward algorithm for likelihood computation.
  • Reconstructing the most probable unobserved time series using the Viterbi algorithm.

Main Results:

  • The proposed INAR(1)-hidden Markov chain models are shown to be flexible for correlated under-reported data.
  • The autocorrelation function of the models is identified to have a simple form.
  • The Viterbi algorithm effectively reconstructs unobserved time series.
  • Applications in public health demonstrate the practical utility of the models.

Conclusions:

  • INAR(1)-hidden Markov chain models provide a powerful tool for analyzing correlated under-reported data.
  • The proposed estimation and reconstruction methods are effective.
  • These models have significant potential for applications in public health and other fields dealing with similar data challenges.