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Fast likelihood-based inference for latent count models using the saddlepoint approximation.

W Zhang1, M V Bravington2, R M Fewster1

  • 1Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand.

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|January 29, 2019
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Summary
This summary is machine-generated.

This study introduces a fast maximum-likelihood method for latent count models using saddlepoint approximations. This approach offers accurate inference, even with small observed counts, improving upon computationally intensive sampling methods.

Keywords:
capture-recapturecontingency tablelatent count modelmulti-list methodpopulation size estimatesaddlepoint approximation

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Area of Science:

  • Statistics
  • Computational Statistics

Background:

  • Latent count models involve unobserved count data summarized into observed data.
  • Current inference relies on slow Bayesian sampling methods.
  • These models are used in population estimation, contingency table analysis, and network flow analysis.

Purpose of the Study:

  • To develop a novel, efficient maximum-likelihood approach for latent count models.
  • To overcome the computational limitations of existing stochastic inference methods.
  • To provide fast and accurate inference for complex count data.

Main Methods:

  • Utilized saddlepoint approximations to construct likelihoods.
  • Developed an efficient maximization algorithm for the saddlepoint likelihood.
  • Validated the method on multinomial distribution cases and compared with existing approaches.

Main Results:

  • The saddlepoint approximation method provides fast and accurate inference.
  • The method is effective even when observed counts are small.
  • Demonstrated efficient computation for large-scale problems.

Conclusions:

  • The saddlepoint likelihood approach offers a significant improvement for latent count model inference.
  • This novel method is computationally efficient and robust.
  • Enables wider application of latent count models in various scientific fields.