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Parameter estimation for discretely observed linear birth-and-death processes.

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Summary
This summary is machine-generated.

Estimating birth and death rates in biological populations is challenging due to unstable likelihoods with common sampling. This study introduces new methods for accurate parameter estimation in discretely observed birth-and-death processes.

Keywords:
Galton-Watson processGaussian approximationlikelihoodlinear birth-and-death processsaddlepoint approximation

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Area of Science:

  • Population Dynamics
  • Stochastic Processes
  • Mathematical Biology

Background:

  • Birth-and-death processes are fundamental for modeling biological population development.
  • Parameter estimation for these models is often numerically unstable, especially with discrete, non-equi-spaced data from population censuses.

Purpose of the Study:

  • To develop and evaluate novel methods for estimating birth, death, and growth rates of discretely observed linear birth-and-death processes.
  • To address challenges posed by numerically unstable likelihoods and non-equi-spaced observational data.

Main Methods:

  • Utilized an embedded Galton-Watson process for parameter estimation.
  • Employed maximization of a saddlepoint approximation to the likelihood function.
  • Analyzed asymptotic properties of the proposed estimators.

Main Results:

  • Presented two robust approaches for estimating birth, death, and growth rates.
  • Demonstrated the effectiveness of the methods through numerical examples.
  • Successfully applied the methodology to real-world monitored population data.

Conclusions:

  • The developed methods offer improved accuracy and stability for estimating parameters in discretely observed birth-and-death processes.
  • These approaches are valuable for analyzing ecological and epidemiological data, even with irregular sampling intervals.