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Estimation for general birth-death processes.

Forrest W Crawford1, Vladimir N Minin2, Marc A Suchard3

  • 1Department of Biostatistics, Yale University, 60 College Street, Box 208034, New Haven, CT 06510 USA.

Journal of the American Statistical Association
|October 21, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method for statistical inference in birth-death processes (BDPs), enabling accurate estimation of birth and death rates even for complex models. The approach avoids computationally intensive simulations, offering a significant advancement for BDP analysis.

Keywords:
Birth-death processEM algorithmMM algorithmcontinuous-time Markov chainmaximum likelihood estimationmicrosatellite evolution

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Area of Science:

  • Mathematical Biology
  • Computational Statistics
  • Ecology

Background:

  • Birth-death processes (BDPs) are fundamental models in various scientific fields, but inferring their rates is challenging.
  • Current methods for statistical inference are often limited to simple linear BDPs or require computationally expensive simulations.
  • Discrete observations necessitate complex data augmentation techniques like expectation-maximization (EM).

Purpose of the Study:

  • To develop a computationally efficient and broadly applicable method for statistical inference of birth and death rates in general BDPs.
  • To overcome the limitations of existing methods that rely on restrictive models or simulations.
  • To enable accurate maximum likelihood estimation for BDPs with arbitrary rate functions.

Main Methods:

  • Developed a novel approach using Laplace transforms and continued fractions to compute conditional expectations for the E-step of the EM algorithm.
  • Expressed E-step conditional expectations as convolutions of computable transition probabilities for general BDPs.
  • Derived new EM algorithms for maximum likelihood estimation, applicable to generalized linear rate models.

Main Results:

  • The proposed Laplace convolution technique provides efficient computation of conditional expectations, eliminating the need for state-space truncation or simulation.
  • The derived EM algorithms successfully perform maximum likelihood estimation for general BDPs with various rate models.
  • The new method demonstrates superior performance compared to existing techniques and includes strategies for accelerating EM convergence.

Conclusions:

  • This work presents a significant methodological advancement for statistical inference in BDPs, applicable to a wider range of models.
  • The efficient computation of conditional expectations via Laplace convolutions removes major bottlenecks in BDP analysis.
  • The validated approach has practical applications in fields such as cancer cell growth and evolutionary genetics.