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Unbiased Bayesian inference for population Markov jump processes via random truncations.

Anastasis Georgoulas1, Jane Hillston1, Guido Sanguinetti1,2

  • 1School of Informatics, University of Edinburgh, Edinburgh, UK.

Statistics and Computing
|July 11, 2017
PubMed
Summary

We developed an efficient Bayesian inference algorithm for population Markov Jump processes, enabling accurate analysis of complex stochastic systems. This method significantly improves computational efficiency for modeling agent interactions in diverse fields.

Keywords:
Markov Chain Monte CarloMarkov Jump ProcessesParameter estimationPseudo-marginal methodsStochastic processes

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Area of Science:

  • Computational Science
  • Statistical Modeling
  • Stochastic Processes

Background:

  • Bayesian inference for continuous-time, discrete-state Markovian population models is computationally challenging.
  • These models, crucial in fields like biology and smart cities, often feature infinite state spaces.
  • Existing methods struggle with the complexity of joint state/parameter estimation.

Purpose of the Study:

  • To propose a novel and efficient algorithm for Bayesian inference in population Markov Jump processes.
  • To address the challenge of infinite state spaces in these stochastic systems.
  • To enable accurate joint state and parameter posterior sampling.

Main Methods:

  • Introduced a class of pseudo-marginal sampling algorithms.
  • Developed a random truncation method for principled treatment of infinite state spaces.
  • Applied the algorithm to population Markov Jump processes.

Main Results:

  • The proposed algorithm achieves considerable computational savings compared to state-of-the-art methods.
  • Demonstrated accuracy and fast convergence on benchmark models.
  • Showcased practical utility with a synthetic biology data set.

Conclusions:

  • The novel algorithm offers an efficient and accurate solution for Bayesian inference in population Markov Jump processes.
  • This approach effectively handles infinite state spaces, a common challenge in stochastic modeling.
  • The method has potential for practical applications in various scientific and engineering domains.