Non-linear regression models for Approximate Bayesian Computation

  title={Non-linear regression models for Approximate Bayesian Computation},
  author={Michael G. B. Blum and Olivier François},
  journal={Statistics and Computing},
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic… 

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Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics

  • J. HeyR. Nielsen
  • Mathematics
    Proceedings of the National Academy of Sciences
  • 2007
An approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically, resulting in an approximation to the full joint posterior density of the model parameters.