Pattern Recognition and Neural Networks
Pattern Recognition and Neural Networks
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Estimating the Support of a High-Dimensional Distribution
Neural Computation
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
Proceedings of the Winter Simulation Conference
Likelihood-free parallel tempering
Statistics and Computing
Adaptive approximate Bayesian computation for complex models
Computational Statistics
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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 regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.