Kernel approximate Bayesian computation in population genetic inferences
By Shigeki Nakagome, Kenji Fukumizu, Shuhei Mano. 2012
61 citations recorded by the source corpus.
Abstract Approximate Bayesian computation (ABC) is a likelihood-free approach for Bayesian inferences based on a rejection algorithm method that applies a tolerance of dissimilarity between summary statistics from observed and simulated data. Although several improvements to the algorithm have been proposed, none of these improvements avoid the following two sources of approximation: 1) lack of sufficient statistics: sampling is not from the true posterior density given data but from an approximate posterior density given summary statistics; and 2) non-zero tolerance: sampling from the posterior density given summary statistics is achieved only in the limit of zero tolerance. The first source of approximation can be improved by adding a summary statistic, but an increase in the number of summary statistics could introduce additional variance caused by the low acceptance rate. Consequently, many researchers have attempted to develop techniques to choose informative summary statistics. The present study evaluated the utility of a kernel-based ABC method [Fukumizu, K., L. Song and A. Gretton (2010): “Kernel Bayes’ rule: Bayesian inference with positive definite kernels,” arXiv, 1009.5736 and Fukumizu, K., L. Song and A. Gretton (2011): “Kernel Bayes’ rule. Advances in Neural Information Processing Systems 24.” In: J. Shawe-Taylor and R. S. Zemel and P. Bartlett and F. Pereira and K. Q. Weinberger, (Eds.), pp. 1549–1557., NIPS 24: 1549–1557] for complex problems that demand many summary statistics. Specifically, kernel ABC was applied to population genetic inference. We demonstrate that, in contrast to conventional ABCs, kernel ABC can incorporate a large number of summary statistics while maintaining high performance of the inference.
Subfields: Artificial Intelligence, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Arthur Gretton
- Kenji Fukumizu
- Dino Sejdinovic
- Bernhard Schölkopf
- Le Song
- Bharath K. Sriperumbudur
- Krikamol Muandet
- Wittawat Jitkrittum
In Statistics and Probability
- Arthur Gretton
- Kenji Fukumizu
- Dino Sejdinovic
- Bernhard Schölkopf
- Le Song
- Bharath K. Sriperumbudur
- Wittawat Jitkrittum
- Krikamol Muandet
Citations in the corpus
- K2-ABC: Approximate Bayesian Computation with Infinite Dimensional Summary Statistics via Kernel Embeddings (2015, methodology): “3Details on consistency of ABC schemes as well as their convergence properties are given in Barber et al. (2013).”
- Kernel Bayes' rule: Bayesian inference with positive definite kernels (2013, methodology): “…al. (2012) propose a KBR approach to reinforcement learning in partially observable Markov decision processes, Boots et al. (2013) apply KBR to reinforcement learning with predictive state representations, and Nakagome et al. (2013) consider a KBR-based method for problems in population genetics.”