On Optimal Selection of Summary Statistics for Approximate Bayesian Computation

@article{Nunes2010OnOS,
  title={On Optimal Selection of Summary Statistics for Approximate Bayesian Computation},
  author={Matthew A. Nunes and David Joseph Balding},
  journal={Statistical Applications in Genetics and Molecular Biology},
  year={2010},
  volume={9}
}
  • M. NunesD. Balding
  • Published 6 September 2010
  • Computer Science
  • Statistical Applications in Genetics and Molecular Biology
How best to summarize large and complex datasets is a problem that arises in many areas of science. We approach it from the point of view of seeking data summaries that minimize the average squared error of the posterior distribution for a parameter of interest under approximate Bayesian computation (ABC). In ABC, simulation under the model replaces computation of the likelihood, which is convenient for many complex models. Simulated and observed datasets are usually compared using summary… 

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References

SHOWING 1-10 OF 44 REFERENCES

Approximate Bayesian computation in population genetics.

A key advantage of the method is that the nuisance parameters are automatically integrated out in the simulation step, so that the large numbers of nuisance parameters that arise in population genetics problems can be handled without difficulty.

Approximately Sufficient Statistics and Bayesian Computation

A sequential scheme for scoring statistics according to whether their inclusion in the analysis will substantially improve the quality of inference, which can be applied to high-dimensional data sets for which exact likelihood equations are not possible.

Non-linear regression models for Approximate Bayesian Computation

A machine-learning approach to the estimation of the posterior density by introducing two innovations that fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling.

ABCtoolbox: a versatile toolkit for approximate Bayesian computations

ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

This paper discusses and applies an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models and develops ABC SMC as a tool for model selection; given a range of different mathematical descriptions, it is able to choose the best model using the standard Bayesian model selection apparatus.

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

Key methods used in DIY ABC, a computer program for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples, are described.

Efficient Approximate Bayesian Computation Coupled With Markov Chain Monte Carlo Without Likelihood

The principal idea is to relax the tolerance within MCMC to permit good mixing, but retain a good approximation to the posterior by a combination of subsampling the output and regression adjustment, which will realize substantial computational advances over standard ABC.

Nearest Neighbor Estimates of Entropy

SYNOPTIC ABSTRACT Motivated by the problems in molecular sciences, we introduce new nonparametric estimators of entropy which are based on the kth nearest neighbor distances between the n sample

On the estimation of entropy

The authors' estimators are different from Joe's, and may be computed without numerical integration, but it can be shown that the same interaction of tail behaviour, smoothness and dimensionality also determines the convergence rate of Joe's estimator.

Likelihood-Based Local Linear Estimation of the Conditional Variance Function

We consider estimation of mean and variance functions with kernel-weighted local polynomial fitting in a heteroscedastic nonparametric regression model. Our preferred estimators are based on a