# Approximate Bayesian computational methods

@article{Marin2012ApproximateBC, title={Approximate Bayesian computational methods}, author={Jean-Michel Marin and Pierre Pudlo and Christian P. Robert and Robin J. Ryder}, journal={Statistics and Computing}, year={2012}, volume={22}, pages={1167-1180} }

Approximate Bayesian Computation (ABC) methods, also known as likelihood-free techniques, have appeared in the past ten years as the most satisfactory approach to intractable likelihood problems, first in genetics then in a broader spectrum of applications. However, these methods suffer to some degree from calibration difficulties that make them rather volatile in their implementation and thus render them suspicious to the users of more traditional Monte Carlo methods. In this survey, we study…

## 755 Citations

### Approximate Bayesian Computation: A Survey on Recent Results

- Computer ScienceMCQMC
- 2014

This survey of ABC methods focuses on the recent literature, and gives emphasis to the importance of model choice in the applications of ABC, and the associated difficulties in its implementation.

### New insights into Approximate Bayesian Computation

- Computer Science, Mathematics
- 2012

This paper analyzes the ABC procedure from the point of view of k-nearest neighbor theory and explores the statistical properties of its outputs, including some asymptotic features of the genuine conditional density estimate associated with ABC.

### Approximate Integrated Likelihood via ABC methods

- Computer Science, Mathematics
- 2014

A novel use of a recent new computational tool for Bayesian inference, namely the Approximate Bayesian Computation (ABC) methodology, is proposed to approximate the integrated likelihood by the ratio of kernel estimators of the marginal posterior and prior for the quantity of interest.

### Approximate Bayesian computation via empirical likelihood

- Computer Science
- 2012

The ABCel algorithm is developed, which bypasses simulations from the model and the choices of the ABC parameters, while being provably convergent in the number of observations.

### Improving Approximate Bayesian Computation via Quasi-Monte Carlo

- Computer ScienceJournal of Computational and Graphical Statistics
- 2018

This work derives ABC algorithms based on QMC (quasi-Monte Carlo) sequences and shows that the resulting ABC estimates have a lower variance than their Monte Carlo counter-parts.

### A Bootstrap Likelihood Approach to Bayesian Computation

- Computer Science
- 2015

This work proposes an alternative method based on a bootstrap likelihood approach, which is easy to implement and in some cases is actually faster than the other approaches considered.

### Efficient learning in ABC algorithms

- Computer Science
- 2012

A sequential algorithm adapted from Del Moral et al. (2012) which runs twice as fast as traditional ABC algorithms and is calibrated to minimize the number of simulations from the model.

### On Maximum Intractable Likelihood Estimation

- Mathematics
- 2012

Approximate Bayesian Computation (ABC) may be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Considering the first step as an explicit…

### Generalized multiple-point Metropolis algorithms for approximate Bayesian computation

- Computer Science
- 2015

This study proposes a generalization of the multiple-point Metropolis algorithm, which proceeds by generating multiple-dependent proposals and then by selecting a candidate among the set of proposals on the basis of weights that can be chosen arbitrarily.

### Bayesian computation via empirical likelihood

- Computer ScienceProceedings of the National Academy of Sciences
- 2013

The Bayesian computation with empirical likelihood algorithm developed in this paper provides an evaluation of its own performance through an associated effective sample size and is illustrated using several examples, including estimation of standard distributions, time series, and population genetics models.

## References

SHOWING 1-10 OF 71 REFERENCES

### Adaptive approximate Bayesian computation

- Computer Science
- 2009

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version, which compares favourably with two other versions of the approximation algorithm.

### Filtering via approximate Bayesian computation

- Computer ScienceStat. Comput.
- 2012

This article presents an ABC approximation designed to perform biased filtering for a Hidden Markov Model when the likelihood function is intractable and uses a sequential Monte Carlo algorithm to both fit and sample from the ABC approximation of the target probability density.

### Sequential Monte Carlo without likelihoods

- Computer ScienceProceedings of the National Academy of Sciences
- 2007

This work proposes a sequential Monte Carlo sampler that convincingly overcomes inefficiencies of existing methods and demonstrates its implementation through an epidemiological study of the transmission rate of tuberculosis.

### Likelihood-free estimation of model evidence

- Computer Science, Mathematics
- 2011

Novel likelihood-free approaches to model comparison are presented, based upon the independent estimation of the evidence of each model under study, which allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models.

### Non-linear regression models for Approximate Bayesian Computation

- Computer ScienceStat. Comput.
- 2010

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.

### Bayesian Computation and Model Selection Without Likelihoods

- Computer ScienceGenetics
- 2010

This work proposes a reformulation of the regression adjustment of population subdivision among western chimpanzees in terms of a general linear model (GLM), which allows the integration into the sound theoretical framework of Bayesian statistics and the use of its methods, including model selection via Bayes factors.

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

- Computer Science, MathematicsJournal of The Royal Society Interface
- 2008

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.

### An adaptive sequential Monte Carlo method for approximate Bayesian computation

- Computer Science, MathematicsStat. Comput.
- 2012

An adaptive SMC algorithm is proposed which admits a computational complexity that is linear in the number of samples and adaptively determines the simulation parameters.

### Approximate Bayesian computation (ABC) gives exact results under the assumption of model error

- Computer ScienceStatistical applications in genetics and molecular biology
- 2013

Under the assumption of the existence of a uniform additive model error term, ABC algorithms give exact results when sufficient summaries are used, which allows the approximation made in many previous application papers to be understood, and should guide the choice of metric and tolerance in future work.