# Approximate Integrated Likelihood via ABC methods

@article{Grazian2014ApproximateIL, title={Approximate Integrated Likelihood via ABC methods}, author={Clara Grazian and Brunero Liseo}, journal={arXiv: Computation}, year={2014} }

We propose a novel use of a recent new computational tool for Bayesian inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC is a way to handle models for which the likelihood function may be intractable or even unavailable and/or too costly to evaluate; in particular, we consider the problem of eliminating the nuisance parameters from a complex statistical model in order to produce a likelihood function depending on the quantity of interest only. Given a proper prior… Expand

#### 7 Citations

The use of a single pseudo-sample in approximate Bayesian computation

- Mathematics, Computer Science
- Stat. Comput.
- 2017

It is shown that the conclusion that multiple pseudo-samples cannot substantially increase (and can substantially decrease) the efficiency of the algorithm as compared to employing a high-variance estimate based on a single pseudo-sample also holds for a Markov chain Monte Carlo version of ABC, implying that it is unnecessary to tune the number of pseudo-Samples used in ABC-MCMC. Expand

Extending approximate Bayesian computation methods to high dimensions via a Gaussian copula model

- Computer Science, Mathematics
- Comput. Stat. Data Anal.
- 2017

This work extends conventional ABC methods to problems of high dimension using a Gaussian copula approximation, and results in an analytic expression for the approximate posterior which is useful for many purposes such as approximation of the likelihood itself. Expand

Approximate maximum likelihood estimation using data-cloning ABC

- Mathematics, Computer Science
- Comput. Stat. Data Anal.
- 2017

It is shown how to exploit the methodology to reduce the number of iterations of a standard ABC-MCMC algorithm and therefore reduce the computational effort, while obtaining reasonable point estimates. Expand

An Approximate Likelihood Perspective on ABC Methods

- Computer Science, Mathematics
- 2017

This article provides a unifying review, general representation, and classification of all ABC methods from the view of approximate likelihood theory, which clarifies how ABC methods can be characterized, related, combined, improved, and applied for future research. Expand

A Tutorial on Fisher Information

- Mathematics, Computer Science
- 2017

This tutorial clarifies the concept of Fisher information as it manifests itself across three different statistical paradigms, including the frequentist paradigm, the Bayesian paradigm and the minimum description length paradigm. Expand

Statistical and computational tradeoff in genetic algorithm-based estimation

- Computer Science, Mathematics
- 2017

This work analyzes parametric estimation problems tackled by GAs, and introduces a framework of GA estimation with fixed computational resources, which is a form of statistical and the computational tradeoff question, crucial in recent problems. Expand

#### References

SHOWING 1-10 OF 34 REFERENCES

Approximate Bayesian computational methods

- Computer Science, Mathematics
- Stat. Comput.
- 2012

In this survey, the various improvements and extensions brought on the original ABC algorithm in recent years are studied. Expand

FREQUENCY PROPERTIES OF INFERENCES BASED ON AN INTEGRATED LIKELIHOOD FUNCTION

- Mathematics
- 2011

One approach to likelihood inference for a parameter of interest in the presence of a nuisance parameter is to use an integrated likelihood in which the nuisance parameter is eliminated from the… Expand

Approximate Bayesian Computation: A Nonparametric Perspective

- Mathematics
- 2009

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate… Expand

Likelihood Methods in Statistics

- Mathematics
- 2001

This book provides an introduction to the modern theory of likelihood-based statistical inference. This theory is characterized by several important features. One is the recognition that it is… Expand

Likelihood ratio statistics based on an integrated likelihood

- Mathematics
- 2010

An integrated likelihood depends only on the parameter of interest and the data, so it can be used as a standard likelihood function for likelihood-based inference. In this paper, the higher-order… Expand

Application of Likelihood Methods to Models Involving Large Numbers of Parameters

- Computer Science
- 1970

These methods indicate that in many situations commonly encountered objective methods of eliminating unwanted parameters from the likelihood function can be adopted and give an alternative method of interpreting multiparameter likelihoods to that offered by the Bayesian approach. Expand

Integrated likelihood methods for eliminating nuisance parameters

- Mathematics
- 1999

Elimination of nuisance parameters is a central problem in statistical inference and has been formally studied in virtually all approaches to inference. Perhaps the least studied approach is… Expand

Integrated likelihood functions for non-Bayesian inference

- Mathematics
- 2007

Consider a model with parameter θ = (ψ, λ), where ψ is the parameter of interest, and let L(ψ, λ) denote the likelihood function. One approach to likelihood inference for ψ is to use an integrated… Expand

Bayesian estimation of quantile distributions

- Mathematics, Computer Science
- Stat. Comput.
- 2009

Approximate Bayesian computation provides an alternative approach requiring only a sampling scheme for the distribution of interest, enabling easier use of quantile distributions under the Bayesian framework. Expand

Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

- Mathematics
- 1977

Abstract Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a… Expand