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Approximate integrated likelihood via ABC methods

Grazian, Clara; Brunero, Liseo (2014), Approximate integrated likelihood via ABC methods, ISBA 2014, 2014-07, Cancun, Mexico

Type
Communication / Conférence
External document link
https://arxiv.org/abs/1403.0387v1
Date
2014
Conference title
ISBA 2014
Conference date
2014-07
Conference city
Cancun
Conference country
Mexico
Pages
28
Metadata
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Author(s)
Grazian, Clara
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Brunero, Liseo
Abstract (EN)
Recent developments allow Bayesian analysis also when the likelihood function L(θ;y) is intractable, that means it is analytically unavailable or computationally prohibitive to evaluate. These methods are known as ``approximate Bayesian computation" (ABC) or likelihood-free methods and are characterized by the fact that the approximation of the posterior distribution is obtained without explicitly evaluating the likelihood function. This kind of analysis is popular in genetic and financial settings. The likelihood may be unavailable because of a high-dimensional latent structure and this situation is closely related to the problem of eliminating nuisance parameters. We propose a novel use of the ABC methodology. 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 for the entire vector parameter, we propose to approximate the integrated likelihood by the ratio of kernel estimators of the marginal posterior and prior distributions for the quantity of interest. We present several examples, both parametric and semiparametric.
Subjects / Keywords
ABC; Nuisance parameters; Integrated likelihood; Neyman and Scott problem; Semiparametric regression
JEL
C11 - Bayesian Analysis: General
C14 - Semiparametric and Nonparametric Methods: General

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