Default prior distributions from quasi- and quasi-profile likelihoods

Ventura, Laura; Cabras, Stefano; Racugno, Walter

doi:10.1016/j.jspi.2010.04.003

Cited by 13 publications

(6 citation statements)

References 26 publications

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“…The theory and use of estimating equations and that of the related quasi-and quasiprofile likelihood functions have received a good deal of attention in recent years; see, among others, Liang and Zeger (1995); Barndorff-Nielsen (1995); Desmond (1997); Heyde (1997); Adimari and Ventura (2002); Severini (2002); Wang and Hanfelt (2003); Jørgensen and Knudsen (2004); Bellio et al (2008). In addition, Ventura et al (2010); Lin (2006); Greco et al (2008) discuss the use of QL functions in the Bayesian setting.…”

Section: Mcmc Algorithmmentioning

confidence: 99%

Approximate Bayesian Computation by Modelling Summary Statistics in a Quasi-likelihood Framework

Cabras¹,

Castellanos²,

Ruli³

2015

Bayesian Anal.

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Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy between prior and posterior. Therefore, more elaborate methods, such as ABC with the Markov chain Monte Carlo algorithm (ABC-MCMC), should be used. However, the elaboration of a proposal density for MCMC is a sensitive issue and very difficult in the ABC setting, where the likelihood is intractable. We discuss an automatic proposal distribution useful for ABC-MCMC algorithms. This proposal is inspired by the theory of quasi-likelihood (QL) functions and is obtained by modelling the distribution of the summary statistics as a function of the parameters. Essentially, given a real-valued vector of summary statistics, we reparametrize the model by means of a regression function of the statistics on parameters, obtained by sampling from the original model in a pilot-run simulation study. The QL theory is well established for a scalar parameter, and it is shown that when the conditional variance of the summary statistic is assumed constant, the QL has a closed-form normal density. This idea of constructing proposal distributions is extended to non constant variance and to real-valued parameter vectors. The method is illustrated by several examples and by an application to a real problem in population genetics.

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Section: Mcmc Algorithmmentioning

confidence: 99%

Approximate Bayesian Computation by Modelling Summary Statistics in a Quasi-likelihood Framework

Cabras¹,

Castellanos²,

Ruli³

2015

Bayesian Anal.

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“…With a given prior π ( R ) for the correlations ρ i , j , the (pseudo‐)posterior takes the form π ( R | data) ∝ π ( R ) L ( R ) for R ∈ Ω , with the likelihood L ( R ) as in or . When L ( R ) is a pseudo‐likelihood, the posterior is called pseudo‐posterior (Pauli et al , ; Ventura et al , ), but it is a proper distribution that we can work with. The joint posterior distribution of the ρ i , j 's can be summarized in various ways, leading to point estimates, credibility intervals and regions.…”

Section: A Bayesian Solutionmentioning

confidence: 99%

Statistical Corrections of Invalid Correlation Matrices

Løland

Huseby

Hjort

et al. 2013

Scandinavian J Statistics

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Suppose estimates are available for correlations between pairs of variables but that the matrix of correlation estimates is not positive definite. In various applications, having a valid correlation matrix is important in connection with follow-up analyses that might, for example, involve sampling from a valid distribution. We present new methods for adjusting the initial estimates to form a proper, that is, nonnegative definite, correlation matrix. These are based on constructing certain pseudo-likelihood functions, formed by multiplying together exact or approximate likelihood contributions associated with the individual correlations. Such pseudo-likelihoods may then be maximized over the range of proper correlation matrices. They may also be utilized to form pseudo-posterior distributions for the unknown correlation matrix, by factoring in relevant prior information for the separate correlations. We illustrate our methods on two examples from a financial time series and genomic pathway analysis.

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“…Also Bayesian robustness with respect to model misspecification have attracted considerable attention. For instance, Lazar (2003), Greco et al (2008), Ventura et al (2010) and Agostinelli and Greco (2013) discuss approaches based on robust pseudo-likelihood functions, such as the empirical likelihood, as replacement of the genuine likelihood in Bayes' formula. Lewis et al (2014) discuss an approach for building posterior distributions from robust M-estimators using constrained Markov Chain Monte Carlo (MCMC) methods.…”

Section: Introductionmentioning

confidence: 99%

Robust approximate Bayesian inference

Ruli

Sartori

Ventura

2020

Journal of Statistical Planning and Inference

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We discuss an approach for deriving robust posterior distributions from M -estimating functions using Approximate Bayesian Computation (ABC) methods. In particular, we use M -estimating functions to construct suitable summary statistics in ABC algorithms.The theoretical properties of the robust posterior distributions are discussed. Special attention is given to the application of the method to linear mixed models. Simulation results and an application to a clinical study demonstrate the usefulness of the method.An R implementation is also provided in the robustBLME package.

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Default prior distributions from quasi- and quasi-profile likelihoods

Cited by 13 publications

References 26 publications

Approximate Bayesian Computation by Modelling Summary Statistics in a Quasi-likelihood Framework

Approximate Bayesian Computation by Modelling Summary Statistics in a Quasi-likelihood Framework

Statistical Corrections of Invalid Correlation Matrices

Robust approximate Bayesian inference

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