Quasi Bayesian likelihood

Lin, Lu

doi:10.1016/j.stamet.2005.12.002

Cited by 15 publications

(15 citation statements)

References 8 publications

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“…We now outline the theoretical framework based on Hilbert space method. For some similar notions see Small and Mcleish (1994) and Lin (2006). Let a p-dimensional function space G be endowed with a family of inner products ·, · θ indexed by θ ∈ Θ.…”

Section: Hilbert-based Likelihoodmentioning

confidence: 99%

“…We call this projection the Hilbert-based quasi-posterior density. Then the resulting quasi-posterior density is available in practice; for details see Small and Mcleish (1994), Small (2003) and Lin (2006) and Example 2 given in Section 4.…”

Section: Hilbert-based Likelihoodmentioning

confidence: 99%

“…According to the point of Bayesian inference, an estimating function is designed to be unbiased in two senses of conditional unbiasedness and average unbiasedness for zero. A recent study by Lin (2006) introduced a theoretical framework of quasi-Bayesian likelihood, in which the quasi-posterior score and likelihood are based on the Hilbert space method. Although the general framework was established in this paper, the validity about Hilbertbased Bayesian inference has been unexplored.…”

Section: Introductionmentioning

confidence: 99%

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Proper Bayesian estimating equation based on Hilbert space method

Lin

Tan

2008

Statistics & Probability Letters

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Section: Hilbert-based Likelihoodmentioning

confidence: 99%

Section: Hilbert-based Likelihoodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Proper Bayesian estimating equation based on Hilbert space method

Lin

Tan

2008

Statistics & Probability Letters

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“…In addition, Lin (2006) and Greco et al (2008) discussed the use of quasi-likelihood functions in the Bayesian setting. In this paper we derive a default prior distribution for a parameter of interest to be used together with a quasi-or a quasi-profile likelihood function derived from estimating functions.…”

Section: Introductionmentioning

confidence: 99%

“…Although the use of a pseudo-likelihood function, in the Bayesian inference cannot be considered as orthodox, it is actually widely shared. Papers which discuss the use of pseudo-likelihoods in the Bayesian perspective are Efron (1993), Racugno (1992, 1994), Raftery et al (1996), Fraser et al (2003), Cabras et al (2006), Lin (2006), Chang and Mukerjee (2006), Greco et al (2008) and Pauli et al (2008). Papers which are more specifically related to the validation of a posterior distribution based on an alternative likelihood are Monahan and Boos (1992), Severini (1999), Lazar (2003), Schennach (2005), Racugno et al (2008) and .…”

Section: Introductionmentioning

confidence: 99%

Default prior distributions from quasi- and quasi-profile likelihoods

Ventura

Cabras

Racugno

2010

Journal of Statistical Planning and Inference

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In some problems of practical interest, a standard Bayesian analysis can be difficult to perform. This is true, for example, when the class of sampling parametric models is unknown or if robustness with respect to data or to model misspecifications is required. These situations can be usefully handled by using a posterior distribution for the parameter of interest which is based on a pseudo-likelihood function derived from estimating equations, i.e. on a quasi-likelihood, and on a suitable prior distribution. The aim of this paper is to propose and discuss the construction of a default prior distribution for a scalar parameter of interest to be used together with a quasi-likelihood function. We show that the proposed default prior can be interpreted as a Jeffreys-type prior, since it is proportional to the square-root of the expected information derived from the quasi-likelihood. The frequentist coverage of the credible regions, based on the proposed procedure, is studied through Monte Carlo simulations in the context of robustness theory and of generalized linear models with overdispersion.

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The how and why of Bayesian nonparametric causal inference

Linero

Antonelli

2022

WIREs Computational Stats

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Spurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high-dimensional) methods have recently seen increased attention in the causal inference literature. In this article, we present a comprehensive overview of Bayesian nonparametric applications to causal inference. Our aims are to (i) introduce the fundamental Bayesian nonparametric toolkit; (ii) discuss how to determine which tool is most appropriate for a given problem; and (iii) show how to avoid common pitfalls in applying Bayesian nonparametric methods in high-dimensional settings. Unlike standard fixeddimensional parametric problems, where outcome modeling alone can sometimes be effective, we argue that most of the time it is necessary to model both the selection and outcome processes. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

show abstract

Quasi Bayesian likelihood

Cited by 15 publications

References 8 publications

Proper Bayesian estimating equation based on Hilbert space method

Proper Bayesian estimating equation based on Hilbert space method

Default prior distributions from quasi- and quasi-profile likelihoods

The how and why of Bayesian nonparametric causal inference

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