Objective priors for the bivariate normal model

By James O. Berger, Dongchu Sun. 2008

103 citations recorded by the source corpus.

Summary Objective Bayesian inference for the multivariate normal distribution is illustrated, using dieren t types of formal objective priors (Jereys, invariant, reference and matching), dieren t modes of inference (Bayesian and frequentist), and dieren t criteria involved in selecting optimal objective priors (ease of computation, frequentist performance, marginalization paradoxes, and decision-theoretic evaluation). In the course of the investigation of the bivariate normal model in Berger and Sun (2006), a variety of surprising results were found, including the availability of objective priors that yield exact frequentist inferences for many functions of the bivariate normal parameters, such as the correlation coecien t. Certain of these results are generalized to the multivariate normal situation. The prior that most frequently yields exact frequentist inference is the rightHaar prior, which unfortunately is not unique. Two natural proposals are studied for dealing with this non-uniqueness: rst, mixing over the right-Haar priors; second, choosing the ‘empirical Bayes’ right-Haar prior, that which maximizes the marginal likelihood of the data. Quite surprisingly, we show that neither of these possibilities yields a good solution. This is disturbing and sobering. It is yet another indication that improper priors do not behave as do proper priors, and that it can be dangerous to apply ‘understandings’ from the world of proper priors to the world of improper priors.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9899dc5641dd76794e61e16508006e528ef3205f

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Citations in the corpus

Generalized Fiducial Inference: A Review and New Results (2016, background): “Examples of recent breakthroughs related to reference prior and model selection are Bayarri et al. (2012), Berger (1992), Berger and Sun (2008), Berger, Bernardo, and Sun (2009), and Berger, Bernardo, and Sun (2012).”
Assessing Mediational Models: Testing and Interval Estimation for Indirect Effects (2010, methodology): “For example, the effect of social affiliation on positive affect has been hypothesized to be mediated, in part, through self-presentation (Dunn, Biesanz, Human, & Finn, 2007). Given a theoretical mediational model, numerous approaches for assessing whether observed data are consistent with it have b”
Derivatives and Fisher information of bivariate copulas (2014, unknown): “Since the information with respect to the dependence parameters is independent of the marginal distributions (Smith 2007), the Fisher information with respect to ρ is the same as for the bivariate Gaussian distribution (Berger and Sun 2008), i.”
Bayesian Inference for Kendall’s Rank Correlation Coefficient (2018, methodology): “) The parametric yoking framework can be extended to other prior distributions that exist for Pearson’s ρ (e.g., the inverse Wishart distribution; Gelman et al. 2003; Berger and Sun 2008), by transforming ρ with the inverse of the expression given in (8):”
Inference in two-piece location-scale models with Jeffreys priors (2014, background): “182) himself preferred this prior for location-scale problems, and in the univariate normal case the independence Jeffreys is a matching prior (Berger and Sun, 2008).”
The case for objective Bayesian analysis (2006, background): “Invariance priors, as mentioned above, matching priors (see Datta and Mukerjee (2004)), and admissible priors (cf.”