Power Laws Distributions in Objective Priors

@article{Ramos2020PowerLD,
  title={Power Laws Distributions in Objective Priors},
  author={Pedro Luiz Ramos and Francisco Aparecido Rodrigues and Eduardo Ramos and Dipak K. Dey and Francisco Louzada},
  journal={Statistica Sinica},
  year={2020}
}
The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the posterior distribution. However, these priors are typically improper and may lead to improper posterior. Here, we show, for a general family of distributions, that the obtained objective priors for the parameters either follow a power-law distribution or has an… 

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References

SHOWING 1-10 OF 36 REFERENCES

Bayesian analysis of the generalized gamma distribution using non-informative priors

ABSTRACT The Generalized gamma (GG) distribution plays an important role in statistical analysis. For this distribution, we derive non-informative priors using formal rules, such as Jeffreys prior,

On a Class of Objective Priors from Scoring Rules (with Discussion)

TLDR
This paper proposes to take a novel look at the construction of objective prior distributions, where the connection with a chosen sampling distribution model is removed and produces a class of priors that can be employed in scenarios where the usual model based priors fail, such as mixture models and model selection via Bayes factors.

Prior Distributions for Objective Bayesian Analysis

TLDR
This paper discusses principles for objective Bayesian model comparison, and singles out some major concepts for building priors, which are subsequently illustrated in some detail for the classic problem of variable selection in normal linear models.

The Selection of Prior Distributions by Formal Rules

Abstract Subjectivism has become the dominant philosophical foundation for Bayesian inference. Yet in practice, most Bayesian analyses are performed with so-called “noninformative” priors, that is,

Reference Bayesian analysis for hierarchical models

TLDR
This proposal is based on a flexible decomposition of the Fisher information for hierarchical models which overcomes the marginalization step of the likelihood of model parameters and gives an upper bound for the prior information.

Overall Objective Priors

TLDR
This paper considers three methods for selecting a single objective prior and study, in a variety of problems including the multinomial problem, whether or not the resulting prior is a reasonable overall prior.

Estimating a Product of Means: Bayesian Analysis with Reference Priors

Abstract Suppose that we observe X ∼ N(α, 1) and, independently, Y ∼ N(β, 1), and are concerned with inference (mainly estimation and confidence statements) about the product of means θ = αβ. This

Objective Bayesian analysis for the Student-t regression model

We develop a Bayesian analysis based on two different Jeffreys priors for the Student-t regression model with unknown degrees of freedom. It is typically difficult to estimate the number of degrees

Inferential Procedures for the Generalized Gamma Distribution

Abstract The maximum likelihood estimators of the parameters of the generalized gamma distribution are shown to have the property that are distributed independently of a and b. Similar properties are

Fitting power-laws in empirical data with estimators that work for all exponents

TLDR
This work first derives the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces, and shows that an almost identical estimator also works perfectly for continuous data.