Bayesian Analysis on Limiting the Student-$t$ Linear Regression Model

Hayashi, Yoshiko

doi:10.48550/arxiv.2008.04522

Cited by 1 publication

(1 citation statement)

References 12 publications

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“…In the latter paper, it is noted that there exists a gap between the models formally covered by the theory of conflict resolution and models commonly used in practice. The latest developments focus on situations where the conflicting information is carried by outlying data points in location-scale models (Desgagné, 2015) and linear regression (Desgagné and Gagnon, 2019;Gagnon et al, 2020aGagnon et al, , 2021Hayashi, 2020). The present paper contributes to the expansion of the theory of conflict resolution by covering conflicting prior information in regression.…”

Section: Conflictsmentioning

confidence: 93%

Robustness against conflicting prior information in regression

Gagnon¹

2021

Preprint

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Including prior information about model parameters is a fundamental step of any Bayesian statistical analysis. It is viewed positively by some as it allows, among others, to quantitatively incorporate expert opinion about model parameters. It is viewed negatively by others because it sets the stage for subjectivity in statistical analysis. Certainly, it creates problems when the inference is skewed due to a conflict with the data collected. According to the theory of conflict resolution (O'Hagan and Pericchi, 2012), a solution to such problems is to diminish the impact of conflicting prior information, yielding inference consistent with the data. This is typically achieved by using heavy-tailed priors. We study both theoretically and numerically the efficacy of such a solution in regression where the prior information about the coefficients takes the form of a product of density functions with known location and scale parameters. We study functions with regularly-varying tails (Student distributions), log-regularly-varying tails (as introduced in Desgagné ( 2015)), and propose functions with slower tail decays that allow to resolve any conflict that can happen under that regression framework, contrarily to the two previous types of functions. The code to reproduce all numerical experiments is available online. 1

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Section: Conflictsmentioning

confidence: 93%

Robustness against conflicting prior information in regression

Gagnon¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

Bayesian Analysis on Limiting the Student-$t$ Linear Regression Model

Cited by 1 publication

References 12 publications

Robustness against conflicting prior information in regression

Robustness against conflicting prior information in regression

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