Robust Bayesian Regression Analysis Using Ramsay-Novick Distributed Errors with Student-t Prior

  title={Robust Bayesian Regression Analysis Using Ramsay-Novick Distributed Errors with Student-t Prior},
  author={Mutlu Kaya and Emel Çankaya and Olcay Arslan},
This paper investigates bayesian treatment of regression modelling with Ramsay - Novick (RN)  distribution  specifically  developed for robust  inferential procedures. It falls into the category of the so-called heavy-tailed distributions generally accepted as outlier resistant densities. RN is obtained by coverting the usual form of a non-robust density to a robust likelihood through  the  modification of its unbounded influence function. The  resulting  distributional form  is  quite… 

Figures and Tables from this paper

Robustness against conflicting prior information in regression
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


Outlier Models and Prior Distributions in Bayesian Linear Regression
SUMMARY Bayesian inference in regression models is considered using heavy-tailed error distri- butions to accommodate outliers. The particular class of distributions that can be con- structed as
Robust Statistical Modeling Using the t Distribution
Abstract The t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer-than-normal tails. An analytical strategy based on maximum
Impacts of atypical data on Bayesian inference and robust Bayesian approach in fisheries
The posterior distributions derived from this proposed approach are found to be robust to atypical data in this study, suggesting that this approach offers a potentially useful addition to Bayesian methods used in fisheries.
PLU Robust Bayesian Decision Theory: Point Estimation
Abstract The development of data analysis techniques that are robust with respect to wild or extreme observations is now a major concern. From a Bayesian point of view, the concept of robustness also
On posterior propriety for the Student-$t$ linear regression model under Jeffreys priors
Regression models with fat-tailed error terms are an increasingly popular choice to obtain more robust inference to the presence of outlying observations. This article focuses on Bayesian inference
Two graphical displays for outlying and influential observations in regression
SUMMARY The paper describes two procedures for detecting observations with outlying values either in the response variable or in the explanatory variables in multiple regression. These procedures are
Normal/Independent Distributions and Their Applications in Robust Regression
Abstract Maximum likelihood estimation with nonnormal error distributions provides one method of robust regression. Certain families of normal/independent distributions are particularly attractive
Bayesian heavy-tailed models and conflict resolution: A review
It is shown that Bayesian modelling with heavy-tailed distributions has been shown to produce more reasonable con‡ict resolution, typically by favouring one source of information over the other.
Hierarchical models with scale mixtures of normal distributions
SummaryIn this paper, we consider the one-way random effects model as a Bayesian hierarchical structure, assuming normality for the first stage. We take scale mixtures of normal (SMN) distributions
Trimmed Least Squares Estimation in the Linear Model
Abstract We consider two methods of defining a regression analog to a trimmed mean. The first was suggested by Koenker and Bassett and uses their concept of regression quantiles. Its asymptotic