Robust Bayesian regression with the forward search: theory and data analysis

Atkinson, Anthony C.; Corbellini, Aldo; Riani, Marco

doi:10.1007/s11749-017-0542-6

Cited by 11 publications

(9 citation statements)

References 21 publications

(17 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If W R is the n × n diagonal matrix of the weights from a robust regression, we replace the information matrix for the subset m , that is, X ( m ) T X ( m ) by X T W R X and the sufficient statistic X ( m ) T y ( m ) by X T W R y . As an example, in Section 6 of Atkinson et al (), we use the trimmed likelihood weights from the R package wle (Agostinelli, ). The calculation of these robust weights, which forms a first stage of their Bayesian analysis, is described in Agostinelli and Greco (, Section 2).…”

Section: Discussionmentioning

confidence: 99%

The Use of Prior Information in Very Robust Regression for Fraud Detection

Riani

Corbellini

Atkinson

2018

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

Summary Misinvoicing is a major tool in fraud including money laundering. We develop a method of detecting the patterns of outliers that indicate systematic mis‐pricing. As the data only become available year by year, we develop a combination of very robust regression and the use of ‘cleaned’ prior information from earlier years, which leads to early and sharp indication of potentially fraudulent activity that can be passed to legal agencies to institute prosecution. As an example, we use yearly imports of a specific seafood into the European Union. This is only one of over one million annual data sets, each of which can currently potentially contain 336 observations. We provide a solution to the resulting big data problem, which requires analysis with the minimum of human intervention.

show abstract

Section: Discussionmentioning

confidence: 99%

The Use of Prior Information in Very Robust Regression for Fraud Detection

Riani

Corbellini

Atkinson

2018

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

show abstract

“…n (x n ) < ∞, we can re-express the R (α) -posterior probabilities (5) in terms of this R (α) -marginal density as π…”

Section: The Contribution Of This Papermentioning

confidence: 99%

“…Then, under suitable assumptions on the prior distribution as before, the corresponding R (α)posterior distribution is defined by (5) which is now equivalent to (1) and can be written as a product of stationary independent terms corresponding to each x i (additivity). Other related measures can be defined from these quantities; we will come back to them again in Section 4.…”

Section: The Contribution Of This Papermentioning

confidence: 99%

“…The second approach of frequentist robustness serves the purpose but differs in the strictest probabilistic sense from the Bayesian philosophy, since one needs to alter the posterior density appropriately to achieve robustness against data contamination or model misspecification; the resulting modified posteriors are generally referred to as pseudo-posterior densities. Different such pseudo-posteriors have been proposed by [2,5,15,28,31,37,46]; but all of them have primarily considered independent stationary models and have different pros and cons. Another recent attempt, in the borderline of these two approaches, has been proposed by [59], who have transformed the given model to a localized model involving hyperparameters to be estimated through the empirical Bayes approach.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

General Robust Bayes Pseudo-Posteriors: Exponential Convergence Results with Applications

Ghosh¹,

Majumder²,

Basu³

2022

STAT SINICA

View full text Add to dashboard Cite

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations [20]. While it has several optimal properties, a major drawback of Bayesian inference is the lack of robustness against data contamination and model misspecification, which becomes pernicious in the use of objective priors. This paper presents the general formulation of a Bayes pseudo-posterior distribution yielding robust inference. Exponential convergence results related to the new pseudo-posterior and the corresponding Bayes estimators are established under the general parametric setup and illustrations are provided for the independent stationary as well as non-homogeneous models. Several additional details and properties of the procedure are described, including the estimation under fixed-design regression models.

show abstract

“…The left-hand panel of Figure 4 suggests that the outliers might be modelled separately. Another example in which outliers can be distinctly modelled is in data on fraud in seafood pricing, in which the FS analysis of Atkinson et al [11] shows that the price of imports from one country into the European Union is consistently under reported, leading to tax evasion. The evidence for the existence of this fraud is strengthened by fitting a separate model to the subset of observations.…”

Section: Fs Analysis Of the Transformed Loyalty Card Datamentioning

confidence: 99%

fsdaSAS: A Package for Robust Regression for Very Large Datasets Including the Batch Forward Search

Torti

Corbellini

Atkinson

2021

Stats

Self Cite

View full text Add to dashboard Cite

The forward search (FS) is a general method of robust data fitting that moves smoothly from very robust to maximum likelihood estimation. The regression procedures are included in the MATLAB toolbox FSDA. The work on a SAS version of the FS originates from the need for the analysis of large datasets expressed by law enforcement services operating in the European Union that use our SAS software for detecting data anomalies that may point to fraudulent customs returns. Specific to our SAS implementation, the fsdaSAS package, we describe the approximation used to provide fast analyses of large datasets using an FS which progresses through the inclusion of batches of observations, rather than progressing one observation at a time. We do, however, test for outliers one observation at a time. We demonstrate that our SAS implementation becomes appreciably faster than the MATLAB version as the sample size increases and is also able to analyse larger datasets. The series of fits provided by the FS leads to the adaptive data-dependent choice of maximally efficient robust estimates. This also allows the monitoring of residuals and parameter estimates for fits of differing robustness levels. We mention that our fsdaSAS also applies the idea of monitoring to several robust estimators for regression for a range of values of breakdown point or nominal efficiency, leading to adaptive values for these parameters. We have also provided a variety of plots linked through brushing. Further programmed analyses include the robust transformations of the response in regression. Our package also provides the SAS community with methods of monitoring robust estimators for multivariate data, including multivariate data transformations.

show abstract

Robust Bayesian regression with the forward search: theory and data analysis

Cited by 11 publications

References 21 publications

The Use of Prior Information in Very Robust Regression for Fraud Detection

The Use of Prior Information in Very Robust Regression for Fraud Detection

General Robust Bayes Pseudo-Posteriors: Exponential Convergence Results with Applications

fsdaSAS: A Package for Robust Regression for Very Large Datasets Including the Batch Forward Search

Contact Info

Product

Resources

About