A new go-to sampler for Bayesian probit regression

2020 ◽  
Vol 13 (1) ◽  
pp. 77-89
Author(s):  
Scott Simmons ◽  
Elizabeth J. McGuffey ◽  
Douglas VanDerwerken
Keyword(s):  
Probit Regression ◽  
Bayesian Probit Regression

scholarly journals Objective Bayesian Inference in Probit Models with Intrinsic Priors Using Variational Approximations

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 513
Author(s):  
Ang Li ◽  
Luis Pericchi ◽  
Kun Wang
Keyword(s):  
Regression Model ◽  
Binary Classification ◽  
Mean Field ◽  
Variational Approximation ◽  
Classification Problems ◽  
Probit Regression ◽  
Variational Approximations ◽  
Intrinsic Prior ◽  
Inference Methods ◽  
Bayesian Probit Regression

There is not much literature on objective Bayesian analysis for binary classification problems, especially for intrinsic prior related methods. On the other hand, variational inference methods have been employed to solve classification problems using probit regression and logistic regression with normal priors. In this article, we propose to apply the variational approximation on probit regression models with intrinsic prior. We review the mean-field variational method and the procedure of developing intrinsic prior for the probit regression model. We then present our work on implementing the variational Bayesian probit regression model using intrinsic prior. Publicly available data from the world’s largest peer-to-peer lending platform, LendingClub, will be used to illustrate how model output uncertainties are addressed through the framework we proposed. With LendingClub data, the target variable is the final status of a loan, either charged-off or fully paid. Investors may very well be interested in how predictive features like FICO, amount financed, income, etc. may affect the final loan status.

Penalized Binary Regression for Gene Expression Profiling

2004 ◽  
Vol 43 (05) ◽  
pp. 439-444 ◽  
Author(s):  
Michae Schimek
Keyword(s):  
Microarray Analysis ◽  
Predictive Performance ◽  
Small Sample ◽  
Probit Regression ◽  
Binary Regression ◽  
Data Set ◽  
Small Sample Sizes ◽  
Bayesian Probit Regression

Summary Objectives: A typical bioinformatics task in microarray analysis is the classification of biological samples into two alternative categories. A procedure is needed which, based on the expression levels measured, allows us to compute the probability that a new sample belongs to a certain class. Methods: For the purpose of classification the statistical approach of binary regression is considered. High-dimensionality and at the same time small sample sizes make it a challenging task. Standard logit or probit regression fails because of condition problems and poor predictive performance. The concepts of frequentist and of Bayesian penalization for binary regression are introduced. A Bayesian interpretation of the penalized log-likelihood is given. Finally the role of cross-validation for regularization and feature selection is discussed. Results: Penalization makes classical binary regression a suitable tool for microarray analysis. We illustrate penalized logit and Bayesian probit regression on a well-known data set and compare the obtained results, also with respect to published results from decision trees. Conclusions: The frequentist and the Bayesian penalization concept work equally well on the example data, however some method-specific differences can be made out. Moreover the Bayesian approach yields a quantification (posterior probabilities) of the bias due to the constraining assumptions.

scholarly journals Bayesian probit regression model for the diagnosis of pulmonary fibrosis: proof-of-principle

2011 ◽  
Vol 4 (1) ◽  
Author(s):  
Eric B Meltzer ◽  
William T Barry ◽  
Thomas A D'Amico ◽  
Robert D Davis ◽  
Shu S Lin ◽  
...  
Keyword(s):  
Pulmonary Fibrosis ◽  
Regression Model ◽  
Probit Regression ◽  
Bayesian Probit Regression ◽  
Proof Of Principle

scholarly journals Cross-validation prior choice in Bayesian probit regression with many covariates

2011 ◽  
Vol 22 (2) ◽  
pp. 359-373 ◽  
Author(s):  
D. Lamnisos ◽  
J. E. Griffin ◽  
M. F. J. Steel
Keyword(s):  
Cross Validation ◽  
Probit Regression ◽  
Bayesian Probit Regression

Rank Status and Happiness in India: A Panel Ordered Probit Estimation of the Effect of Ordinal Relative Comparison on Well-being

2020 ◽  
Vol 11 (01) ◽  
Author(s):  
T. Lakshmanasamy ◽  
K. Maya
Keyword(s):  
Life Satisfaction ◽  
Fixed Effects ◽  
Reference Group ◽  
Well Being ◽  
Ordered Probit ◽  
Probit Regression ◽  
Differential Effects ◽  
Comparison Income ◽  
Average Reference ◽  
The Rich

Most often the social comparison or relative income hypothesis has been used as an explanation for the lack of systematic relationship between income and happiness, using the ordered probit regression method. The identification of relevant reference group and the estimation of the differential effects of comparison income have been controversial. To overcome these twin issues, this paper uses an ordinal comparison income approach based on rich/poor dichotomy and rank income. The rank income of an individual is defined as his relative position in the income distribution within the reference group and the average income of the reference group is used to define the rich/poor classification. The differential effects of ordinal incomes across life satisfaction distribution is estimated by the panel fixed effects ordered profit regression model using the WVS data for India. The estimated results show that ordinal income comparison, rather than cardinal average reference income, is a better predictor of life satisfaction levels. Raising income level is relatively important for less satisfied people while increasing rank status is important for highly satisfied people in India.

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