scholarly journals Convergence properties of Gibbs samplers for Bayesian probit regression with proper priors

2017 ◽  
Vol 11 (1) ◽  
pp. 177-210 ◽  
Author(s):  
Saptarshi Chakraborty ◽  
Kshitij Khare
Keyword(s):  
Probit Regression ◽  
Convergence Properties ◽  
Gibbs Samplers ◽  
Proper Priors ◽  
Bayesian Probit Regression

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 Surprising Convergence Properties of Some Simple Gibbs Samplers under Various Scans

2015 ◽  
Vol 5 (1) ◽  
pp. 51 ◽  
Author(s):  
Gareth O. Roberts ◽  
Jeffrey S. Rosenthal
Keyword(s):  
Gibbs Sampler ◽  
Convergence Properties ◽  
Gibbs Samplers

We examine the convergence properties of some simple Gibbs sampler examples under various scans. We find some surprising results, including Gibbs samplers where deterministic-scan is much more efficient than random-scan, and other samplers where the opposite is true.  We also present an example where the convergence takes precisely the same time with any fixed deterministic scan, but modifying the scan in any way leads to significantly slower convergence.

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
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