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Article

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

by †,‡, *,†,‡ and †,‡
Río Piedras Campus, University of Puerto Rico, 00925 San Juan, Puerto Rico
*
Author to whom correspondence should be addressed.
14 Ave. Universidad Ste. 1401, San Juan, PR 00925, USA.
These authors contributed equally to this work.
Entropy 2020, 22(5), 513; https://doi.org/10.3390/e22050513
Received: 3 March 2020 / Revised: 14 April 2020 / Accepted: 26 April 2020 / Published: 30 April 2020
(This article belongs to the Special Issue Data Science: Measuring Uncertainties)
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. View Full-Text
Keywords: objective Bayesian inference; intrinsic prior; variational inference; binary probit regression; mean-field approximation objective Bayesian inference; intrinsic prior; variational inference; binary probit regression; mean-field approximation
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MDPI and ACS Style

Li, A.; Pericchi, L.; Wang, K. Objective Bayesian Inference in Probit Models with Intrinsic Priors Using Variational Approximations. Entropy 2020, 22, 513. https://doi.org/10.3390/e22050513

AMA Style

Li A, Pericchi L, Wang K. Objective Bayesian Inference in Probit Models with Intrinsic Priors Using Variational Approximations. Entropy. 2020; 22(5):513. https://doi.org/10.3390/e22050513

Chicago/Turabian Style

Li, Ang; Pericchi, Luis; Wang, Kun. 2020. "Objective Bayesian Inference in Probit Models with Intrinsic Priors Using Variational Approximations" Entropy 22, no. 5: 513. https://doi.org/10.3390/e22050513

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