Credit scoring models based on accepted applications may be biased and their consequences can have a statistical and economic impact. Reject inference is the process of attempting to infer the creditworthiness status of the rejected applications. In this research, we use deep generative models to develop two new semi-supervised Bayesian models for reject inference in credit scoring, in which we model the data generating process to be dependent on a Gaussian mixture. The goal is to improve the classification accuracy in credit scoring models by adding reject applications. Our proposed models infer the unknown creditworthiness of the rejected applications by exact enumeration of the two possible outcomes of the loan (default or non-default). The efficient stochastic gradient optimization technique used in deep generative models makes our models suitable for large data sets. Finally, the experiments in this research show that our proposed models perform better than classical and alternative machine learning models for reject inference in credit scoring.
 Sample selection bias as a specification error This paper discusses the bias that results from using non-randomly selected samples to estimate behavioral relationships as an ordinary specification error or «omitted variables» bias. A simple consistent two stage estimator is considered that enables analysts to utilize simple regression methods to estimate behavioral functions by least squares methods. The asymptotic distribution of the estimator is derived.(This abstract was borrowed from another version of this item.) The novel electric heating element is particularly useful as a water heating element, although its use is not so limited. The element comprises the usual met al-sheathed heater having electrical termination at one end of the sheath. The customary water heating element has a sheath of hair-pin formation, with the ends of the two legs of the sheath connected to structure which serves as a mounting member and an electrical connector. Such structure in the present application is of molded plastic with a met al insert. Abstract Most credit assessment models used in practice are based on simple credit scoring functions estimated by discriminant analysis. These functions are designed to distinguish whether or not applicants belong to the population of ‘would be’ defaulters. We suggest that the traditional view that emphasizes default probability is too narrow. Our model of credit assessment focuses on expected earnings. We demonstrate how maximum likelihood estimates of default probabilities can be obtained from a bivariate ‘censored probit’ framework using a ‘choice-based’ sample originally intended for discriminant analysis. The paper concludes with recommendations for combining these default probability estimates with other parameters of the loan earnings process to obtain a more meaningful model of credit assessment.