Bayesian Logistic Regression Models for Credit Scoring by Gregg Webster

Table 4.15
Bayesian logistic regression model with non-informative prior on the “new” 
data………………………………………………………………………………………...79 
Table 4.16
Geweke test statistics for each variable for the Bayesian logistic regression model 
with non-informative prior……………………………………………………………......81 
 

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Table 4.17
Classification table for the logistic regression model with cut-off probability of 
0.3…………………………………………………………………………………………82 
Table 4.18
Classification table for the Bayesian logistic regression model with informative 
prior and cut-off probability of 0.3……………………………………………………......82 
Table 4.19 
Classification table of the Bayesian logistic regression model with non-
informative prior and cut-off probability of 0.3………………………………………......83 
Table 4.20 
Comparison of Models 1, 2 and 3 when the cut-off probability is 0.3…………..83 
Table 4.21 
Classification table of logistic regression model with cut-off probability of 
0.48……………………………………………………………………………………......84 
Table 4.22
Classification table of Bayesian logistic regression model with informative prior 
and cut-off probability of 0.48…………………………………………………………….85 
Table 4.23
Classification table of the Bayesian logistic regression model with non-
informative prior and cut-off probability of 0.48………………………………………....85 
Table 4.24
Comparison of Models 1, 2 and 3 when the cut-off probability is 0.48…………86 
 
 

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Chapter 1: Introduction 
 
1.1 Context of the Research 
Consumer credit is one of the main driving forces which allowed for the rise (and possible 
demise) of most of the leading industrialized countries. The growth in home ownership 
and consumer spending over the last 50 years would not have occurred without credit. 
When a financial institution grants credit to an applicant the financial institution trusts the 
applicant to pay back the credit. The applicant may, however, default on payments back to 
the institution. It is the task of the financial institution to make sure that the number of 
defaults is minimized so that risk is reduced. This is done by screening the applicants when 
they apply for credit. Scoring methods are used to estimate the credit worthiness of an 
applicant. These credit scoring methods estimate the probability that an applicant will 
default or become delinquent. Credit scoring methods use statistical methods based on 
historical credit data to build a model which predicts whether an applicant will default or 
not. The financial institution can then use the model to decide whether or not to grant 
credit to the applicant also considering how much risk the institution is willing to take on. 
As mentioned, building a credit scoring model requires the use of historical data. There 
may, however, be situations when there is limited historical data. This might occur when 
the financial institution is expanding into a new economic location (country) and no data is 
available at first. Data quantity issues might also occur when there is a change in the 
scoring procedure. In these situations it is difficult to build a good scoring model as there 
is initially not enough data available. Thus, expert information can be important. An 
existing reliable generic scoring model may be available at first which could be used for 
scoring. This generic scoring model could then be modified as new data becomes 
available. Institutions already using scorecards may be able to combine their expert 
knowledge with new sources of information to obtain improved scoring models. In order 
to do this, a Bayesian approach is proposed where the expert knowledge is combined with 
the limited amount of data. The aim is to see whether the combination of expert knowledge 
with data gives a better model than one that uses only the limited amount of data.

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The scope of Bayesian inference has greatly improved since it was discovered that Markov 
Chain Monte Carlo (MCMC) Methods could be used to sample from the posterior 
distributions. The general MCMC algorithm is called the Metropolis-Hastings (MH) 
algorithm.