Bayesian Logistic Regression Models for Credit Scoring by Gregg Webster

4.6.2 Cut-off probability of 0.48 
 
For a comparison, if a cut-off probability was chosen to minimize the total error rate on the 
validation set, the cut-off probability is 0.48. Using this cut-off probability would mean 
more risk for the financial institution. When 0.48 is used as a cut-off the following results 
are obtained.
Logistic regression model
Table 4.21 
Classification table of logistic regression model with cut-off probability of 
0.48. 
Predicted 
Good 
Bad 
Actual 
Good 
1215 
107 
Bad 
137 
203 

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96 
Of the 1,662 applicants in the test set, the logistic regression model (Model 1) now rejects 
310 and accepts 1,352 applicants (Table 4.21). 107 (34.5%) or the rejected applicants are 
in fact good. 137 (10.1%) of the accepted applicants are bad. The overall classification 
error rate is 14.7%.
Bayesian logistic regression model with informative prior 
Table 4.22
Classification table of Bayesian logistic regression model with informative 
prior and cut-off probability of 0.48.
Predicted 
Good 
Bad 
Actual 
Good 
1267 
55 
Bad 
152 
188 
Of the 1,662 applicants in the test set, the Bayesian logistic regression model with 
informative prior (Model 2) now rejects 243 and accepts 1,419 applicants (Table 4.22). 55 
(22.6%) of the rejected applicants are in fact good. 152 (10.7%) of the accepted applicants 
are bad. The overall classification error rate is 12.5%.
Bayesian logistic regression model with a non-informative prior
Table 4.23
Classification table of the Bayesian logistic regression model with non-
informative prior and cut-off probability of 0.48.