Bayesian Logistic Regression Models for Credit Scoring by Gregg Webster

 Variable 
Mean 
SD 
2.50% 
97.50% 
(Intercept) 
-7.20E+00 
5.52E-02 -7.31E+00 -7.09E+00 
LOAN 
-2.23E-05 
2.90E-06 -2.81E-05 
-1.68E-05 
MORTDUE 
-3.86E-06 
6.77E-07 -5.27E-06 
-2.57E-06 
VALUE 
3.03E-06 
4.89E-07 2.10E-06 
4.03E-06 
REASONHomeImp 1.71E-01 
1.01E-01 -2.59E-02 
3.67E-01 
JOBOffice 
-7.14E-01 
1.48E-01 -1.00E+00 -4.22E-01 
JOBOther 
3.36E-02 
8.64E-02 -1.38E-01 
1.98E-01 
JOBProfExe 
1.51E-02 
1.27E-01 -2.19E-01 
2.77E-01 
JOBSales 
8.21E-01 
3.48E-01 1.12E-01 
1.48E+00 
JOBSelf 
3.11E-01 
3.00E-01 -3.24E-01 
8.70E-01 
YOJ 
-1.58E-02 
5.21E-03 -2.56E-02 
-4.65E-03 
DEROG 
7.36E-01 
7.20E-02 5.93E-01 
8.82E-01 
DELINQ 
8.35E-01 
5.01E-02 7.36E-01 
9.38E-01 
CLAGE 
-5.22E-03 
3.21E-04 -5.86E-03 
-4.62E-03 
NINQ 
1.46E-01 
2.35E-02 1.00E-01 
1.91E-01 
CLNO 
-2.80E-02 
2.57E-03 -3.32E-02 
-2.31E-02 
DEBTINC 
1.92E-01 
1.38E-03 1.89E-01 
1.94E-01 

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87 
still have the same interpretation and interpretations for the parameters of LOAN, DEROG 
and DEBTINC are: 
-
The parameter of LOAN is -2.23E-05 and is significant at the 5% significance level. The 
reason for this is that the 95% credibility interval does not contain zero. A unit increase in 
LOAN with all other variables held fixed, means that there will be 2.23E-05 decrease in 
the log-odds of default. 
-
The parameter of DEROG is 7.36E-01 and is significant at the 5% significance level since 
its credibility interval does not contain zero. A unit increase in DEROG with all other 
variables held fixed, means that there will be a 7.36E-01 increase in the log-odds of 
default.
-
The parameter of DEBTINC is 1.92E-01 and is significant at the 5% significance level 
because its credibility interval does not contain zero. A unit increase in DEBTINC with all 
other variables held fixed, means that there will be a 1.92E-01 increase in the log-odds of 
default.
Trace plots of the Markov chain and density plots of the posterior distributions are given in 
Figure 4.20. Trace and density plots are only given for the first four parameters. The 
remaining trace and density plots can be found in the Appendix D1.

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88 
Fig. 4.20
Trace and density plots of the posteriors for the first four variables using an 
informative prior.
From Figure 4.20, looking at the trace plot of the Markov chain, the Markov chain is 
relatively stationary. This implies that the Markov chain has reached or is close to its 
stationary distribution. A concern is that the Markov chain still appears to be quite strongly 
correlated. The density plots of the first four variables show an irregular bell shaped 
distribution. The remaining trace and density plots are similar (Appendix D1). 
The Geweke diagnostic statistics are now calculated for each variable and are given in 
Table 4.14.

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89