bayesian networks as a decision support tool in credit scoring … · 2015. 7. 28. · bayesian...

Bayesian Networks 1

Chapter 1

Bayesian Networks as aDecision Support Tool

in Credit Scoring DomainWitold Abramowicz, Marek Nowak and Joanna Sztykiel

The Poznan University of Economics

Copyright © 2003, Idea Group Publishing.

ABSTRACTThe main purpose of this article is to discuss applicability of Bayesian belief

networks (bbn) within the procedures of working capital credit scoring, conductedin commercial banks. A brief description of Bayesian formulation of causaldependence and its strength is given. Inferential and diagnostic features of bbn areillustrated using sample structure. As an example we present and compare resultsof estimating a credit risk using two techniques: traditional credit-scoring system andbbn structure.

INTRODUCTIONThe history of the credit scoring ideas started in the early 40’s, but the

prosperity of the scoring techniques widespread in the 50’s, when William Fair andEarl Isaac set up Fair, Isaac and Company in San Francisco (Janc & Kraska,2001). The first credit scoring system was called numerical scoring system.Credit scoring in a bank is a supportive procedure of granting individual and/orbusiness credits.

In the system, the rules of gathering information are formalized, so they givethe basis for credit approval. This information is substantial for assessment of risk

2 Abramowicz, Nowak and Sztykiel

level of a credit. Risk management reduces risk of granted credits, minimizes thenumber of irregular credits and consequently reduces the costs of capital reserves.Thus, quality of the system directly influences return of assets of the bank.

The quality measures of the system are:• reliability of evaluation of economic and financial position of a customer,• correctness of risk estimation assigned to a specific class of economic and

financial position

Taking bank security into consideration, it is recommended to take rigorousmeasures in the crediting strategy. However, following them too strictly, canunnecessarily limit accessibility to credits, degrade market share and influenceprofitability of the bank.

Apart from the risk reduction, the quality of service is very important as well.Quality level can be measured using the following criteria:• credit accessibility• time required by a bank to process a single credit application• credit cost

From the point of view of the bank, the additional criterion is consistence ofrisk classification - for customers of similar profiles, the decisions should beconsistent, when comparing different agencies of the same bank.

The tool that improves quality of service and minimizes risk of credit cansubstantially increase competitiveness of the bank.

Solutions presented in this article can be applied to working-capital credits forenterprises that are obliged to perform all standard financial statements such as:• balance sheet• income statement• cash-flow

CREDIT SCORING SYSTEMOne of the important functions realized by credit scoring system is information

processing. Every information processing system includes:• input information,• module of processing information,• output information.

In the case of credit scoring system input information consists of :• registry information,• financial information (financial statements),

Bayesian Networks 3

• benchmarking information,• inner information of the bank on creditability of the customer

The outcome of the processing information is a symbol of credit risk classrelevant to the level of risk of the transaction.

The information on the risk level can be helpful in such decision problems as:• granting or denying a credit,• defining terms of credit,• scope and frequency of monitoring a customer’s financial position

As the scope of input information is defined, the credibility of the outcomeresults, and costs of the processing (e.g. time, involved resources) are closelyrelated to the processing technique.

In this article, we present two techniques of information processing in thecredit-scoring system:• traditional credit-scoring method (chapter 4)• using Bayesian belief network (chapter 6)

INTRODUCTION TO BAYESIAN NETWORKSBayesian networks are classified as graphical, decision-analytical models.

Their most remarkable feature is the capability to encode both quantitative andqualitative knowledge. This means, we can rely in this model on statistical dataanalysis and experience of domain experts as well. Sometimes referred to as causalnetworks, Bayesian models are constructed as graph models, where nodes areused to encode parameter characteristics (descriptive variables), and directionallinks between them encode often complex correlations, usually of causal nature.

The network, as a whole, embodies the structure of problem domain, whilelocal interactions between parameters are quantified in the form of conditionalprobability tables. This representation of modeled phenomenon is in concert withintuitive approach to its description, which, as is believed, is basis of the reasoningof human experts. At the same time, Bayesian models are founded on robuststatistical methods, despite the fact they are formulated using non-frequentistdefinition of probability.

Practical applications of Bayesian networks derive from their analytical anddiagnostic capabilities. The constructed model gives us a state-of-knowledgeencodement of modeled phenomenon. Information gathered during observation ofreal phenomenon, gives us values of at least, some of model parameters – whichwhen stated unambiguously, become facts in the system. In the structure ofBayesian network this means initialization of the state of nodes to one of possible,


predefined values. Propagation of probabilities in network perturbed this way,leads to new equilibrium state, where newly calculated and usually changedprobability distributions reflect the fact that new information has been gained.Inspection of new probability distributions makes inference regarding non-observ-able variables possible.

It should be mentioned that number of observed facts could be different,depending on the rate of change of the phenomenon/process, costs of acquiringinformation or number of variables that cannot be observed directly for differentreasons (as the example we can bring the prognostic model where some variablesare naturally known post factum).

The Bayesian model reveals in the last case one of its strongest advantages –capability for doing inference, when noisy or incomplete data are available.

The propagation of probabilities in Bayesian networks can be of highcomputational complexity. At the end of the 80’s, a significant breakthrough inpropagation algorithms was made. Nevertheless, in extreme cases of densenetworks or specific topologies, the problem remains NP-hard. Approximatemethods of propagation and algorithms tailored to specific structures become ofresearch interests to overcome problem of intractability.

As an elementary toy-problem we describe the following situation:A bank classifies customers into two categories A and B,In group A account debiting occurs with 0.2 probability, P(D|A)=0.20,In group B account debiting occurs with 0.05 probability, P(D|B)=0.05,15% of all customers belong to group A

Question : randomly chosen account appears to be debited, what is theprobability of its belonging to group A customer?

The problem can be easily solved using Bayes theorem

)()()()()()(

)()()|()(

notAPnotADPAPADPAPADP

DPAPADPDAP

+==

Therefore, we can expect to find solution using Bayesian networks as well. Infact, two-node network <Customer Category> linked to <Debit> node models theproblem fully.

Table 1: Probability table P(<Customer Category>)

Customer CategoryA B

0.15 0.85

Source: the authorss’ own research.

Bayesian Networks 5

Table 2 : Probability table P(<Customer Category >|<Debit>)

DebitCustomer Category yes no

A 0.2 0.8B 0.05 0.95

Source: the authors’ own research.

The network that encodes knowledge of debit statistics in hypothetical bankis given in Figure 1.

Substituting actual value of debiting probability i.e. P(Debit=Yes)=1, afterpropagation procedure and reaching equilibrium state of the network, we come toconclusion that given debiting, the probability of being member of category Acustomer is 0.414. The solution has been obtained using Andersen propagationalgorithm (Andersen, 1989).

Figure 1 : Simple debit model – uninitialized network

Figure 2 : Initialized network after propagation procedure.


The given example shows diagnostic function of Bayesian model. The networkhas been used to perform diagnosis of possible causes on the basis of discoveredeffects. In situation of reverse state of knowledge, we would be able to infer oneffects given states of possible, although not necessarily all, causes.

THE SCOPE OF THE ECONOMIC-FINANCIALANALYSIS OF AN ENTERPRISE

Typical process of granting credit covers stages as following:The system presented in this paper is conceived to be helpul in the third stage

of the process. This stage of preparing information for credit decision is the longestand most expensive part of credit granting process. Striving for consistency of thecriteria in all agencies of bank, involves definition of precise rules and using the sameprocessing techniques.

Necessary conditions for granting working-capital credit:1

• current credit capacity of a customer,• the estimated credit risk of the transaction has to be below the admissible level• customer is able to furnish collateral appropriately

Current credit capacity of a customer means his ability to repay the credit andinterests in time. The ground to estimate the ability is the economic-financial analysisof his current position.

To estimate credit risk of the transaction one needs the information on:the class of the economic-financial position (result of the analysis),previous credit performance2

Table 3 : Stages of credit granting process

No Stage Result Performer1 initial acceptance of

the credit application application acceptance credit inspector2 estimation of legality authentication (or lack of) credit inspector

of the enterpreneur the information and docu-ments within an application

3 making analysis:- creditability- credit risk level data for the credit decision credit inspector

4 deciding on the credit terms of credit authorized person

Source: the authors, based on scoring methodology (one of 10 biggest Polishbanks acc. to “Gazeta Bankowa”).

Bayesian Networks 7

The result of the estimation defines credit risk level.The key problem for credit decision is defining the class of economic-financial

position of a customer.It was not our aim to create a model for estimating the position, but

presentation, and to some extent comparing the effectiveness of two techniques,using the same model. We use a model of estimation whosescope is in accordancewith typical systems that are in use in many Polish banks.

To define the position of an enterprise we use a number of characteristics(factors), which characterize both, the financial position of an enterprise and itsbusiness surroundings. Some of them are quantitative characteristics, others arequalitative. All are grouped in nine areas of the analysis (Table 4).

credit risc class

market positionprofitability

objectivesestimation

previous credit performance

economic-financial positionclass

subjectivesestimation

activity

indebtness

ROS

ROA

ROE

financial liquiditycurrent ratio

quick ratio

average collectionperiod

inventoryturnover

total assetturnover

debt ratio

constant capital /fixed assets

backing creditrepayment

sales

product

market competition

customers / suppliers

relability ofentrepreneur

managementcompetence

creditability

previous relationswith the Bank

characteristics of thebranchbranch

technology

Figure 3 : The model of credit risk estimationSource: the authors, based on scoring methodology ( one of 10 biggest Polishbanks, acc. to “Gazeta Bankowa”).


Quantitative characteristics use only financial data to calculate standardfinancial ratios (ROS, current ratio, etc). That part of the analysis is calledestimation of objective factors.

Qualitative characteristics present causal relations, which we cannot simplyqualify, at least so far. They can be estimated only in a subjective way, and are calledsubjective factors.

The structure of the characteristics in the model is hierarchic, which makessynthetic estimation of every area possible.

Multi-criteria estimation model makes it possible to regard different aspectsof business activity, and makes analysis wider.

The most significant parameters of the system are weights fixed for differentattributes3 and characteristics. Weights correspond with the influence on credit risklevel. Generally, traditional scoring systems use statistical techniques for calculatingweights (Janc et al., 2001).

BUILDING A CREDIT-SCORING SYSTEMEstimating credit risk level in credit-scoring system is based on scoring factors

covered by model. Scores are defined according to normative point scales. Asnormative can be considered (Sierpi, 1998):• average results in a chosen branch,• model values,• previous results of the enterprise.

Added characteristic scores make the synthetic estimation of the area. All theconsidered areas‘ estimations make the total score that defines the economic –financial position class.

Table 4 : Areas of enterprise analysis

Quantitative factors Qualitative factors1 profitability market position of the firm2 financial liquidity management competence3 activity reliability of an enterpreneur4 indebtedness character of the industry5 - previous credit performance


Bayesian Networks 9

Building a Traditional Scoring SystemThe building scoring system process can be split into several stages:

1. defining aims and assumptions of the system4,2. collecting data of through-the-door population5

3. analyzing data and defining a model (set of characteristics and their attributes),4. constructing scoring tables,5. verification of tables.

More information on aspects of building scoring system can be found inliterature (Janc et al., 2001). Scoring tables we present below are in use in one ofthe biggest Polish banks. The normatives are changed periodically.

Table 5 : The scoring table for the „profitability” area (normative point scale)Profitability

very good good medium weak bad

criteria current value

Pt current value

Pt current value

Pt current value

Pt current value

Pt

1 ROS ROS > 2S 7 2S>ROS>1S 5 1S>ROS>0,5S 3 0,5S>ROS>0 2 ROS < 0 0

2 ROA ROA > 2A 5 2A>ROA>1A 4 1A>ROA>0,5A 3 0,5A>ROA>0 2 ROA < 0 0

3 ROE ROE > 2E 5 2E>ROE>1E 4 1E>ROE>0,5E 3 0,5E>ROE>0 2 ROE < 0 0

Source: the authors, based on scoring methodology (one of 10 biggest Polish banks acc. to “GazetaBankowa”).a) ratios ROS, ROA, ROE – based on financial statements data,b) for a new enterprise, calculations are based on forecast results and assumptions of business plan,c) normative values of S, A, E are fixed by Headquarters of the Bank.

Financial liquidity very good good medium weak bad


Pt current value

Pt current value

Pt current value

Pt current value

Pt

1 current ratio (CR)

x 7 x 5 x 3 x 2 x 0

2 quick ratio (QR)

x 7 x 5 x 3 x 2 x 0

Activity very good good medium weak bad


Pt current value

Pt current value

Pt current value

Pt current value

Pt

1 avg. collection period

x 4 x 3 x 2 x 1 x 0

2 inventory turnover

x 4 x 3 x 2 x 1 x 0

3 total assets turnover

x 4 x 3 x 2 x 1 x 0

Table 6 : The scoring tables for the rest of objective factors areas


Indebtedness very good good medium weak bad


Pt current value

Pt current value

Pt current value

Pt current value

Pt

1 debt ratio x 7 x 5 x 3 x 2 x 0 2 constant capital/

fixed assets x 5 x 4 x 3 x 1 x 0

3 backing credit repayment1

x 5 x 4 x 2 x 1 x 0

1

Reliability of the enterpreneur high good weak bad

criteria Pt Pt Pt Pt 1 reliability of an entrepreneur 4 3 1 0

2 previous relations with the Bank

4 3 1 0

Market position of an enterprise high good weak bad

criteria Pt Pt Pt Pt 1 sale possibilities 4 3 1 0

2 mark of product 4 3 1 0 3 competition 3 2 1 0 4 customers / suppliers 2 1 1 0

Characteristics of the industry (branch) high good weak bad

criteria Pt Pt Pt Pt 1 progress level 3 2 1 0

2 technology 3 2 1 0 Management competence

high good weak bad criteria Pt Pt Pt Pt 1 experience and competence 5 3 2 0

Table 7 : Subjective factors, scoring tables

Table 6 : The scoring tables for the rest of objective factors areas (continued)

Bayesian Networks 11

It is stated that current credit capacity of an enterprise is fulfilled underfollowing conditions:a) economic – financial position class - A-1, B-2, or C-3,b) score of both objective and subjective factors are not less than their minima:

35 and 15 points respectively.

Credit risk class in relation to economic – financialposition class

Table 9 : The score corresponding to the class of the economic-financialposition and the previous credit performance.

credit risk class previous credit performanceeconomic-financial 1 - 3 3 - 6

position class regular months monthsA-1 I II IIIB-2 I II IIIC-3 II III IIID-4 III III IVE-5 III IV IV

Source: the authors, based on scoring methodology ( one of 10 biggest Polishbanks acc. to “Gazeta Bankowa”).

Economic – financial position class in relation to totalscore

Table 8 : The score corresponding to the class of the economic-financialposition

economic-financial position class scoreA-1 90 - 100B-2 74 - 89C-3 57 - 73D-4 40 - 56E-5 below 40



The Example of the Estimation of Current Credit Capacityand Credit Risk Class Using Traditional Credit-ScoringMethod.

Estimation of the economic-financial position

The enterprise XXX The branch YYY A qualitative factors area / characteristic value of the

factors score

I profitability 12 1 return on sales [ROS] 0,69% 5 2 return on assets [ROA] 0,51% 3 3 return on equity [ROE] 0,80% 4 II financial liquidity 14 1 current ratio 2,2 7 2 quick ratio 1,2 7

III activity 8 1 avg. collection period 28 3 2 inventory turnover 39 3 3 total assets turnover 1,3 2

IV indebtedness 16 1 debt ratio 0,2 7 2 constant capital/ fixed assets 2 5 3 backing credit repayment 1,4 4 B quantitative factors area / characteristic score I reliability 6 1 reliability of the enterpreneur 3 2 previous relations with the Bank 3 II market position of an enterprise 10 1 sale level 4 2 mark of product 3 3 competition 2 4 customers / suppliers 1

III character of the industry (branch) 5 1 progress level 2 2 technology 3

IV management competence 2 1 experience and competence 2

Table 10 : Example - the score corresponding to factors


Total score

Table 11 : The score corresponding to qualitative and quantitative factors

minimum1 total score for quantitative factors 50 352 total score of qualitative factors 23 15

73

Economic-financial class C-3minimum score

1 quantitative factors yes2 qualitative factors yes

Conclusions:1. The enterprise has current credit capacity,2. The enterprise isn’t indebted in the Bank, so far.

Credit risk of the transaction is Class II.

Credit risk Class II:1. Credit is allowed but on condition of collateral beyond the Customer’s assets.2. Ceiling rate of interests for working-capital credits.3. Intensive monitoring of the Customer’s position is recommended.4. Analysis of the financial statements - repeated quarterly.

CREDIT SCORING SYSTEM – THE BAYESIANNETWORK IMPLEMENTATION

The Bayesian model is a result of formal encoding of the domain expertknowledge, the factors influencing the phenomenon and their mutual interactions.Economic model being the objective of this paper has been created outside thesystem. Its aim is to analyze the standing of the enterprise from the point of view ofits creditworthiness.

At first the primary goal is defining descriptive parameters of the model – thenodes of Bayesian network. At this stage, the domain expert has a crucial work todo. The topology of network and its detailed nature is then specified. Unspecifiedparameters, lacking or misdirected connections between nodes result in inconsis-tencies of model, ambiguity of causal relationships and finally in inaccuracy ofexpertise.

The process of network structure generation, given nodes, can be boostedusing dedicated computer programs. Statistical dependencies between model


parameters support the expert to eliminate redundant inter-node connections,preventing from non-convergence of propagation algorithms due to overloadedstructure. Iterative generation process typically leads to computationally tractablestructure.

The next step, quantitative specification of model, requires filling-up condi-tional probability tables. The computer aided, statistical analysis of historical datacan reveal strength of causal dependencies between nodes. During all proceduresthe domain expert can moderate generation process.

The aim of the economic model we work with in this article is to analyzestanding of an enterprise from crediting banks’ perspective. We defined nine groupsof factors (i.e. scope of analysis) used to classify customers according to credit risk-level.

It should be pointedout that directions of links between nodes are consistentwith discovered, causal relationships. Figure 5 shows synthetic nodes only. Inreality the network is builtup with some dozens of nodes setting up hierarchicalstructure. Due to its complexity we show only part of the structure related to“Creditability of enterpreneur” and “Management quality”

Figure 4 : Bayesian network model of credit-risk analysis.



The network shown on Figure.6 has not been initialized, i.e. no data are putinto the system, yet. Probability distributions come from statistical analyses ofhistorical records or/and domain expert estimations.

Tables of probability distributions are equivalents of “normative scoringtables”, and in both systems value range and discretisation of random variables areidentical.

When deterministic dependencies between nodes were declared in Bayesiansystem (we use for this purpose square-shaped 0/1 probability distributions) we gotclassification strictly identical with that obtained in scoring tables methodology. Asan example, ROI evaluation given in section 5 is revisited and results are presentedin Figure 6.

Finally, synthetic credit-risk evaluation referring to the example given in section5 is presented in Figure 7

Figure 5 : The detail of Bayesian network relating to “Creditability ofenterpreneur” and “Management quality”

Source: the authors, based on scoring methodology (one of 10 biggest Polishbanks, acc. to “Gazeta Bankowa”).


Figure 7: Evaluation of synthesized credit-risk level based on financial andeconomic analysis of an enterprise.



Figure 6 : Evaluation of economic-financial condition of the enterprise -“profitability” section.


Figure 8: The sub-network that models influence of subjective factors oncredit-risk evaluation.


Table.12. Conditional probability distributions in “Quality of management”node

Quality of managementeducation experience strategy of development high good poor badgood high defined 1 0 0 0good high none 0,2 0,3 0,3 0,2good small defined 0,7 0,15 0,1 0,05good small none 0 0,15 0,15 0,7poor high defined 0,75 0,15 0,1 0poor high none 0,05 0,1 0,15 0,7poor small defined 0,3 0,45 0,15 0,1poor small none 0 0 0 1

Source: the authors’ own research, fictitious data.

Qualitative subjective factors are modeled with Bayesian network (structureshown on Figure 8). It can be seen that the network is initialized using factualinformation regarding “Subjective” node.

After propagation procedure, the network reaches equilibrium state. Then, thereadout of probability distributions delivers diagnostic statements about probablecause of subjectively good condition of the enterprise. As it was already stated, thequality of diagnoses is determined by correctness of network structure andconditional probability tables. Table 12 shows an example of tabularized probabil-


ity distribution, referring to “Quality of management” statistically dependent on“Education”, “Experience/” and “Strategy of development”. All these factors arepresent in structure shown on Figure .9. “Quality of Management” can be found(with different probability) in one of the states: “high”, “good”, “poor”, “bad” and,for instance, “Strategy” in: “defined” or “none”.

The presented Bayesian network has the property of making coherentinferences and diagnosing, also when only incomplete information is available. Itsnatural feature is being susceptible to iterative refinement, made by supplyingupdated distribution tables, new connections or nodes. Acting in the world, wheregreat repositories of historical data are still growing, and become easily accessibleto the banks, we believe that it is feasible to build robust system that gives statisticallysound expertise, and not confined to bare tabular procedures. Other, than quitepopular neural networks, Bayesian networks supply explanations to given diag-noses or prognoses.

Their outcomes are not so vastly conditioned by size and completeness ofdatasets, as in the case of neural networks.

On the other hand symbolical methods of information processing, (althoughof long tradition and sharing 85% of applications market) are bad performers, whennoisy information is input to the system. Rule-based knowledge representations arehardly modifiable; searching through rulebase is computationally intensive and timedemanding.

For instance, rulebase with 2000 records is considered to be huge.

CONCLUSIONSComparison of the presented methods of information processing in credit

scoring system – cost analysis.When evaluating credit application, a credit inspector follows four procedural

steps:1. input of data, supplied by applying customer2. evaluation of objective and subjective factors3. scoring - based on worksheet tables4. verification of calculations

The documents are furthermore passed to an authority that, after the secondverification of submitted materials, is eligible to refuse or grant a credit.

The system proposed in this article significantly reduces the time of inputtingthe data to application form sheet.

Evaluation of subjective factors is a tedious and time-consuming task. Thisevaluation can be however decomposed, into elementary objective choices,


although it leads to significant increase of the number of factors to be considered.Again, the time of the analysis is unfavorably impacted. Bayesian networks are freefrom this drawback – time of the analysis is negligible when compared with scoring-table method.

REFERENCESAlfred Janc, Marcin Kraska : Credit scoring- nowoczesna metoda oceny zdolnosci

kredytowej. Warszawa BMiB 2001Jan Czekaj, Zbigniew Dresler,. Zarzdzanie finansami przedsiebiorstw. Warszawa

PWN, 1999Tadesse Heile, Ocena ryzyka kredytowego na podstawie wybranych polskich i

zachodnich banków. w: Finanse i bankowosc a wej[cie Polski do UE, SGH,W-wa-PuBtusk, 1999 pp.79-88.

Tadesse Heile, Monitoring kredytowy jako instrument ryzyka kredytowego. w:Bankowosc w okresie przemian systemowych, Zeszyty Naukowe AE, P-D,p. 262.

Marek J. Druzdzel, Tsai-Ching Lu and Tze-Yun Leong. Interactive construction ofdecision models based on causal mechanisms. In Working notes of the AAAI1998 Spring Symposium on Interactive and Mixed-Initiative Decision-Theoretic Systems, pages 38-44, Stanford, CA, March 23-25, 1998

Maria SierpiDska: Ocena przedsiebiorstwa wedBug standardów swiatowych.Warszawa PWN, 1998

Table : 12 The factors considered in Bayesian network structure of creditscoring system

Bayesian network Scoring-table method1 Imprecise information is accepted by Exclusively deterministic evaluation of

the use of random variable distributions factors possible2 Incomplete data are accepted Incomplete set of input data is

prohibitive for further analysis3 Both backward and forward reasoning Diagnosing possible causes of an effect

possible – diagnosing in Bayesian is not possiblenetworks reveals „weaknesses” of anapplicant and can suggest areas ofin-depth analyses

4 The model can be verified using No empirical verification possiblereal-world data



Sumit Sarkar, Ram S. Sriram, Shibu Joykutty. Belief Networks for Expert SystemDevelopment in Auditing. „Intelligent systems in accounting, finance andmanagement”. 1996 Vol.5,147-163.

Finn V. Jensen. An Introduction to Bayesian Networks. London: UCL Press,1996.

S. Andersen. Hugin – A Shell For Building Bayesian Belief Universes For ExpertSystems. „Proceedings of 11th International Joint Conference”. 1989, pp.1080-1085..

Judea Pearl. Fusion , Propagation, and Structuring in Belief Networks. „ArtificialIntelligence” 1986 (29) pp.241-288.

ENDNOTES1 none of that conditions is a satisfactory condition2 as far as a new consumer is concerned (with no established credit at the bank),

the position of the enterprise stays the only criteria3 attributes mean possible states of a characteristic4 e.g. what is the difference between good and bad customer5 Alfred Janc, Marcin Kraska, 2001 : Credit scoring. p. 436 backing of credit repayment = (cash flow+interests)/(instalments+interests) –

forecast

bayesian networks as a decision support tool in credit scoring … · 2015. 7. 28. · bayesian...

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