## Statistical Science

- Statist. Sci.
- Volume 17, Issue 3 (2002), 235-255.

### Statistical Fraud Detection: A Review

Richard J. Bolton and David J. Hand

**Full-text: Open access**

#### Abstract

Fraud is increasing dramatically with the expansion of modern technology and the global superhighways of communication, resulting in the loss of billions of dollars worldwide each year. Although prevention technologies are the best way to reduce fraud, fraudsters are adaptive and, given time, will usually find ways to circumvent such measures. Methodologies for the detection of fraud are essential if we are to catch fraudsters once fraud prevention has failed. Statistics and machine learning provide effective technologies for fraud detection and have been applied successfully to detect activities such as money laundering, e-commerce credit card fraud, telecommunications fraud and computer intrusion, to name but a few. We describe the tools available for statistical fraud detection and the areas in which fraud detection technologies are most used.

#### Article information

**Source**

Statist. Sci. Volume 17, Issue 3 (2002), 235-255.

**Dates**

First available in Project Euclid: 16 January 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.ss/1042727940

**Digital Object Identifier**

doi:10.1214/ss/1042727940

**Mathematical Reviews number (MathSciNet)**

MR1963313

**Zentralblatt MATH identifier**

1013.62115

**Keywords**

Fraud detection fraud prevention statistics machine learning money laundering computer intrusion e-commerce credit cards telecommunications

#### Citation

Bolton, Richard J.; Hand, David J. Statistical Fraud Detection: A Review. Statist. Sci. 17 (2002), no. 3, 235--255. doi:10.1214/ss/1042727940. https://projecteuclid.org/euclid.ss/1042727940

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- patent (Gopinathan et al., 1998). (As of this writing, a patent search on key words "fraud detection" yields 80 patents.) In particular, their extensive list of variables, created to summarize past activity so that a neural network can be applied, illustrates the problem engineering necessary to transform the fraud detection problem into one that is amenable to standard modeling techniques. It would be useful to have a precise definition of a class (or of several classes) of fraud detection problems, which takes into account the variety of characteristics that make statistical fraud detection difficult. If such a characterization exists already in statistics, the machine learning and data mining communities would benefit from its introduction. Not knowing of one, Tom Fawcett and I attempted to define one class of "activity monitoring" problems and illustrate sev
- eral instances (Fawcett and Provost, 1999). Earlier we defined "superimposition fraud" (Fawcett and Provost, 1997a) to try to unify similar forms of wireless telephone fraud, calling card fraud, credit card fraud, certain computer intrusions and so on, where fraudulent usage is superimposed upon legitimate usage and for which similar solution methods may apply. However, neither of these captures all of the important characteristics. The characterization of such a class of problems is important for several reasons. First of all, different fraud detection problems are considerably similar-it is important to understand how well success of different techniques generalizes. Is the similarity superficial? Are there deeper characteristics of the problem or data that must be considered? [This seems to be the case, e.g., with classification problems (Perlich,
- Provost and Simonoff, 2001).] Also, to succeed at detecting fraud, different sorts of modeling techniques must be composed, for example, temporal patterns may become features for a sy stem for estimating class membership probabilities, and estimators of class membership probability could be used in temporal evidence gathering. Furthermore, sy stems using different solution methods should be on equal footing for comparison. Seeming success on any subproblem does not necessarily imply success on the greater problem. Finally, it would be beneficial to focus researchers from many disciplines, with many complementary techniques, on a common, very important set of problems. The juxtaposition of knowledge and ideas from multiple disciplines will benefit them all and will be facilitated by the precise formulation of a problem of common interest.Of course I am not arguing that research must address all of these criteria simultaneously (immediately), and I am not being strongly critical of prior work on fraud detection: we all must abstract away parts of such a complicated problem to make progress on others. Nevertheless, it is important that researchers take as an ultimate goal the solution to the full problem. We all should consider carefully whether partial solutions will or will not be extensible. Fraud detection is a real, important problem with many real, interesting subproblems. Bolton and Hand's review of the state of the art shows that there is a lot of room for useful research. However, the research community should make sure that work is progressing toward the solution to the larger problem, whether by the development of techniques that solve larger portions or by facilitating the composition of techniques in a principled manner.
- 2001). The class of problems is novel, even in machine learning. No one tool (neural nets, etc.) is instantly applicable to all of these problems. The algorithms have to be designed to fit the data. This means that an essential part of the venture is immersion in and exploration of the data. My experience is that good predictive algorithms do not appear by a selection, unguided by the data, from what algorithms are available. Furthermore, the process is one of successive informed revision. If an algorithm, for instance, has too high a false alarm rate, then one has to
- (Kelly, Hand and Adams, 1999). Still on a temporal theme, the adaptability of fraud detection tools to the changing behavior of fraudsters must be addressed so as to ensure the continued effectiveness of a fraud detection sy stem: as new detection strategies are introduced, so fraudsters will change their behavior accordingly. Models of behavior can help with this, although the indicators of fraud that are independent of a particular account may require a different strategy. We take Breiman's point that many of the methods we described were developed outside the narrow statistical community. However, we had not intended the word "statistical" to refer merely to the stochastic data model-based statistics of his recent article (Breiman,
- 2001). Rather, we had intended it in the sense of Chambers' "greater statistics" (Chambers, 1993), "every thing related to learning from data." Of course, the point that Breiman makes, that the tools we have described have not been developed by conventional statisticians, is something of an indictment of statisticians
- (Hand, 1998). We endorse Provost's conclusion about the importance of looking at the full problem. It is all too easy to abstract a component problem and then overrefine the solution to this, way bey ond a level which can be useful or relevant in the context of the overall problem. Conversely, it is all too easy to be misled to a focus on a peripheral or irrelevant aspect of the subproblem. Academic researchers have often been criticized for this in other contexts. Of course, the fact is that many of the
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Zentralblatt MATH: 1093.68088

Digital Object Identifier: doi:10.1162/153244304322972694

#### See also

- Includes: Foster Provost. Comment.
- Includes: Leo Breiman. Comment.
- Includes: Richard J. Bolton, David J. Hand. Rejoinder.

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