Question

How is probability theory applied in fraud detection?

Answer 1

Fraud that involves cell phones, insurance claims, tax return claims, credit card transactions etc. represent significant problems for governments and businesses, but yet detecting and preventing fraud is not a simple task. Fraud is an adaptive crime, so it needs special methods of intelligent data analysis to detect and prevent it. These methods exist in the areas of Knowledge Discovery in Databases (KDD), Data Mining, Machine Learning and Statistics.

Techniques used for fraud detection fall into two primary classes: statistical techniques and artificial intelligence:

• Data preprocessing techniques for detection, validation, error correction, and filling up of missing or incorrect data.
• Calculation of various statistical parameters such as averages, quantiles, performance metrics, probability distributions, and so on. For example, the averages may include average length of call, average number of calls per month and average delays in bill payment.
• Models and probability distributions of various business activities either in terms of various parameters or probability distributions.
• Computing user profiles.
• Time-series analysis of time-dependent data.
• Clustering and classification to find patterns and associations among groups of data.
• Matching algorithms to detect anomalies in the behavior of transactions or users as compared to previously known models and profiles. Techniques are also needed to eliminate false alarms, estimate risks, and predict future of current transactions or users.

• Data mining to classify, cluster, and segment the data and automatically find associations and rules in the data that may signify interesting patterns, including those related to fraud.
• Expert systems to encode expertise for detecting fraud in the form of rules.
• Pattern recognition to detect approximate classes, clusters, or patterns of suspicious behavior either automatically (unsupervised) or to match given inputs.
• Machine learning techniques to automatically identify characteristics of fraud.
• Neural networks that can learn suspicious patterns from samples and used later to detect them.

Other techniques such as link analysis, Bayesian networks, decision theory, and sequence matching are also used for fraud detection.

Benford Law:

It has been known for a long time that if an extensive collection of numerical data expressed in decimal form is classified according to first significant digit, without regard to position of decimal point, the nine resulting classes are not usually of equal size. Benford’s Law, also known as the first-digit law, has long been seen as a tantalizing and mysterious law of nature.Benford’s Law is likely useful when applied under several conditions. For instances, set of numbers that result from mathematical combination of numbers whereby the result come from two distributions e.g. account receivable.transaction-level data where sample is not needed e.g. disbursement, sales, expenses; on large database set, full year’s transactions will provide more accurate result; and for account that appear to conform which the mean of a set of number is greater than the median and the skewness is positive e.g. most set of accounting numbers.Digital analysis based on Benford’s Law is an audit technique that is applied to an entire population of transactional data.researchers have since used these digit patterns to detect data anomalies by testing either the first, first-two, or last-two digit patterns of reported statistics or transactional data. Auditors have long applied various forms of digital analysis when performing analytical procedures.Benford’s law as applied to auditing is simply a more complex form of digital analysis.Benford’s Law, one must start with measuring deviation. The deviation of the distribution of digits between what is observed and what is expected in many ways. One method is the “Chi Square” test, a standard statistical test for measuring the degree of similarity between elements in a table. Based upon this statistic, and the number of “degrees of freedom”, it is possible to assign a probability that any variation between actual and observed is due to chance alone. The higher the Chi Square, the less likely that any difference can be explained by chance alone.

Dempster-shafer theory:

In order to make analysis more accurate and effective we propose an approach based on the Dempster-Shafer theory, that allows for combining evidence from multiple and heterogeneous data sources and get to a degree of belief that takes into account all the available evidence. The proposed approach has been validated with the respect to a challenging demonstration case, namely the detection of frauds performed against a Mobile Money Transfer service.

The Dempster-Shafer (DS) theory of evidence has significant weaknesses when dealing with conflicting information sources, as demonstrated by preeminent mathematicians. This problem may invalidate its effectiveness when it is used to implement decision-making tools that monitor a great number of parameters and metrics. Indeed, in this case, very different estimations are likely to happen and can produce unfair and biased results. In order to solve these flaws, a number of amendments and extensions of the initial DS model have been proposed in literature. In this work, we present a Fraud Detection System that classifies transactions in a Mobile Money Transfer infrastructure by using the data fusion algorithms derived from these new models. We tested it in a simulated environment that closely mimics a real Mobile Money Transfer infrastructure .Results show substantial improvements of the performance in terms of true positive and false positive rates with respect to the classical DS theory.