With the global financial crisis, articles describing the role of mathematics in investment banking have suddenly filled the popular press.What these articles have generally not touched on is the role of mathematics, and especially statistics, in the personal banking sector.

This sector, also called the retail or consumer banking sector, is that concerned with individuals; with bank accounts, credit cards, car finance, mortgages, personal loans, debit cards, and so on.It is an area which has been revolutionised over recent decades, as dramatic advances in computer technology have completely changed its practice.

Subjective decision-making, perhaps following a face-to-face interview with a bank manager, has been replaced by the use of highly sophisticated statistical models of customer behaviour.

In particular, predictive models are universally used by all financial institutions, and also by organisations such as supermarkets, retailers, and other bodies with large numbers of customers.Classical models such as regression and logistic regression are widely used, but so also are more recent developments such as neural networks, and esoteric tools such as random forests, support vector machines, and multivariate adaptive regression splines.

These and other models are used to drive a wide range of decisions, from deciding to whom to grant a loan or give a credit card, choosing and adjusting credit card limits, detecting whether a transaction is intrinsically suspicious and likely to be fraudulent, identifying mortgage fraud rings, deciding when a customer might be interested in a further financial product so that there is a cross-selling opportunity, and so on.

An obvious characteristic of the sector is that it deals with large numbers – large numbers of customers, of accounts, of transactions, for example.This makes it a very rich ground for data mining – the science of using advanced statistical tools to detect relatively small but nonetheless valuable configurations in the data.Such patterns can form the basis for effective decision-making, to provide the best service for the customer to ensure they come back to the institution again and again.

Indeed, one of the founders of Capital One described the credit card sector as not so much a banking industry, as a data industry, and credit scoring has been described as the most successful commercial application of statistical methods in recent decades.

Overall, the vast data sets, and the scope for using cutting-edge statistical tools, make this a very intellectually stimulating areas for statisticians who want to work in a dynamic, rapidly changing area, where what they do has a real impact.

Professor David J. Hand is Professor of Statistics in the Department of Mathematics at Imperial CollegeLondon.