Uses of Bayesian Statistics

Bayesian statistics has a wide variety of possible uses, some of which are described below.

Spacecraft Pointing Errors

Satellites have complex systems to control their orientation – the direction the satellite is pointing in. This is one of the most crucial aspects of satellite control. A communications satellite, for example, must remain pointing towards the earth at all times, while the Herschel telescope must keep its field of view fixed during its entire observation period. The orientation of a satellite has many possible sources of error due to movement of the satellite and uncertainty in the sensor measurements. All these error sources, together with others such as payload thermal distortion and misalignment, contribute to the overall error in the spacecraft instruments. The European Space Agency (ESA) developed a rigorous set of statistical algorithms to capture individual sources of error and combine them to give overall performance. This approach is encapsulated in ESA’s Pointing Error Handbook, originally written by staff now at Tessella that can be used by companies developing spacecraft to construct detailed pointing error budgets. Central to the methodology is the use of Bayesian methods to update the probability distributions of the individual errors when new information is received, in order to make optimal use of available information. These probability distributions can then be recombined to obtain a new estimate of the distribution of the overall error.ESA also commissioned Tessella’s Analytic Pointing Performance software tool, which fully implements the Bayesian methodology from the Pointing Error Handbook to allow pointing performance to be calculated.

Kalman Filters

A Kalman filter is an example of a Bayesian estimator: an estimator or decision rule that calculates the optimal result based on the given criteria. A Kalman filter estimates the state of a dynamic system from a series of incomplete and noisy measurements. One example application is inertial tracking of people. Appropriate sensors are attached to a person and the data gathered is used to track their position as they move around, using a Kalman filter algorithm. At each time step the filter uses a model of the dynamics of the object or person to predict its current position and velocity. It then corrects this prediction, based on the current set of measurements. The estimate obtained by this method is the one that minimizes the mean squared error over all the properties being measured. The Kalman filter naturally takes into account the relative uncertainty of the measurements and the model, relying more on the measurements than the model if the measurements are believed to be more accurate. It also tracks the error in the estimates over time. Furthermore, often it can be set up to track and continually recalibrate sensor biases over time. There are also similar techniques such as the Extended Kalman Filter (for non-linear problems), the Unscented Kalman Filter and the Particle Filter. These techniques have been used in many different applications including radar tracking (see below), inertial navigation, spacecraft and aircraft attitude determination, and numerical weather forecasting.

Banking and Finance

Bayesian techniques have wide-ranging uses within the financial sector. Bayes' Theorem is commonly exploited within hedging and within asset and portfolio management. Banks and credit card companies also use Bayesian methods to determine whether or not to grant customers credit and to what limit. Bayes' Theorem is extremely effective within banking, where the objective is to assess risk and make forecasts, predictions and inferences based on this assessment. Risk assessment is inherently subjective and a central idea within Bayesian statistics is that of Subjective probability.

Security and Fraud Detection

Bayesian methods provide a method of detecting credit card fraud. The way in which a stolen credit card is used will be different to its normal use, but spending patterns can also change for legitimate reasons. Bayes' Theorem is crucial in assessing the likelihood of fraud given the spending patterns. Bayesian methods are used to find patterns of behavior, rather than individual anomalies that could lead to incorrect results. AT&T developed a similar system to detect telephone fraud. Again, patterns of behavior are sought, in this case calls to a previously uncalled country, calls of unusually long duration, etc. The system also considers the total financial loss being incurred by a possibly fraudulent series of calls.

Medical Diagnostics

In medicine, Bayes' Theorem has assisted in diagnosis – identifying a patient's ailments as a particular disorder – and in prognosis –forecasting the natural course of disease. It is also integral to some models being used to determine optimal treatments for various disorders for individual patients. In the early 1980s, researchers attempted to build a rule-based system for lymph-node-pathology diagnosis, but the system was not reliable enough to meet the needs of pathologists. They then built another system using simple Bayesian methods. The system uses inference models and details of previous cases to create a differential diagnosis of plausible diseases based on the patient’s symptoms. The user can also ask the system to identify the features that would be most useful for distinguishing between competing diagnoses, considering the costs and benefits of each observation or test. The assessments from this system were much more reliable than the rule-based method, and analyses took only one fifth of the time. The system was commercialized as Intellipath.

Spam Filtering

Bayesian systems are widely used in the continuing fight against spam, the unsolicited marketing and other junk email that deluges most email systems. Numerous Bayesian anti spam email filters have been developed. Many are open source and can be downloaded from the internet. They make use of a simple Bayesian component that “learns” how to recognize spam and differentiate it from non spam. This is achieved by training the software – telling it which of the emails you receive are acceptable, and which are spam. The software analyses the words in the message, and builds up a model of the indicators that a message might be spam. After training, the system can then accurately determine which messages is spam. When first introduced, these systems were capable of spotting 99% of all spam emails. Unfortunately, a combination of Bayesian and non-Bayesian methods is required for modern spam filters, since many anti-Bayesian spam generators have been developed in response to the Bayesian filters.

Other uses

Bayesian methods have been used in a diverse range of other software systems. The US Navy have developed real-time software for determining the performance of various ship self-defense weapon systems against varying types and ranges of incoming attack weapons. Traditional techniques to solve the problem had been unsuccessful, but an approach that involved the use of Bayesian Networks led to a solution that was both effective and efficient. NASA’s Mission Control Center in Houston use Bayesian Networks to interpret live telemetry and provide advice on the likelihood of failures of the space shuttle's propulsion systems. It also considers time criticality and recommends actions of the highest expected utility. Intel uses Bayesian Networks for diagnosis of faults in processor chips. Given end-of-line tests on semiconductor chips, a statistical process can be used to infer possible processing problems. Nokia Networks uses the Hugin Decision Engine, a commercial tool making use of Bayesian Networks, in a prototype tool for efficient diagnosis of problems with mobile networks. By having an automated tool that reads network performance data and from that estimates and monitors network problems ranked by probability, the network operator gets an efficient troubleshooting procedure saving both expensive expert resources and downtime of the network.