Encyclopedia of Computer Science and Technology

Bell, C. Gordon 41has changed. There are now two fewer face cards (12 - 2 = 10)and four fewer non-face cards (40 - 4 = 36), so the probabilitythat a given card is a face card becomes 10/36 or 5/18.While this is pretty straightforward, in many situationsone cannot easily calculate the shifting probabilities. WhatBayes discovered was a more general formula:P(T|E) =P(E|T) * P(T)P(E)In this formula T is a theory or hypothesis about afuture event. E represents a new piece of evidence thattends to support or oppose the hypothesis. P(T) is an estimateof the probability that T is true, before considering theevidence represented by E. The question then becomes: IfE is true, what happens to the estimate of the probabilitythat T is true? This is called a conditional probability, representedby the left side of the equation, P(T|E), which isread “the probability of T, given E.” The right side of Bayes’sequation considers the reverse probability—that E will betrue if T turns out to be true. This is represented by P(E|T),multiplied by the prior probability of T and divided by theindependent probability of E.Practical ApplicationsIn the real world one generally has imperfect knowledgeabout the future, and probabilities are seldom as clear cutas those available to the card counter at the blackjack table.However, Bayes’s formula makes it possible to continuallyadjust or “tune” estimates based upon the accumulatingevidence. One of the most common applications of Bayesiananalysis is in e-mail filters (see spam). Bayesian spamfilters work by having the user identify a sample of messagesas either spam or not spam. The filter then looks forpatterns in the spam and non-spam messages and calculatesprobabilities that a future message containing thosepatterns will be spam. The filter then blocks future messagesthat are (above some specified threshold) probablyspam. While it is not perfect and does require work on thepart of the user, this technique has been quite effective inblocking spam.A Bayesian algorithm’s effectiveness can be expressed interms of its rate of false positives (in the spam example, thiswould be the percentage of messages that have been mistakenlyclassified as spam). If the rate of “true positives” istoo low, the algorithm is not effective enough. However, ifthe rate of false positives is too high, the negative effects(blocking wanted e-mail) might outweigh the positiveones (blocking unwanted spam).Further ReadingKantor, Andrew. “Bayesian Spam Filters Use Math that WorksLike Magic.” USA Today online, September 17, 2004. Availableonline. URL: http://www.usatoday.com/tech/columnist/andrewkantor/2004-09-17-kantor_x.htm. Accessed March15, 2007.Lee, Peter M. Bayesian Statistics: An Introduction. 3rd ed. NewYork: Wiley, 2004.Sivia, D. S. Data Analysis: A Bayesian Tutorial. 2nd ed. New York:Oxford University Press, 2006.“Thomas Bayes, 1702–1761.” St. Andrews University Mac Tutor.Available online. URL: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Bayes.html. Accessed March 15, 2007.BBS See bulletin board system.Bell, C. Gordon(1934– )AmericanEngineer, Computer DesignerChester Gordon Bell (also known as Gordon Bennet Bell)was born August 19, 1934, in Kirksville, Missouri. As ayoung boy Bell worked in his father’s electrical contractingbusiness, learning to repair appliances and wire circuits.This work led naturally to an interest in electronics, andBell studied electrical engineering at MIT, earning a B.S. in1956 and an M.S. in 1957. After graduation and a year spentas a Fulbright Scholar in Australia, Bell worked in the MITSpeech Computation Laboratory (see speech recognitionand synthesis). In 1960 he was invited to join the DigitalEquipment Corporation (DEC) by founders Ken Olsen andHarlan Anderson.Bell was a key architect of DEC’s revolutionary PDPseries (see minicomputer), particularly as designer of theinput/output (I/O) hardware in the PDP-1 and the multitaskingPDP-6. Bell left DEC to teach computer science atCarnegie Mellon University (1966–72), but then returned toDEC until his retirement in 1983 following a heart attack.During this time Bell developed a deployment plan for thenew VAX series minicomputers, which were data-processingworkhorses in many organizations during the 1970sand 1980s.As a close observer of the computer industry, Bell formulated“Bell’s Law of Computer Classes” in 1972. It basicallystates that as new technologies (such as the microprocessor)emerge, they result about once a decade in the emergenceof new “classes” or computing platforms, each beinggenerally cheaper and being perceived as a distinct productwith new applications. Within a given class, price tends tohold constant while performance increases. Examples thusfar include mainframes, minicomputers, personal computersand workstations, networks, cluster or grid computing,and today’s ubiquitously connected wireless, portabledevices. Bell has indeed suggested that the trend to ubiquitouscomputing will continue (see ubiquitous computingand wearable computers).After retirement Bell soon became active again. Hefounded Encore Computer, a company that specialized inmultiprocessor computers, and later was a founding memberof Ardent Computer as well as participating in the establishmentof the Microelectronics and Computer TechnologyCorporation, a consortium that attempted to be America’sanswer to a surging competitive threat from Japanese companies.Bell was also active in debates over technology policy,playing an instrumental role as an assistant directorin the National Science Foundation’s computing initiatives