William Kaye Estes is one among the founders of mathematical psychology and a leading statistical learning theorist. Estes demonstrated the comparison of experimental observations of behavior with computer simulation model. His work of mathematical psychology reflects theoretical matters relating to perception, choice, learning, memory and categorization. A major concern about the theorist is creation of clear understanding and application of statistical methods in psychology.
One major consideration in mathematical psychology is the application of Markov process in real life situations. Markov process arises in statistics and probability. It is a random process whereby expected or future behavior cannot be predicted by considering past behavior (FABBS Foundation, n d). Some applications of Markov analysis in real life situation is in the case of traffic flow, business behavior or progress of an epidemic. A real life situation reflected in Markov analysis is traffic flow which is a major problem in many parts of the world especially developing cities.
Markov process as is applied in traffic flow clearly describes probalistic behavior of traffic queues in many urban centers. This is applied properly in areas that are closely seen especially in an intersection considering spatial extension. Markov process is applied in traffic flow in estimation of travel times that is vehicles arrivals and departure or traffic volumes through applications of origin destinations. Detecting devices record the arrival and departure time of vehicles, airplanes or trains.
Vehicle concentration at various road segments is a clear indication of a posterior distribution which provides a clear estimate of traffic flow (FABBS Foundation, n d). Estimation of origin destinations is difficult but application of simulation model easily finds traffic counts at intersections. Application of Markov process therefore simulates transportation network which reflects the actual traffic counts. Reference FABBS Foundation. William Kaye Estes. Retrieved on 22nd July 2010 from, http://www. fabbs. org/Estes_Honor. html