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This programme looks at a traffic flow problem in order to illustrate the statistical technique of point estimation by using the 'method of maximum likelihood'.
Module code and title: M341, Fundamentals of statistical inference M341; 04 16-06-1977 1977 00:24:00 + Show more... David Saunders Stewart Gartside; A. Daniel Lunn BBC Open University Estimate; Inference; Likelihood; Statistics; T-junction; Traffic Film shots of traffic flow at a T-junction. Stewart Gartside uses a scale model of a T-junction and moving cars to outline the problem to be solved by statistics: to determine if a simple T-junction is adequate for the traffic involved. Gartside, still with the model, explains how data is collected for this problem. He then shows a histogram which has plotted on it data obtained from such an experiment. Gartside goes on to explain why a probability model is needed to solve a problem like this. He proposes a negative exponential model. A computer animation builds up a negative exponential curve. The original histogram above is plotted over this curve and the fit is compared. Gartside, using the scale traffic model, the histogram and the negative exponential curve as visual aids, explains why it is necessary to shift the distribution slightly to allow for the existence of a non-zero minimum inter-vehicle time. Gartside integrates the P.D.F. as a first step towards finding the probability of a time interval from 5 seconds to infinity. Daniel Lunn introduces the concept of likelihood and explains what he means by it. He demonstrates with a likelihood function for a single observation. The mathematics are captioned. With Gartside giving five observed readings of time intervals between cars, Lunn goes on to make the problem more realistic. A computer animation plots the likelihood function for different parametric values of the distribution. Lunn points out the area of maximum likelihood. Lunn explains a method of obtaining maximum likelihood without use of graphs. He differentiates the likelihood function to arrive at the maximum likelihood. Lunn goes on to discuss a method for determining how good the estimate of maximum likelihood is. He uses a graph plotter to plot the estimator. Lunn and Gartside briefly discuss reasons for using the method above on the mean of the data rather than keeping information on individual inter-vehicle times. Gartside then goes on to use the method of maximum likelihood to directly establish the time gap probability. In doing so he illustrates the invariance principle. Credits (over film shots of a policeman directing traffic). 6HT/72487 00525_4233 1115 no