Available online
Description
This programme looks at the idea of probability as degree of belief and shows how Bayes' Theorem can incorporate the effect of experimental data on belief.
This programme looks at the idea of probability as degree of belief and shows how Bayes' Theorem can incorporate the effect of experimental data on belief.
| Module code and title: | M341, Fundamentals of statistical inference |
|---|---|
| Item code: | M341; 05 |
| First transmission date: | 21-07-1977 |
| Published: | 1977 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:30 |
| + Show more... | |
| Producer: | David Saunders |
| Contributors: | A. Daniel Lunn; Adrian Smith |
| Publisher: | BBC Open University |
| Keyword(s): | Bayes; Belief; Satistics; Subjective |
| Footage description: | Film shots of a geologist inspecting a landscape. Adrian Smith (V/O) introduces the programme. Adrian Smith, in the studio, outlines the problem from the viewpoint of the geologist. How does he decide, on belief alone, which of two types of rock, basalt or granite, the terrain is likely to be composed of. Smith demonstrates a devise called a 'spinner' which can be used to attach a probability number to his belief. He goes on to explain how experimental evidence can be gathered which might modify the geologist's view. Film shots of a helicopter doing an aerial survey of rock types using a magnetometer. Daniel Lunn, using graphic displays and an animation, explains how Bayes' Theorem combines the two ingredients of belief and experimental evidence. Adrian Smith applies Bayes' Theorem to the geology problem above. He sets up the notation and then does the calculation arriving at a probability figure for the rock being granite. Daniel Lunn, with an urn containing a number of red and white balls, introduces an example in which Bayes' Theorem' is used to model real situations with dichotomised populations where there are several hypotheses. To illustrate that there is no such thing as a single definitive prior distribution, Adrian Smith shows a histogram for two prior distributions which model the same case - one an individual who had no idea at all of the distribution of balls in the urn and another from one who had some clues. Lunn and Smith then apply the same experimental data to the two prior distributions. Animated histograms model the situation. Data is input for 10,20 and finally 100 trials. Daniel Lunn introduces an examination of the use of Bayes Theorem in a case with an infinite number of hypotheses. The example is concerned with measurements errors in scales used to weigh a potato. Shots of the scales and of an animated caption. Smith guesses at the weight of the potato. To arrive at a useful prior distribution for this weight, he uses a computer to work out a probability density curve. Results are shown on the VDU. Lunn applies the prior distribution data from the computer to Bayes' Theorem. A computer animation plots the likelihood curve and prior distribution for each set of scales used. Smith sums up the programme. |
| Master spool number: | 6HT/72422 |
| Production number: | 00525_4234 |
| Videofinder number: | 1116 |
| Available to public: | no |
