Example
The goal is to calculate the Bayesian average of the heights of various occupations of adult American men. In the larger population of adult American men, the average height is 176 cm. A value of C is chosen as 10. For the purpose of this example, the occupations used will be "Basketball Players", "Actors" and "Students". For the basketball players, a group of 15 individuals are identified with an average height of 191 cm among them. For the students, a group of 10 individuals is identified with an average height of 179 cm. For the actors, only James Cromwell is available, for an average height of 201 cm.
| Group | N | Group mean | Bayesian average |
|---|---|---|---|
| Basketball players | 15 | 191 cm | 185 cm |
| Students | 10 | 179 cm | 177.5 cm |
| Actors | 1 | 201 cm | 178 cm |
Here, the Bayesian average correctly reduces the effect of a single anomalously large value. If the sample sizes for basketball players were similarly small, the Bayesian average would have mis-estimated basketball players as being far closer to average.
Read more about this topic: Bayesian Average
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
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