Where do Confidence Bounds Come From

Abstract

Chris and Fred discuss where the ideas of ‘confidence bounds’ come from … and perhaps what they mean.

Key Points

Join Chris and Fred as they discuss how we come up with things we call ‘confidence bounds.’ What are they? … and how do they help?

Topics include:

• What are ‘confidence bounds’? Confidence bounds are usually explained as limits on what we believe some actual value is. A simple example might be when we judge a distance. For example, if you are standing in a field and see a tree, you might think to yourself that the tree might be 70 – 100 meters away. Your best guess might be around 85 meters, but the values 75 and 100 represent the ‘confidence bounds’ on this best guess because you know there is uncertainty involved.
• So how do we get ‘confidence bounds’? .. it starts with ‘likelihoods.’ Let’s say that you find a size 6.5 shoe in the street (adjusting for the difference in how manufacturers calculate their shoe sizes fore male and female shoes.) We also know that women’s feet tend to need shoes of sizes of 6.5 to 7.5. We also know that men’s feet tend to need shoes of sizes 9 to 10. Some women will randomly have large feet that can exceed sizes 10, 11, 12 and so on. And likewise, some men will randomly have small feet that are less than sizes 6.5, 6, 5.5 and so on. But that said, we know that the shoe with size 6.5 that we found is more likely to be worn by a woman. And that is the basis of everything!
• Gammas, Chi-squareds, Students-t … what are we talking about? Some really smart people have been able to take the concept of likelihood for things like the mean (times to failure) for random processes. And probability distributions have been developed to help us get confidence bounds based on how each thing fails. These probability distributions quantify the likelihood that potential mean (times to failure) values are ‘true.’ Which can be really helpful … sometimes.

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Show Notes

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