Question

Define confidence belt and credible set. What is the confidence interval and credible probabilities?

Answer 1

A confidence belt is the lines on a probability plot or fitted line plot that depict the upper and lower confidence bounds for all points on a fitted line within the range of data. On a fitted line plot, the confidence interval for the mean response of a specified predictor value are the points on the confidence belt directly above and below the predictor value.

A credible interval is an interval in which an (unobserved) parameter has a given probability.

Suppose we are running an experiment on the distribution of birth weights of children born in a given town. If the subjective probability that the birthweight β is somewhere between 2.8 kgs and 3.5 is 90 %, we can say that 2.8 ≤ β ≤ 3.5 is a 90% credible interval.

If you find out that the 95% credible interval for your statistics final score is 70 to 90, this means you have a 95% chance of having a score between those two numbers.

A Confidence Interval is a range of values we are fairly sure our true value lies in.

A credible interval is an interval in which an (unobserved) parameter has a given probability and these probabilities are called credible probabilities.