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Is a credible interval the same as a confidence interval?
credible intervals incorporate problem-specific contextual information from the prior distribution whereas confidence intervals are based only on the data; credible intervals and confidence intervals treat nuisance parameters in radically different ways.
How do you find the binomial confidence interval?
Normal Approximation Method of the Binomial Confidence Interval
- where p = proportion of interest.
- n = sample size.
- α = desired confidence.
- z1- α/2 = “z value” for desired level of confidence.
- z1- α/2 = 1.96 for 95% confidence.
- z1- α/2 = 2.57 for 99% confidence.
- z1- α/2 = 3 for 99.73% confidence.
Is the binomial distribution an exact confidence interval?
The term “Exact Confidence Interval” is a bit of a misnomer. Neyman noted [4] that “exact probability statements are impossible in the case of the Binomial Distribution”. This stems from the fact that k, the number of successes in n trials, must be expressed as an integer.
What is the 95% credible interval in probability?
The 95% credible interval, (0.49, 0.92), means that the probability that is in the interval of (0.49, 0.92) is 0.95. Note the intuitive nature of this interpretation compared to the frequentist confidence interval.
What’s the difference between a confidence interval and a probability statement?
The confidence interval then is a statement about the likelihood that the interval we obtain actually has the true parameter value. Thus, the probability statement is about the interval (i.e., the chances that interval which has the true value or not) rather than about the location of the true parameter value.
How is the confidence interval based on quantiles?
Based on that property, the confidence interval is based on quantiles of that (posterior) distribution What does that mean, here, that we have a 95% credible interval. Well, this time, we do not draw using the empirical mean, but some possible probability, based on that posterior distribution (given the observations)