How does one update a confidence interval using Bayes rule?
Say, for example, an experiment shows that the mean lies in [A, B] with 95% confidence. Later, a colleague says they ran a similar experiment and found that the mean lies in [C, D] with 95% confidence (or any other CI).
How does one "merge" the two data under Bayes?
Please help out with any misconceptions, I'm not a trained statistician.