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Florian Hartig
Florian Hartig
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BruceET's answer is excellent but pretty long, so here's a quick practical summary:

  • if the prior is flat, likelihood and posterior have the same shape
  • the intervals, however, are not necessarily the same, because they are constructed in different ways. A standard Bayesian 90% CI covers the central 90% of the posterior. A frequentist CI is usually defined by a point-wise comparison (see BruceET's answer). For an unbounded location parameter (e.g. estimating the mean of a normal distribution), difference are usually small, but if you estimate a bounded parameter (e.g. binomial mean) close to the boundaries (0/1), differences can be substantial.
  • of course, the interpretation is different too, but I interpret the question mainly as "when will the values be the same?"

BruceET's answer is excellent but pretty long, so here's a quick practical summary:

  • if the prior is flat, likelihood and posterior have the same shape
  • the intervals, however, are not necessarily the same, because they are constructed in different ways. A standard Bayesian 90% CI covers the central 90% of the posterior. A frequentist CI is usually defined by a point-wise comparison (see BruceET's answer). For an unbounded location parameter (e.g. estimating the mean of a normal distribution), difference are usually small, but if you estimate a bounded parameter (e.g. binomial mean) close to the boundaries (0/1), differences can be substantial.

BruceET's answer is excellent but pretty long, so here's a quick practical summary:

  • if the prior is flat, likelihood and posterior have the same shape
  • the intervals, however, are not necessarily the same, because they are constructed in different ways. A standard Bayesian 90% CI covers the central 90% of the posterior. A frequentist CI is usually defined by a point-wise comparison (see BruceET's answer). For an unbounded location parameter (e.g. estimating the mean of a normal distribution), difference are usually small, but if you estimate a bounded parameter (e.g. binomial mean) close to the boundaries (0/1), differences can be substantial.
  • of course, the interpretation is different too, but I interpret the question mainly as "when will the values be the same?"
Source Link
Florian Hartig
Florian Hartig
  • 8.7k
  • 30
  • 52

BruceET's answer is excellent but pretty long, so here's a quick practical summary:

  • if the prior is flat, likelihood and posterior have the same shape
  • the intervals, however, are not necessarily the same, because they are constructed in different ways. A standard Bayesian 90% CI covers the central 90% of the posterior. A frequentist CI is usually defined by a point-wise comparison (see BruceET's answer). For an unbounded location parameter (e.g. estimating the mean of a normal distribution), difference are usually small, but if you estimate a bounded parameter (e.g. binomial mean) close to the boundaries (0/1), differences can be substantial.