Linked Questions

3
votes
2answers
437 views

Different Confidence vs. Credible Interval (Continuous case, noninformative prior) [duplicate]

Okay, so, credible intervals aren't the same as confidence intervals. We all know that. In fact, they're only guaranteed to be the same when they're about a location or a scale parametre with a ...
3
votes
0answers
109 views

Bayesian vs. Frequentist inference [duplicate]

I have a $X_1$,$X_2$,...,$X_n$ sequence of binary random interchangeable variables. Given $\theta$*=$\theta$, $X_1$,$X_2$,...,$X_n$ $\thicksim$ iid Ber($\theta$) With a prior distribution $\pi$($\...
1
vote
0answers
45 views

Are credible intervals confidence regions? [duplicate]

I understand that I'm asking a very pedantic question, but as far as I'm aware a confidence region is a multi-dimensional generalization of a confidence interval and therefore as a credible interval ...
84
votes
7answers
10k views

Are there any examples where Bayesian credible intervals are obviously inferior to frequentist confidence intervals

A recent question on the difference between confidence and credible intervals led me to start re-reading Edwin Jaynes' article on that topic: Jaynes, E. T., 1976. `Confidence Intervals vs Bayesian ...
47
votes
6answers
7k views

Bayesian statistics tutorial

I am trying to get upto speed in Bayesian Statistics. I have a little bit of stats background (STAT 101) but not too much - I think I can understand prior, posterior, and likelihood :D. I don't want ...
38
votes
6answers
3k views

What is the connection between credible regions and Bayesian hypothesis tests?

In frequentist statistics, there is a close connection between confidence intervals and tests. Using inference about $\mu$ in the $\rm N(\mu,\sigma^2)$ distribution as an example, the $1-\alpha$ ...
31
votes
5answers
5k views

What do confidence intervals say about precision (if anything)?

Morey et al (2015) argue that confidence intervals are misleading and there are multiple bias related to understanding of them. Among others, they describe the precision fallacy as following: The ...
11
votes
2answers
37k views

How are margins of error related to confidence Intervals?

Can somebody tell me the difference between margins of error and confidence intervals? On the Internet I see these two meanings getting used interchangeably. Is it right to say, "Confidence ...
12
votes
2answers
1k views

Does a confidence interval actually provide a measure of the uncertainty of a parameter estimate?

I was reading a blog post by the statistician William Briggs, and the following claim interested me to say the least. What do you make of it? What is a confidence interval? It is an equation, of ...
12
votes
3answers
10k views

Can you explain why statistical tie is not naively rejected when $p_1-p_2 < 2 \,\text {MOE}$?

I need help explaining, and citing basic statistics texts, papers or other references, why it is generally incorrect to use the margin of error (MOE) statistic reported in polling to naively declare a ...
9
votes
3answers
4k views

Bayesian AB testing

I am running an AB Test on a page that receives only 5k visits per month. It would take too long to reach traffic levels necessary to measure a +-1% difference between the test and control. I have ...
11
votes
3answers
6k views

What does a confidence interval (vs. a credible interval) actually express? [duplicate]

Possible Duplicate: What, precisely, is a confidence interval? Yes, similar questions have been asked before, but many of the answers seem contradictory and don't address my issue. (Or my ...
7
votes
1answer
2k views

Taking into account the uncertainty of p when estimating the mean of a binomial distribution

I have a binomial distribution with parameters $N$ and $p$, and the estimate for the mean of my distribution is N$\times p$. The values of $N$ and $p$ are such that we can use the Gaussian ...
4
votes
3answers
6k views

Hypothesis testing for a correlation that is zero or negative

I would like to test for a correlation that is zero or negative using the following hypothesis test: $H_0: p>0$ (Null hypothesis: the correlation is positive) $H_A: p\le0$ (Alternative hypothesis: ...
4
votes
2answers
4k views

Probability that multiple confidence intervals contain the true population mean

Suppose you take 3 samples and report a 99% confidence interval for each dataset. How would you go about calculating the probability that all the datasets contain the true population mean? No other ...

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