Linked Questions

279
votes
9answers
152k views

What's the difference between a confidence interval and a credible interval?

Joris and Srikant's exchange here got me wondering (again) if my internal explanations for the difference between confidence intervals and credible intervals were the correct ones. How you would ...
270
votes
13answers
83k views

Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?

It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our ...
93
votes
12answers
15k views

What, precisely, is a confidence interval?

I know roughly and informally what a confidence interval is. However, I can't seem to wrap my head around one rather important detail: According to Wikipedia: A confidence interval does not ...
48
votes
14answers
6k views

Clarification on interpreting confidence intervals?

My current understanding of the notion "confidence interval with confidence level $1 - \alpha$" is that if we tried to calculate the confidence interval many times (each time with a fresh sample), it ...
58
votes
7answers
15k views

Examples of Bayesian and frequentist approach giving different answers

Note: I am aware of philosophical differences between Bayesian and frequentist statistics. For example "what is the probability that the coin on the table is heads" doesn't make sense in ...
36
votes
6answers
5k views

If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?

I'm very new to Bayesian statistics, and this may be a silly question. Nevertheless: Consider a credible interval with a prior that specifies a uniform distribution. For example, from 0 to 1, where 0 ...
24
votes
4answers
6k views

Weakly informative prior distributions for scale parameters

I have been using log normal distributions as prior distributions for scale parameters (for normal distributions, t distributions etc.) when I have a rough idea about what the scale should be, but ...
19
votes
4answers
2k views

What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level?

After reading the great answer for this question by @Ben, I am a bit confused by the part " set the relative tail sizes as a control variable, and then you find the formula for the length of the ...
14
votes
4answers
2k views

Is 95% specific to the confidence interval in any way?

I am aware of the misconception that a "95% confidence interval means there is a 95% chance that the true parameter falls in this range," and that the correct interpretation is that if you ...
15
votes
4answers
3k views

From a Bayesian probability perspective, why doesn't a 95% confidence interval contain the true parameter with 95% probability?

From the Wikipedia page on confidence intervals: ...if confidence intervals are constructed across many separate data analyses of repeated (and possibly different) experiments, the proportion of ...
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
5answers
391 views

why regularization is slower slope and not higher?

I am reading about regularization in Aurelien Geron's book. I do understand that given a model $\beta_0$+ $x$ $\beta_1$ , regularization means: If we allow the algorithm to modify $\beta_1$ but we ...
4
votes
3answers
7k 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
6k views

Explain confidence intervals in simple terms

For one newly handling statistical analysis, please can you explain in the simplest of terms, with an example, what is a confidence interval?
9
votes
1answer
963 views

Should I report credible intervals instead of confidence intervals?

After stumbling upon the concept in a statistics textbook, I tried to wrap my head about it, and finally came to a conclusion which seems to fit all the explanations which I have seen so far: A ...

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