# Linked Questions

283 votes
16 answers
96k 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 ...
• 12.8k
296 votes
10 answers
170k 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 ...
• 5,637
103 votes
12 answers
17k 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 ...
• 7,445
49 votes
14 answers
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 ...
• 543
61 votes
11 answers
16k 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 ...
38 votes
6 answers
6k 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 ...
• 723
24 votes
4 answers
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 ...
• 4,112
21 votes
4 answers
3k 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 ...
• 393
14 votes
4 answers
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 ...
• 503
15 votes
4 answers
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 ...
• 6,472
11 votes
3 answers
7k 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 ...
• 211
7 votes
5 answers
600 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 ...
• 659
4 votes
3 answers
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
5 answers
372 views

### Basic Sampling - Provide confidence of estimate

I tried searching the site but nothing came up. I have a simple situation for a business problem - We have a population of 50 million files. We want to review a sample and see whether a file contains ...
4 votes
2 answers
7k 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?
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