Linked Questions
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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 ...
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310
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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 ...
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110
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12
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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 ...
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51
votes
14
answers
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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 ...
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65
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11
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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 ...
41
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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 ...
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11
votes
7
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Are “Data are fixed” in Bayesian viewpoint and “Data are random” in frequentist viewpoint talking about the same thing mathematically?
In my opinion, in BOTH Bayesian and Frequentist inferences, observational data $x$ are modelled as the observed value of a random variable $X$ which follows a certain probability distribution. ...
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25
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4
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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 ...
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24
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4
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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 ...
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13
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11
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When is it important for a practitioner to understand CIs?
I have a physician friend who asks me questions about stats. He gets confused about stuff, e.g., the definition of a confidence interval (CI) and its intricacies. For example, he finds the following ...
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4
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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 ...
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12
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Do the 2.5th and 97.5th percentile of the theoretical sampling distribution of a statistic always contain the true population parameter?
I am trying to understand the validity of bootstrap percentile confidence intervals and I have stumbled on the following from these slides:
Suppose we want to set a 95% confidence interval on $θ$, ...
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16
votes
4
answers
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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 ...
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8
votes
5
answers
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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 ...
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3
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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 ...
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