Linked Questions

307 votes
16 answers
113k 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 ...
Mike Lawrence's user avatar
102 votes
9 answers
15k 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 ...
Dikran Marsupial's user avatar
37 votes
3 answers
6k views

I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x?

Suppose the 95% confidence interval for $\ln(x)$ is $[l,u]$. Is it true that the 95% CI for $x$ is simply $[e^l, e^u]$? I have the intuition the answer is yes, because $\ln$ is a continuous function. ...
Tamay's user avatar
  • 505
12 votes
7 answers
2k views

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. ...
Ken T's user avatar
  • 485
12 votes
2 answers
4k views

Can we reject a null hypothesis with confidence intervals produced via sampling rather than the null hypothesis?

I have been taught that we can produce a parameter estimate in the form of a confidence interval after sampling from a population. For example, 95% confidence intervals, with no violated assumptions, ...
Nikli's user avatar
  • 321
8 votes
3 answers
2k views

Why are confidence intervals of hazard ratios not symmetric?

My understanding is that the confidence interval for a hazard ratio should be symmetrical about the mean (the distance between the lower limit and the mean is the same as the distance between the mean ...
James Moore's user avatar
4 votes
4 answers
10k views

Continuous approximation to binomial distribution

Consider an integer variable $k$ that follows a binomial distribution, $$\binom{N}{k}p^{k}\left(1-p\right)^{N-k}$$ with total draws $N$ and probability of success $p$. I am interested in the ...
a06e's user avatar
  • 4,440
12 votes
1 answer
1k views

The basic logic of constructing a confidence interval

Consider a model with a parameter of interest, $\theta$, and its point estimator, $\hat\theta$. For simplicity, assume $\hat\theta\sim N(\theta,\sigma^2/n)$ (in numerous instances this could be ...
Richard Hardy's user avatar
3 votes
2 answers
804 views

Differences between a frequentist and a Bayesian density prediction

What are some essential differences between a frequentist density forecast/prediction and a Bayesian posterior for an outcome of a random variable? Of course, there will be differences in how they ...
Richard Hardy's user avatar
4 votes
2 answers
1k views

What is "likelihood-based LDA" and "likelihood-based QDA", how do they relate to LDA and QDA, and how they are implemented in R?

I am currently studying discriminant analysis. I have encountered the phrases "likelihood-based LDA" (with some prior) and "likelihood-based QDA" (with some prior). I know what LDA ...
The Pointer's user avatar
  • 2,086
2 votes
1 answer
278 views

Expressing one-sided p values of directional hypothesis tests as Bayes factors

Assume we want to test the directional hypothesis that $µ<0$. From a frequentist angle we use a one-tailed $t$-test and imagine we obtain a 1-sided $p$ value of say 0.07, which then would imply ...
Tom Wenseleers's user avatar
1 vote
1 answer
173 views

Practical consequences of wrong interpretation of confidence intervals

Can you give me a simple (but preferably common) example (or R/Python simulation) of what are practical consequences of wrong interpretation of frequentist confidence intervals? Especially when they ...
3 votes
1 answer
91 views

If Likelihood is not a PDF then why is the PDF of Multivariate Normal equivalent to the likelihood of I.I.D. Normals?

I am understanding why likelihoods are not PDFs using links such as What is the reason that a likelihood function is not a pdf. However I am getting more confused. For instance, the likelihood of I.I....
user1176663's user avatar
5 votes
2 answers
69 views

Priors in a bayesian model? Equivalent GLMM

I have this mixed effects logistic regression model. All the predictors are categorical (I need to maintain also age categorical, not as a continuous variable). The predictors are codified with ...
Katherine's user avatar
  • 165
1 vote
0 answers
138 views

Why is a frequentist confidence interval equivalent to a credible interval with flat priors?

It's a commonly quoted result that frequentist confidence intervals are equivalent to a bayesian credible interval assuming a flat prior. Ignoring for now questions about invariance under ...
Albert Hsiung's user avatar