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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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### 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 ...
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### 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. ...
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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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### 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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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....