Fiducial
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What does "fiducial" mean (in the context of statistics)?
The fiducial argument is to interpret likelihood as a probability. Edit: not exactly, see the answer of @Sextus for more details. Even if likelihood measures the plausibility of an event, it does not satisfy the axioms of probability measures (in particular there is no guarantee that it sums to 1), which is one of the reasons this concept was
Stats.stackexchange.comWhat is the fiducial argument and why has it not been accepted?
The fiducial argument has not been accepted because the idea doesn't work. The fiducial distribution is disguised as something that looks like a probability distribution (and people might have wanted it to behave like a probability distribution) but it is not the same as a probability distribution. It is only a function of probabilities.
Stats.stackexchange.comMultiple comparisons with p-value corrections of fiducial limits?
May 9, 2017 · I understand that if the fiducial limits are not overlapping for a pairwise comparison, they are different. However, how would one correct for multiple comparisons when there is more than one comparison? fct=LL2.3u(upper=1), type="binomial") This question is statistical data analysis and should be re-opened.
Stats.stackexchange.comUnderstanding the Behrens–Fisher problem - Cross Validated
This section of this article says: Ronald Fisher in 1935 introduced fiducial inference in order to apply it to this problem. He referred to an earlier paper by W. V. Behrens from 1929. Behrens and Fisher proposed to find the probability distribution of. T ≡ x¯1 − x¯2 s21/n1 +s22/n2− −−−−−−−−−−√ T ≡ x ¯ 1 − x
Stats.stackexchange.comparameterization - Parametrizing the Behrens–Fisher distributions
Behrens and Fisher's solution of the Behrens-Fisher problem involves the Behrens-Fisher distribution with $\theta$ depending on the observations because it is a pseudo-Bayesian (in fact, a fiducial) solution: this data-depending distribution is a posterior-like distribution of $\tau$ (with $\delta$ the only random part in the definition of $\tau$ because the data are fixed).
Stats.stackexchange.comRevisiting the Rule of Three - Cross Validated
Nov 22, 2020 · With no successes, the Wilson score interval is: CIp(1 − α) = [0, χ21, α n + χ21, α]. Taking α = 0.05 for a 95% confidence interval gives: CIp(0.95) = [0, 3.841459 n + 3.841459]. For large n this is fairly similar to the "rule of three" but it should be more accurate than this rule of thumb. As to showing that the rule has the required
Stats.stackexchange.cominference - Behrens–Fisher problem - Cross Validated
Jul 24, 2012 · Savage points to the gems of wisdom more than this one flaw. This problem was the one that exposed the difference between fiducial inference and the Neyman-Pearson hypothesis testing approach. Prior to that Fisher recognized philosophical differences but thought that the two methods gave the same answers.
Stats.stackexchange.comCompare 90th%iles of two samples (confidence interval, test)
Dec 17, 2023 · Interpret the fiducial distributions as probabilitiy distributions (this is an approximation, the fiducial distribution does not behave exactly like a probability distribution) and compute the probabilities for the joint probabilities of the two parameters/percentiles to be inside the 2-d bins/cells created by the grid.
Stats.stackexchange.comHow to compute confidence interval from a confidence distribution
Jan 4, 2015 · From a statistical model I obtained a fiducial distribution that it's also a confidence distribution. Saying, from a random variable X distributed as a Binomial, I obtained the fiducial distribution of the parameter p which is a Beta. And I know that this fiducial distribution is also a confidence distribution.
Stats.stackexchange.comregression - Using Fieller's theorem to calculate the confidence
Jun 24, 2015 · The problem of calculating confidence/likelihood intervals for the ratio of two means is addressed in Chapter 7 of the book Statistical Inference in Science, and in Chapter 10 of Empirical Bayes and Likelihood Inference.
Stats.stackexchange.com