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- What does fiducial mean (in the context of statistics)?
In the view of fiducial inference, $\lambda$ is also a random variable but it does not have a prior distribution, just a fiducial distribution that depends only on $(x_1, \ldots, x_n)$ To follow up on the example above, the fiducial distribution is $\lambda^n e^{-\lambda(x_1+\ldots+x_n)}$ This is the same as the likelihood, except that it is
- Understanding the Behrens–Fisher problem - Cross Validated
Although the fiducial argument is generally considered to be Fisher's only big flaw and has been discredited, the approach is not totally dead and there has been new research in it in recent years I think that fiducial inference was Fisher's way to try to be an "objective Bayesian"
- Multiple comparisons with p-value corrections of fiducial limits?
LD50 values have uncertainties, so how does one say they are (statistically) different without a test? We originally discussed differences based on non-overlapping fiducial limits, but a reviewer requested formal testing with correction for multiple comparisons How'd you address this request? Suggested papers to cite? $\endgroup$ –
- Whats the difference between a confidence interval and a credible . . .
Fisher extended the strategy of conditioning on the ancillary statistic to a general theory called Fiducial Inference (also called his greatest failure, cf Zabell, Stat Sci 1992), but it didn't become popular due to lack of generality and flexibility Fisher was trying to find a way different from both the classical statistics (of Neyman
- Doing maximum p-value estimation instead of maximum likelihood
$\begingroup$ This isn't exactly what you're asking, but you may be interested in reading about "Fiducial Inference" (This really answers the question "How can we turn a p-value into a confidence interval" rather than your question "How can we turn a p-value into a point estimate", but it may still be of interest) $\endgroup$
- Compare 90th percentiles of two samples (confidence interval, test)
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
- Revisiting the Rule of Three - Cross Validated
It is an adaptation from an image in the answer to the question 'The basic logic of constructing a confidence interval', which is itself an adaptation of "The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial C J Clopper and E S Pearson Biometrika Vol 26, No 4 (Dec , 1934), pp 404-413"
- Fiducial Inference in Machine Learning - Cross Validated
I was looking at the Fiducial Inference page on wikipedia, which is an alternative to the traditional Frequentist and Bayesian standpoints Although it was out of favour in mainstream statistics for many years, there seems to have been a resurgence in interest in recent years (see for example Jan Hannig's recent publications on the subject )
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