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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
- 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
- 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 )
- What exactly does the term inverse probability mean?
Yes indeed: only a Bayesian probability is truly technically a probability No indeed: a fiducial distribution is not equal to a probability(*) But fiducial and frequentist inference are still just as well about inverting the direction and making statements about parameters given the observation
- 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? $\endgroup$ –
- How to derive the standard error of linear regression coefficient
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- maximum likelihood - Differences between Sampler, MonteCarlo . . .
6) Fisher formalism is very useful for estimation of the standard deviation compared to the fiducial values but we need to know these fiducial values before and second point, we have to assume that posterior distribution is always Gaussian, haven't we ? (or that likelihood is Gaussian, I don't remember if someone could indicate this
- What do confidence intervals say about precision (if anything)?
He says this: "It is sometimes asserted that the fiducial method generally leads to the same results as the method of [CIs] It is difficult to understand how this can be so, since it has been firmly laid down that the method of confidence intervals does not lead to probability statements about the parameters of the real world, whereas the
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