Questions tagged [fiducial]
An alternative to the frequentists and Bayesian principled arguments
16
questions
2
votes
1answer
27 views
Did Fisher consider a joint fiducial distribution for the Gaussian model?
Consider the Gaussian model $y_i \sim_{\text{iid}} \mathcal{N}(\mu,\sigma^2)$, $i = 1, \ldots, n$, with unknown mean $\mu$ and unknown standard deviation $\sigma$.
The random variable $t = \tfrac{\...
1
vote
0answers
53 views
Optimal decisions based on frequentist estimators
Consider a decision problem aimed at minimizing the expected loss1 where the argument is a parameter estimate. In a Bayesian setting, given a posterior distribution of the parameter and the loss ...
1
vote
1answer
33 views
Terminology in interval estimation
(1) Confidence intervals
(2) Posterior probability intervals
(3) Fiducial intervals
Is there some conventional term that encompasses these three sorts of intervals, but does not include prediction ...
6
votes
2answers
560 views
What is a generalized confidence interval?
Quoting Weerahandi, Generalized Confidence Intervals (1993):
Confidence interval (Property 1) --- Consider a particular situation of interval estimation of a parameter $\theta$. If the same ...
3
votes
2answers
99 views
Changing the size of a confidence interval in order to emphasize results
I've been asked to perform a statistical analysis at my work and report on the results. I'm using a 2-sided t-test comparing 2 groups where H0=0 and Ha≠0 at a significance level of .05. For my results ...
2
votes
0answers
155 views
Coverage probability from fiducial/confidence distribution
I am trying to realize how to compute confidence intervals from a fiducial distribution/confidence distribution with possibly more than one parameter. But for now I would just like to understand if I ...
11
votes
2answers
406 views
Fisher for dummies?
Short version: is there an introduction to Ronald Fisher's writings (papers and books) on statistics that is aimed at those with little or no background in statistics? I'm thinking of something like ...
24
votes
2answers
2k views
What does “fiducial” mean (in the context of statistics)?
When I Google for
"fisher" "fiducial"
...I sure get a lot of hits, but all the ones I've followed are utterly beyond my comprehension.
All these hits do seem to ...
3
votes
1answer
106 views
What principled arguments are made with data?
Consider the frequentist argument: "I will believe A since not-A makes the data improbable".
Consider the Bayesian argument: "I will believe A since given my beliefs on A and the data generating ...
-1
votes
1answer
350 views
Probability distribution of $\sigma$ [closed]
Suppose $n = 5$, $s = 0.0771$.
The question is: what's the $P(\sigma < 7.63\%)$?
5
votes
2answers
116 views
Fiducial distribution and sequential monte-carlo algorithm
I have spent a little time reading "Generalized fiducial inference for normal mixed models" by Cisewski and Hannig. First of all I am interested in understanding how to simulate the fiducial ...
8
votes
1answer
1k views
Understanding the Behrens–Fisher problem
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 ...
9
votes
1answer
246 views
Parametrizing the Behrens–Fisher distributions
"On the Behrens–Fisher Problem: A Review" by Seock-Ho Kim and Allen S. Cohen
Journal of Educational and Behavioral Statistics, volume 23, number 4, Winter, 1998, pages 356–377
I'm looking at this ...
33
votes
4answers
4k views
What is the fiducial argument and why has it not been accepted?
One of the late contributions of R.A. Fisher was fiducial intervals and fiducial principled arguments. This approach however is nowhere near as popular as frequentist or Bayesian principled arguments. ...
5
votes
1answer
173 views
Fiducial Inference in Machine Learning
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 ...
279
votes
9answers
152k views
What's the difference between a confidence interval and a credible interval?
Joris and Srikant's exchange here got me wondering (again) if my internal explanations for the difference between confidence intervals and credible intervals were the correct ones. How you would ...
