Talk:Statistical inference

message: Please merge the pages 'statistical inference' and 'Inferential statistics' , but be aware that the page on statistical inference has more concice information than the other page. 
Thanks for making this article. I've been wanting it for a long time. It has a bearing on environmental issues, because the case for a global warming catastrophe or ozone depletion is entirely based on statistics. User:Ed Poor
:(William M. Connolley 21:49, 6 Nov 2003 (UTC)
replies: text: Why is that an objection to the proposed merger?  No one's proposing getting rid of this information---just incorporating some of it into that other article, and maybe putting some of it somewhere else. Michael Hardy 22:55, 4 October 2006 (UTC)
thread_title: Merge?

message: A randomization test uses the randomization described in the experimental protocol and implemented, and is not assumed. Similarly, in sampling, the random sampling scheme defines a distribution of the sample statistic.
In contrast, in nonparametric statistics, a permutation test plays with the data regardless of its origins. If a supposed distribution is nice but otherwise nonparametric, then permutation tests characterize best tests (Lehmann's TSH; c.f. Paul Rosenbaum's book on observational studies). Unfortunately, observational data are not i.i.d. but d.d.d., dependent and differently distributed (Freedman, Statistical models), so the relevance of permutation tests on observational data depends on implausible assumptions.  
McPastry repeatedly has removed the description of randomization procedures for randomized data (data from randomized experiments or random samples) and substituted permutation tests for "data sets". I have asked McPastry repeatedly to stop such editing. Kiefer.Wolfowitz (talk) 09:14, 2 March 2010 (UTC)
thread_title:  Randomized data versus playing with data sets  

message: I thank the other editors for recent improvements, which try to preserve the truth of others' (particularly my) statements (while trying to correct errors).Kiefer.Wolfowitz (talk) 14:50, 3 March 2010 (UTC)
thread_title:  Progress 

message: I did look at Wikipedia articles on scientific theories, often by scientists with path-breaking work in other areas, that are widely dismissed by other scientists. The term for theories like fiducial probability is fringe science. I apologize for bringing up the example of flat-earth theories, which seems to have provided less stimulation to science than has fiducial inference, whose influences on Barnard etc. were noted on Wikipedia in this article. Kiefer.Wolfowitz (talk) 23:40, 4 March 2010 (UTC)
thread_title:  [[Fiducial inference]] and [[fringe science]] 

message: I removed the following unscourced statements:
:Barnard's work has inspired further work by D. A. Fraser, P. Dawid, Per Martin-Löf and Steffan Lauritsen on sufficient statistics and statistical models. In the case of "structural" influence, there seem to be few applications outside of group-transformation families and one-parameter exponential families. Work by Barnard and Harold Jeffreys has also influenced approaches to "objective" Bayesian inference by George E. P. Box and E. T. Jaynes. Box used "locally" objective priors; Jaynes proposed maximum entropy prior distributions. Many of these approaches are related to harmonic analysis, in particular to the theory of representations of semigroups.
Thanks. Kiefer.Wolfowitz (talk) 21:07, 11 June 2010 (UTC)
replies: text: Was that the tagged synthesis? If not it should be pointed out, if so the flag removed. 72.228.189.184 (talk) 19:13, 24 May 2012 (UTC)
replies: text: The synthesis tag is dated March 2012, later than  11 June 2010. The synthesis relates (throughout the article) to various opinions being expressed for which there are no sources given (which should be given, otherwise it is OR) in relation to a number of published works, for which citations are given, but this is done in such a way as it looks as if the citations back-up the opinions. What is needed are some published summaries of the whole field (or wide subfields) of statistical inference (and its development) that can be used as sources for statements about importance, development, relevance, etc..  The tag was originally placed because of a more blatant synthesis which has been removed & replaced by something presumably better, but overall the problem seems to remain, possibly at a lower level. Melcombe (talk) 19:59, 24 May 2012 (UTC)
thread_title:  Barnard's influence 

message: The following may be original research, so (according to wp:nor) I don't include it in the article, but I have found it useful and enlightening.
An unknown number may be estimated by an order of magnitude, which is the mean value of the probability distribution, and an uncertainty, which is the standard deviation of the distribution. 
If the uncertainty is zero then the result is certain.
Deduction is estimating a part from the whole.
Induction is estimating the whole from a part.
Prediction is estimating from one part to another.
The following J expressions apply.
       deduce =: %~`*/"2@(,:(%:@*-.))@(+/@[%~1,,:)
       predict=: (deduce~-@>:)~
       induce =: (,:0:)+[predict(-+/)~
Example. Based on a test the pupils in a school class are classified into categories. 
       a =: 20 5 0 NB. There are 20 pupils in category A, 5 in category B, and 0 in category C.
The first line of the following answers contains the orders of magnitude, and the second line contains the uncertainties. 
       a deduce 0  NB. certain deduction when the sample is empty
 0 0 0
 0 0 0
       a deduce 25 NB. certain deduction when the sample is the whole population
 20 5 0
  0 0 0
       25 0 0 deduce 10 NB. certain deduction when all pupils are in the same category
 10 0 0
  0 0 0
       a deduce 10 NB. uncertain deduction in the general case
 8 2 0
 1 1 0
       a induce 1000 NB. How are the 1000 pupils in the whole school distributed?
 751.25 213.929 34.8214
 79.516 75.3499 34.0783
       a predict 25 NB. How are 25 pupils in another class distributed?
   18.75 5.35714 0.892857
 2.92691 2.77356  1.25439
Prediction is generally somewhat uncertain. 
       a predict 0 NB. trivially certain prediction
 0 0 0
 0 0 0
       0 0 0 predict 3 NB. uncertain prediction
 1 1 1
 1 1 1
       0 1 predict 3 NB. more information gives better predictions
 1 2
 1 1 
       0 0 0 996  predict 4 NB. plenty of information gives good predictions
     0.004     0.004     0.004    3.988
 0.0633086 0.0633086 0.0633086 0.109544
The deduce program is the well known formula for mean value and standard deviation of the multivariate hypergeometric distribution. The possibly original research is the observation that the prediction formula follows from the deduction formula by increasing by one and changing sign.
       a
 20 5 0
       -(1+a)
 _21 _6 _1
       (-(1+a))deduce 25 NB. this is how prediction works. Amazing!
   18.75 5.35714 0.892857
 2.92691 2.77356  1.25439
Bo Jacoby (talk) 10:41, 18 December 2012 (UTC)
thread_title:  [[deductive reasoning|deduction]] and [[statistical inference|induction]] and [[prediction]]