Talk:Principle of indifference

message: "Evidently we require not mere absence of knowledge of reasons favoring one alternative over another, but knowledge of the absence of such reasons."
W C Kneale, Probability and Induction (1949)
I like this quote. Do you? Boris Tsirelson (talk) 18:16, 2 May 2009 (UTC)
thread_title:  I like this quote 

message: It appears this article is misclassified (Philosophy... ). "The Principle of Indifference" is key to the study of Bayesian Probability. Given that there has been no substantial discussion or revision of this article in several years (2006 or so), I suggest the article be restarted in the appropriate classification.Dennis Lindley has written definitively on the subject and I'll be looking in his direction to restart it elsewhere (Bayesian, Probability, ...).
I was looking to refresh my memory when I found this article and have now bitten off more than I intended. 
Jmiche (talk) 08:55, 5 November 2009 (UTC)
replies: text: I think it's fair to consider it a philosophy of probability (or science) matter, but also to consider it a probability or statistics matter. Given that, according to the article, its earliest recognizable formulation was by logicians, and the restatement by an economist, it isn't misclassified as much as it is used by multiple areas of study. JJL (talk) 15:09, 5 November 2009 (UTC)
thread_title:  Misclassified 

message: The "solution" to the box example using the principle of transformation groups is horrendous.  I'm removing it until I or someone gets a chance to re-write it.  Here's the text:
:To apply this to the above box example, we have three problems, with no reason to think one problem is "our problem" more than any other - we are indifferent between each.  If we have no reason to favour one over the other, then our prior probabilities must be related by the rule for changing variables in continuous distributions.  Let L be the length, and V be the volume.  Then we must have
:
::f(L)=|{\partial V \over \partial L}|f(V)=3 L^{2} f(L^{3})
:
:Which has a general solution: f(L) = {K \over L} Where K is an arbitrary constant, determined by the range of L, in this case equal to:
:
::K^{-1}=\int_{3}^{5}{dL \over L} = log({5 \over 3})
:
:To put this "to the test", we ask for the probability that the length is less than 4.  This has probability of:
:
::Pr(L<4)=\int_{3}^{4}{dL \over L log({5 \over 3})}= {log({4 \over 3}) \over log({5 \over 3})} \approx 0.56.
:
:For the volume, this should be equal to the probability that the volume is less than 43 = 64.  The pdf of the volume is 
:
::f(V^) {1 \over 3} V^{-{2 \over 3}}={1 \over 3 V log({5 \over 3})}.  
:
:And then probability of volume less than 64 is
:
::Pr(V<64)=\int_{27}^{64}{dV \over 3 V log({5 \over 3})}={log({64 \over 27}) \over 3 log({5 \over 3})}={3 log({4 \over 3}) \over 3 log({5 \over 3})}={log({4 \over 3}) \over log({5 \over 3})} \approx 0.56.
:
:Thus we have achieved invariance with respect to volume and length.  You can also show the same invariance with respect to surface area being less than 6(42) = 96.  However, note that this probability assignment is not necessarily a "correct" one.  For the exact distribution of lengths, volume, or surface area will depend on how the "experiment" is conducted.  This probability assignment is very similar to the maximum entropy one, in that the frequency distribution corresponding to the above probability distribution is the most likely to be seen.  So, if one was to go to N people individually and simply say "make me a box somewhere between 3 and 5 cm, or a volume between 27 and 125 cm, or a surface area between 54 and 150 cm", then unless there is a systematic influence on how they make the boxes (e.g. they form a group, and choose one particular method of making boxes), about 56% of the boxes will be less than 4 cm - and it will get very close to this amount very quickly.  So, for large N, any deviation from this basically indicates the makers of the boxes were "systematic" in how the boxes were made.
Problems: (1) It's super confusing.  (2) It doesn't at all make clear that this is based on a symmetry transformation (which, for the box?).  (3) This is wrong/misleading: "So, for large N, any deviation from this basically indicates the makers of the boxes were "systematic" in how the boxes were made." (4) Should use different letter for pdfs f(L) and f(V), say g(V). (5) Needs to actually call them pdfs. (6) Many others... Jess (talk) 16:52, 30 December 2013 (UTC)
thread_title:  Principle of transformation groups and the box example 

message: Under 'Dice' the part: "A symmetric dice has n faces..." has me wondering: should that read "A symmetric die has n faces..."
Fix?
71.139.161.9 (talk) 06:01, 15 September 2014 (UTC)
thread_title:  "A symmetric dice has n faces..." 

message: This section omits Gerolamo Cardano. 
Before anyone else, Cardano expressed the Principle of Indifference in his Book on Games of Chance.  He called it a principle of equality.  His book was not published for 100 years.
He should probably be added, but I think it may take a bit of rewriting of the section.Tadamsmar (talk) 18:56, 30 July 2019 (UTC)
thread_title:  History section has problems 

message: Lede, second paragraph: "The principle of indifference is meaningless under the frequency interpretation of probability,..."
I would have thought that evidence that two distributions are different would be admissible as "relevant evidence" in the sense of the principle.  Vaughan Pratt (talk) 22:51, 24 October 2020 (UTC)
thread_title:  Meaningless in frequentist statistics?