Talk:Galton–Watson process

message: The external links are both dead. Need updating. — Preceding unsigned comment added by 137.112.148.179 (talk) 03:00, 16 November 2005‎
:no, the second one is ok, but you need Acrobat or something to see it. Not very "accessible" 203.218.141.99 07:32, 11 April 2006 (UTC)
thread_title:  Dead external links 

message: I just went through the Galton-Watson paper mentioned in the history section, which concludes by saying (incorrectly) that "whenever the survival probabilities can be represented by a polynomial, ... all the surnames, therefore, tend to extinction." It comes to this false conclusion because it says,
We get the equation
:_rm_0=\frac{1}{(a+b)^q}\left \{ a+b\cdot_{r-1}m_0\right \}^q
:[Here rm0 denotes the probability of extinction after r generations.]
whence it follows that as r increases indefinitely the value of rm0 approaches indefinitely to the value y where
:y=\frac{1}{a+b}\left \{ a+by\right \}
that is where y=1.
The first formula is correct, but the second is not; it should be
:y=\frac{1}{(a+b)^q}\left \{ a+by\right \}^q
this does have y=1 as one solution, but there are other solutions if the expected number of male descendants is greater than 1. Moreover, the sequence (rm0) will approach one of the other solutions, so the probability of the surname surviving indefinitely is nonzero. This is in agreement with the Wikipedia article, but not the Galton-Watson paper.
Meanwhile, all of this is original research, so Wikipedia can't include any of it without a citation. skeptical scientist (talk) 19:53, 31 January 2009 (UTC)
thread_title:  Is it worth mentioning the original paper is wrong? 

message: The definition uses (n+1) in the superscript, it is not clear what this means. The paragraph below implies is is \xi_j^{(n)} is a sequence. I am not sure what it means to be summing whole sequences (as opposed to elements), especially ones with a different number of elements. I think something else is meant here. If it is not wrong, I think there is something missing in the explanation of the notation. --MATThematical (talk) 16:20, 16 June 2010 (UTC)
replies: text: I added one sentence describing the correspondence between formal definition and analogy with family names; hopefully this makes the definition easier to parse. I'm not exactly sure if it's fair to call \{\xi_j^{(n)}\} a sequence, as it's a function, not from natural numbers to random variables, but from pairs (j,n) of natural numbers with j ≤ Xn to random variables (and so not technically a sequence, or perhaps an infinite sequence of finite sequences). However, each individual term \xi_j^{(n)} is a natural-number-valued random variable, and those can certainly be summed. skeptical scientist (talk) 13:28, 19 January 2012 (UTC)
thread_title: Definition unclear

message: I modified the sentence "Assume, as was taken for granted in Galton's time, that surnames are passed on to all male children by their father".
Indeed it is quite absurd to suggest that this assumption was ever taken for granted. Children out of wedlock have always been a known reality. Moreover, even within the traditional family paradigm this assumption was not at all the standard in all cultures, so that it is not a question of "time" but also of place.  — Preceding unsigned comment added by 128.178.14.162 (talk) 12:48, 20 June 2014 (UTC)
thread_title:  edit on assumption 

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*Added archive http://www.webcitation.org/6bTLDd2kR?url=http://hsblogs.stanford.edu/morrison/files/2011/02/27.pdf to http://hsblogs.stanford.edu/morrison/files/2011/02/27.pdf
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thread_title:  External links modified 

message: I think there should probably be a warning about the fact that Francis Galton is the father of eugenics. As it likely affected the study. I think in the history section there should be more context given to "In 1869, Galton published Hereditary Genius, in which he treated the extinction of different social groups." 
Perhaps "In 1869, Galton published Hereditary Genius, which has earned him the name the Father of Eugenics . 128.119.202.49 (talk) 20:09, 28 May 2024 (UTC)
thread_title:  Eugenics