Talk:Chernoff bound

message: The other page just presents a bit more technical stuff. Could probably be merged pretty easily. Thoughts?
I think Chernoff bound is just a special case of the Chernoff bounds. So, it should be presented
appropriately. Definitely merged, in either case. Else, its too confusing.  —Preceding unsigned comment added by 24.47.50.165 (talk) 15:46, 18 December 2007 (UTC)
thread_title:  Merge with Chernoff Bounds 

message: This seems to have left some problems:
*What is a "Poisson trail": is this defined somewhere? (link?)
*Appears to duplicate material later in article, under "Theorem (relative error)".
*Incompleteness: eg \Pr(X_i) = p_i possibly needs an "=1" in it, depending on what a "Poisson trail" is.
Melcombe (talk) 09:11, 13 June 2008 (UTC)
thread_title:  Addition 13 June 2008 

message: The formula in the leader to this article seem very useful, but there is no indication as to where they come from in the main body of the article. Not being familiar with the subject, I can't add it myself, but I know I would find it rather useful to see where those formula came from. me_and (talk) 15:10, 25 November 2008 (UTC)
thread_title:  Missing proof/example 

message: I would love to use the inequality:
 \mathbf{P}\left ( X>mp+x \right ) \leq \exp \left (-\frac{x^2}{2mp(1-p)} \right ) .
However, I haven't been able to verify it (looked at other inequalities, multiple books, etc..) Is it true? Any reference / proofs?
Thanks!  — Preceding unsigned comment added by 128.32.44.125 (talk) 02:47, 8 February 2014 (UTC)
thread_title:  Where does the inequality with p(1-p) come from? 

message: In the intro Chernoff Bounds are described as only requiring independence (and I believe, bounded expectation). However the proof given in section 4.2 only accepts Poisson variables, rather than general random, positive variables. Does anyone know a more general proof?  — Preceding unsigned comment added by Thomasda (talk • contribs) 16:26, 2 June 2014 (UTC)
thread_title:  General Proof 

message: Hey, I noticed the links (there's two) to the book "Probability and Computing: Randomized Algorithms and Probabilistic Analysis" pointing to google books pages are dead. 
I looked up, but am not a 100% sure what the appropriate steps are to replace them, and how to execute these. 
The book seems to be online in pdf form here http://bayanbox.ir/view/340405828745623973/probability-and-computing-mitzenmacher-upfal.pdf
OldMacDonalds (talk) 19:32, 4 February 2015 (UTC)
thread_title:  Dead Links 

message: There used to be a coin tossing example on the page, which was great except for the fact that it was not consistent with the formula given on present version of the page for the Chernoff bound. I decided that doing without the section was better than including a section that was at best confusing and at worst wrong. It would be great if someone reworked it or perhaps found a better version of the Chernoff bound, that made the argument true. MathHisSci (talk) 15:43, 20 August 2015 (UTC)
thread_title:  Coin tossing example 

message: Formula (1) claims that a minimum is attained for s>0. This does not seem obvious for me, as I don't see why the limit of s to zero cannot be lower, i.e. why it isn't the case that the infimum is not in the set. I've looked at a few proofs, but I've been unable to find one that proofs this. ShearedLizard (talk) 15:46, 2 March 2018 (UTC)
replies: text: Formula (1) assumes that a> EX; otherwise the derivative has the wrong sign at t=0 as you say.  There is also another problem, namely that E e^{tX} might not be finite for all positive t. If we allow infinite expectations and assume a> EX we get closer to the truth.  Perhaps using inf instead of min is needed too, but I suspect not since the argument looks continuous in t. This is all too messy so I propose removing (1) and similar expressions, and also adding the condition that E e^{tX} is finite. The common practice of minimizing over t can be demonstrated with in the examples. McKay (talk) 05:18, 7 March 2018 (UTC)
thread_title:  Why does the minimum exist?