Comments on: Why divide the sample variance by N-1? https://www.visiondummy.com/2014/03/divide-variance-n-1/ A blog about intelligent algorithms, machine learning, computer vision, datamining and more. Fri, 21 Jul 2017 05:50:18 +0000 hourly 1 https://wordpress.org/?v=3.8.39 By: Vincent Spruyt https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-406 Wed, 21 Jun 2017 05:34:04 +0000 http://www.visiondummy.com/?p=196#comment-406 Hi Michael, it’s an honor, great work! Thanks a lot!

]]> By: Michael Cheng https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-405 Tue, 20 Jun 2017 11:20:39 +0000 http://www.visiondummy.com/?p=196#comment-405 Hi, there, I like your essay very much. I hope you do not mind that I have translated your article to Chinese.
Here is the link: http://commanber.com/2017/06/17/sample-variance/
I will remove my article immediately if you do not allow me to release the Chinese version of your article.
Thanks very much!
Have a good day!

]]> By: Chris https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-385 Tue, 30 May 2017 21:01:17 +0000 http://www.visiondummy.com/?p=196#comment-385 Outstanding explanation of one of the “mysteries” of statistics that has long defied a good explanation. Thanks for taking the time to post.

]]> By: scott https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-267 Fri, 22 Apr 2016 12:20:55 +0000 http://www.visiondummy.com/?p=196#comment-267 Check “we can write their joint likelihood function as the sum of all individual likelihoods…” directly before equation 5. I think it should read “the product of individual likelihoods” instead of sum.

Thank you for your articles, I have found them very helpful.

]]> By: Dobrin https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-247 Fri, 05 Feb 2016 14:53:11 +0000 http://www.visiondummy.com/?p=196#comment-247 Nicely written article, but I think you are super confused about your “hat” notation. In Statistics, the hat is reserved to denote the estimator or the estimate (depending on the context), whereas without a hat is the population parameter. In your equation (4) mu and sigma are clearly the parameters of the normal distribution, however in the preceding paragraph you say these are estimators, namely the empirical average and empirical variance.

]]> By: sung https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-231 Sat, 26 Dec 2015 08:35:17 +0000 http://www.visiondummy.com/?p=196#comment-231 Hi Vincent,
can you please give a proof that the maximum likelihood method guarantees an unbiased estimator is also minimum variance?

]]> By: Pablo https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-227 Wed, 02 Dec 2015 14:20:28 +0000 http://www.visiondummy.com/?p=196#comment-227 Hi Vincent, this is a really great article… Well written and nicely explained!

Just a small typo I found: In the section “Estimating the variance if the mean is unknown”, subsection “Parameter estimation” in the third equation there is missing an s in the denominator of the first log-summand. Not a big thing, since it is eliminated anyways but just wanted to let you know.

]]> By: Billy https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-198 Wed, 09 Sep 2015 13:45:28 +0000 http://www.visiondummy.com/?p=196#comment-198 Thanks very much. Beautiful post. It’s not easy to find why you have to divide the sample variance by n-1, on many statistics books….!
Bye.

]]> By: Vincent Spruyt https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-144 Sat, 07 Mar 2015 14:21:52 +0000 http://www.visiondummy.com/?p=196#comment-144 Hi Jacques, thanks for your comment. I will defintely have a look at the book you mentioned! Although it is true that the variance of the estimator increases a bit by introducing Bessel’s correction, a slight increase in variance is often prefered over a biassed estimator. However, as you mention, it is indeed important to consider the Gaussian assumptions in the above derivations. For non-Gaussian distributions you might indeed want to considere different options, but then again the variance is usually not a very interesting statistic for non-Gaussian distributions. Thanks again for your valuable feedback!

]]> By: Vincent Spruyt https://www.visiondummy.com/2014/03/divide-variance-n-1/#comment-143 Sat, 07 Mar 2015 14:17:06 +0000 http://www.visiondummy.com/?p=196#comment-143 Obviously you are right, Tushant. Thanks for your input! I just fixed this typo.

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