10 ms·

Nice little paper, although maybe a little stilted. It's a good idea to think about these basic quantities a bit more deeply and why you might want to use one m

Nice little paper, although maybe a little stilted. It's a good idea to think about these basic quantities a bit more deeply and why you might want to use one measure of central tendency more than another. It's good to have a solid rationale for it, and I thought this was a nice brief overview of some perspectives I wasn't aware of. For some reason I thought the mean could be thought of as a single number that is most representative of a sample or population in an information loss (algorithmic/kolgomorov complexity, maybe relative entropy?) sense, or maximum likelihood sense (maybe under some distributional constraints?). I might be misremembering that though, and it's difficult to figure out the right search terms to track it down.

ummonk 5y ago
Information loss / maximum likelihood only applies in special case distributions. E.g. take a distribution of variable X and the arithmetic mean might be the appropriate average. But then if you look at sqrt(X) then the appropriate average would be RMS.
verygoodname 5y ago
You can use "maximum entropy" arguments to convince yourself or others that a Gaussian distributional assumption is the best (e.g. if the only thing you know is that your distribution has support over ]-inf,+inf[ and that its variance is bounded, the maximum entropy distribution is a Gaussian) and, in such a case, the sample arithmetic mean will give you the maximum likelihood estimate of the population "location" parameter (and, yes, along with variance, it will contain all required information to perfectly summarize your sample, since these are sufficient statistics, under a Gaussian assumption). TL;DR: If you can safely assume additiveness/normality, then... yes, mostly. Otherwise, not necessarily.
- a9h74j 5y ago
  I assume not only physicists have the rule: never trust a scalar or statistic unless you can also see the distribution (histogram) behind it.

ummonk 5y ago

Information loss / maximum likelihood only applies in special case distributions. E.g. take a distribution of variable X and the arithmetic mean might be the appropriate average. But then if you look at sqrt(X) then the appropriate average would be RMS.

verygoodname 5y ago

You can use "maximum entropy" arguments to convince yourself or others that a Gaussian distributional assumption is the best (e.g. if the only thing you know is that your distribution has support over ]-inf,+inf[ and that its variance is bounded, the maximum entropy distribution is a Gaussian) and, in such a case, the sample arithmetic mean will give you the maximum likelihood estimate of the population "location" parameter (and, yes, along with variance, it will contain all required information to perfectly summarize your sample, since these are sufficient statistics, under a Gaussian assumption). TL;DR: If you can safely assume additiveness/normality, then... yes, mostly. Otherwise, not necessarily.

a9h74j 5y ago
I assume not only physicists have the rule: never trust a scalar or statistic unless you can also see the distribution (histogram) behind it.