On 18. Sep 2018, at 09:41, Hans Dembinski wrote:

there is a minor overhead in the return value. Whenever you query the adaptive_storage, two doubles - one for the value and one for the variance -, which is slightly wasteful if you don't care about the variance, then you would need only one double. I don't know how smart compilers are in this case, the compiler may even remove the code that fills the second double when it is not used. In memory, the adaptive_storage uses only a single integer for each counter if you don't use weighted fills.

Ah, sorry, I don't have a stroke, I am just an hurry, should have read again before sending. There is a minor overhead when the return value is created as you call ".at(…)". Whenever you query the adaptive_storage, two doubles are filled - one for the value and one for the variance -, which is slightly wasteful if you don't care about the variance. In that case, you would need only one double. I don't know how smart compilers are in this case, the compiler may even remove the code that fills the second double if it is not used. In memory, the adaptive_storage uses only a single integer for each counter if you don't use weighted fills.

Hi, Sorry to get back to the issue of variance. I am unsure about the justification of choosing the variance based on the Poisson distribution instead of the binomial distribution. My understanding is that the Poisson distribution is based on a distribution of a number of event given a continuous domain of opportunities (say a period of time). Whereas a binomial distribution is for a number of event for a discrete number of opportunities (say coin flips). Both seem appropriate in some use cases. However, the histogram class has no sense of the passage of time, whereas it does know the number of discrete opportunities (every time operator () is called). And the typical use of histogram seems to be to distribute a given number of samples over the bins that they belong to. So, would it not be more appropriate to estimate variance based on the binomial distribution? I am not a statistician, so happy to be put right. Alex

On Mon, 1 Oct 2018 at 15:04, Hans Dembinski via Boost wrote:

Poisson is correct, for example, when you monitor a random process for a while which produces some value x at random points in time with a constant rate. You bin the outcomes, and then stop monitoring at an arbitrary point in time. This is the right way to model many physics experiments. It is also correct if you make a survey with a random number of participants, i.e. when you pass the survey to a large number of people without knowing beforehand how many are going to respond.

Multinomial is correct, when there is a predefined fixed number of events, each with a random exclusive outcome, and you bin those outcomes. The important point is that the number of events is fixed before the experiment is conducted. This is the main difference to the previous case, where the total of events is not known beforehand. This would be correct, if you make a survey with a fixed number of participants, which you invite explicitly and don't start the analysis before all have return the survey.

From what you are saying, and I have no knowledge at all in this matter [just reading what you say], it seems that a policy approach, to allow for both distributions, seems appropriate. Don't want to give you more work, but you just made the [that] point yourself.

degski -- *“If something cannot go on forever, it will stop" - Herbert Stein*