What is Weighted Histogram Analysis and How Does it Work?

[ss k]

I would like to understand the 'weighted histogram analysis method' (wham), which is far to go, but before that am not sure what a weight is? {{Though I understand what is probability density function which has been already discussed on this forum here, and I assume applying weights is a different thing }}

Could someone please give a simple example which can help me to understand what a 'weight' is, and how it is calculated (or known), and then how the calculated (or known) weight is used on the same data?

 

[jim mcnamara]

Here is a non-mathematical definition of a weighted average (mean), which may be a good starting point, from wikipedia:

an average resulting from the multiplication of each component by a factor reflecting its importance

so there is an effect imparted by the person or software doing the analysis. Example:
http://www.mathwords.com/w/weighted_average.htm

Now you get what weighted in the sense of data means.So here is a discussion of WHAM methodology:
https://www.quora.com/How-does-the-Weighted-Histogram-Analysis-Method-WHAM-work

 

[FactChecker]

Are you asking this in the specific context of chemistry and energy landscape (https://en.wikipedia.org/wiki/Umbrella_sampling) or in the more general statistical context of sampling techniques (https://en.wikipedia.org/wiki/Importance_sampling)?

 

[ss k]

Hi Jim, Hi FactChecker
Sorry for much delayed response.
Thanks for your replies. I had searched those links but the following link about umbrella sampling (mainly first link) is more intuitive, and helpful in understanding why we need WHAM.

https://engineering.ucsb.edu/~shell/che210d/Biased_sampling.pdf

https://engineering.ucsb.edu/~shell/che210d/Histograms.pdf