Equation 8 and 9

[ramess101]

@mrshirts @jpotoff

Michael expressed a concern that I have had for a while but failed to mention. In the manuscript we refer to Pr_i(N,U) as the probability, when really I believe it is the number of snapshots that fall in the histogram bin N,U.

Here are the equations and text as they were found previously:

I think we want this to read K_snaps,i(N,U), since this would more clearly denote a histogram "count" rather than a probability.

Does this look correct?

[ramess101]

@mrshirts @jpotoff

This is how Pana described the equations. Notice that I changed f_i(N,E) to Pr_i(N,U), because he described it as a probability. But his description that K_i=sum over f_i makes it seem like this is really the histogram count.

[ramess101]

@mrshirts @jpotoff

When I looked through the actual histogram reweighting code, it appears that I do not use the normalized histogram probability, rather I use the histogram "count." It is possible that the probability can be used in a different format, but the way the equations are actually written I think it should be the count.

[mrshirts]

The K_snaps,i(N,E) formalism looks correct to me. That's what reduces to the sum over observations.