If there are nonequal width bins, then larger bins have more probability and thus a lower free energy. Example; if there are 100 samples, and 50 of them are uniformly between 0 and 90, and 50 are between 90 and 100, and there are two bins, they will have equal free energy, but the PMF should be lower in the 90-100, bin, since it has 10x the density of points.
If one subtracts -ln(bin_width) from each bin, the resulting free energies are a better match.
Right now, we expect people to do it themselves. But perhaps we should do it automatically.
If there are nonequal width bins, then larger bins have more probability and thus a lower free energy. Example; if there are 100 samples, and 50 of them are uniformly between 0 and 90, and 50 are between 90 and 100, and there are two bins, they will have equal free energy, but the PMF should be lower in the 90-100, bin, since it has 10x the density of points.
If one subtracts -ln(bin_width) from each bin, the resulting free energies are a better match.
Right now, we expect people to do it themselves. But perhaps we should do it automatically.