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Hi Jacob, It seems reasonable for your straight line case that the two would be equivalent. I would guess though that as the function to be fitted against becomes more complex (e.g. a rectangular hyperbola in enzyme kinetics) it would be advantageous to have more points of the independent variable measured a fewer number of times (assuming you measured each one enough to get a reasonable estimate of the experimental error). Another reason I can think of to measure more points less frequently is so you can detect possible deviations in the data from the expected function (there might be a peak in the middle of your straight line for some reason). Looking forward to reading other responses! Philip On Thu, Jan 22, 2015 at 5:20 PM, Keller, Jacob <[log in to unmask]> wrote: > Dear Crystallographers, > > This is more general than crystallography, but has applications therein, > particularly in understanding fine phi-slicing. > > The general question is: > > Given one needs to collect data to fit parameters for a known function, > and given a limited total number of measurements, is it generally better to > measure a small group of points multiple times or to distribute each > individual measurement over the measureable extent of the function? I have > a strong intuition that it is the latter, but all errors being equal, it > would seem prima facie that both are equivalent. For example, a line (y = > mx + b) can be fit from two points. One could either measure the line at > two points A and B five times each for a total of 10 independent > measurements, or measure ten points evenly-spaced from A to B. Are these > equivalent in terms of fitting and information content or not? Which is > better? Again, conjecture and intuition suggest the evenly-spaced > experiment is better, but I cannot formulate or prove to myself why, yet. > > The application of this to crystallography might be another reason that > fine phi-slicing (0.1 degrees * 3600 frames) is better than coarse (1 > degree * 3600 frames), even though the number of times one measures > reflections is tenfold higher in the second case (assuming no radiation > damage). In the first case, one never measures the same phi angle twice, > but one does have multiple measurements in a sense, i.e., of different > parts of the same reflection. > > Yes, 3D profile-fitting may be a big reason fine phi-slicing works, but > beyond that, perhaps this sampling choice plays a role as well. Or maybe > the profile-fitting works so well precisely because of this diffuse-single > type of sampling rather than coarse-multiple sampling? > > This general math/science concept must have been discussed somewhere--can > anyone point to where? > > JPK > > ******************************************* > Jacob Pearson Keller, PhD > Looger Lab/HHMI Janelia Research Campus > 19700 Helix Dr, Ashburn, VA 20147 > email: [log in to unmask] > ******************************************* >