Re: [ccp4bb] How the IMEAN is calculated in scalepack2mtz
Thank you all for the information and F estimator write-up. With regards Karthik On 13-03-2017 03:56 AM, Phil Evans wrote: Sorry Ian, I was attributing this to Kevin apologies Phil On 12 Mar 2017, at 21:56, Ian Tickle wrote: Eleanor, Phil is right about the bias of the weighted mean, here's how I do it using a minimum mean-squared error estimator which seems to give more accurate results than either the unweighted or the weighted mean: http://staraniso.globalphasing.org/Optimal-F-estimator.pdf This is actually about Fmean but the same applies to Imean. This actually only makes a significant difference to the result if there's a big difference between sd(I+) and sd(I-), which is obviously not very common. Cheers -- Ian On 12 March 2017 at 17:58, Eleanor Dodson wrote: You read: h k l IPLUS SIGIPLUS INEG SIGINEG Then program calculates this: SIGIMEAN = SIGIPLUS*SIGINEG/(SIGIPLUS+SIGINEG) IMEAN = (IPLUS/SIGIPLUS + INEG/SIGINEG)*SIGIMEAN ie: IMEAN = ( IPLUS*SIGINEG + INEG * SIGIPLUS ) / /(SIGIPLUS+SIGINEG) Is that the right thing to do? Not sure! Eleanor Dodson On 11 March 2017 at 15:18, Karthikeyan Subramanian wrote: Dear CCP4bb, How IMEAN and SIGIMEAN is calculated in scalepack2mtz if the input is with anomalous intensity (obtained from HKL2000). Any guide/reference is highly appreciated. Thanks in advance, With regards Karthikeyan S. Principal Scientist IMTECH, Chandigarh
Re: [ccp4bb] How the IMEAN is calculated in scalepack2mtz
Hi Eleanor I reran my simulation including your method. Let's just look at the two extreme cases in my original table: sd(F+) = 10, sd(F-) = 1 (5th row) and sd(F+) = 1000, sd(F-) = 100 (last row: the case where my method performs worst but still better than the others!). I used the same 'true' values as before: F+ = 578, F- = 1369, Fmean = 973. For the first case, the values of su(Fmean) for the methods 'unweighted', 'variance-weighted', 'RMS-error-weighted' (my method) and 'sd-weighted' (your method) are 5 1 5 1 respectively, so as expected the two weighted methods give the lowest variances. Similarly the mean biases are: 0 388 0 323, so again as expected the weighted methods are the most biased. The RMS errors are: 5 388 5 323 so in this case the 'variance-weighted' and 'sd-weighted' methods both perform poorly with the highest overall errors, though your method is somewhat better than the 'variance-weighted' one. For each statistic I'm including the first 3 values for comparison but they are of course exactly the same as before: only the last value for the 'sd-weighted' method is new. For the second case with sd(F+) = 1000, sd(F-) = 100 and the same values for the true Fs, the results from the 4 methods in the same order as before are: su(Fmean):38699 171 115. bias(Fmean):87 389 274 339. RMSE(Fmean): 396 402 323 358. So again the results for su(Fmean) and bias(Fmean) are as expected (i.e. the 'sd-weighted' method performs intermediate between 'unweighted' and 'variance-weighted'). However using the RMSE measure the 'RMS-error-weighted' method performs best. Using the RMSE measure as the definitive metric (which IMO is the only sensible procedure), in no case does the 'RMS-error-weighted' method perform worse than any of the others. Cheers -- Ian On 13 March 2017 at 08:22, Ian Tickle wrote: > > Eleanor > > I notice that you are calculating a weighted mean using 1/sd(I) as the > weight whereas in least squares one would of course normally use > variance-weighting, i.e. 1/sd(I)^2. I assume this is intentional and is a > way to reduce the bias effect of weighting, so that the resulting bias of > the mean would be intermediate between that of an unweighted and a > variance-weighted mean, though the variance of the mean would no longer be > a minimum. > > Assuming that it was indeed intentional, I will see if I can find the > program I used to simulate the various ways of calculating the mean using > the MSE as the measure of accuracy and see how this method compares with > the others. > > Cheers > > -- Ian > > > > On 12 March 2017 at 17:58, Eleanor Dodson > wrote: > >> You read: >> h k l IPLUS SIGIPLUS INEG SIGINEG >> Then program calculates this: >> >>SIGIMEAN = SIGIPLUS*SIGINEG/(SIGIPLUS+SIGINEG) >> >> IMEAN = (IPLUS/SIGIPLUS + INEG/SIGINEG)*SIGIMEAN >> >> ie: IMEAN = ( IPLUS*SIGINEG + INEG * SIGIPLUS ) / /(SIGIPLUS+SIGINEG) >> >> Is that the right thing to do? Not sure! >> >> Eleanor Dodson >> >> >> >> On 11 March 2017 at 15:18, Karthikeyan Subramanian >> wrote: >> >>> Dear CCP4bb, >>> >>> How IMEAN and SIGIMEAN is calculated in scalepack2mtz if the input is >>> with anomalous intensity (obtained from HKL2000). Any guide/reference is >>> highly appreciated. >>> >>> Thanks in advance, >>> >>> With regards >>> >>> Karthikeyan S. >>> >>> Principal Scientist >>> >>> IMTECH, Chandigarh >>> >> >> >
Re: [ccp4bb] How the IMEAN is calculated in scalepack2mtz
Eleanor I notice that you are calculating a weighted mean using 1/sd(I) as the weight whereas in least squares one would of course normally use variance-weighting, i.e. 1/sd(I)^2. I assume this is intentional and is a way to reduce the bias effect of weighting, so that the resulting bias of the mean would be intermediate between that of an unweighted and a variance-weighted mean, though the variance of the mean would no longer be a minimum. Assuming that it was indeed intentional, I will see if I can find the program I used to simulate the various ways of calculating the mean using the MSE as the measure of accuracy and see how this method compares with the others. Cheers -- Ian On 12 March 2017 at 17:58, Eleanor Dodson wrote: > You read: > h k l IPLUS SIGIPLUS INEG SIGINEG > Then program calculates this: > >SIGIMEAN = SIGIPLUS*SIGINEG/(SIGIPLUS+SIGINEG) > > IMEAN = (IPLUS/SIGIPLUS + INEG/SIGINEG)*SIGIMEAN > > ie: IMEAN = ( IPLUS*SIGINEG + INEG * SIGIPLUS ) / /(SIGIPLUS+SIGINEG) > > Is that the right thing to do? Not sure! > > Eleanor Dodson > > > > On 11 March 2017 at 15:18, Karthikeyan Subramanian > wrote: > >> Dear CCP4bb, >> >> How IMEAN and SIGIMEAN is calculated in scalepack2mtz if the input is >> with anomalous intensity (obtained from HKL2000). Any guide/reference is >> highly appreciated. >> >> Thanks in advance, >> >> With regards >> >> Karthikeyan S. >> >> Principal Scientist >> >> IMTECH, Chandigarh >> > >
Re: [ccp4bb] How the IMEAN is calculated in scalepack2mtz
Sorry Ian, I was attributing this to Kevin apologies Phil > On 12 Mar 2017, at 21:56, Ian Tickle wrote: > > > Eleanor, > > Phil is right about the bias of the weighted mean, here's how I do it using a > minimum mean-squared error estimator which seems to give more accurate > results than either the unweighted or the weighted mean: > > http://staraniso.globalphasing.org/Optimal-F-estimator.pdf > > This is actually about Fmean but the same applies to Imean. > > This actually only makes a significant difference to the result if there's a > big difference between sd(I+) and sd(I-), which is obviously not very common. > > Cheers > > -- Ian > > > > On 12 March 2017 at 17:58, Eleanor Dodson wrote: > You read: > h k l IPLUS SIGIPLUS INEG SIGINEG > Then program calculates this: > >SIGIMEAN = SIGIPLUS*SIGINEG/(SIGIPLUS+SIGINEG) > > IMEAN = (IPLUS/SIGIPLUS + INEG/SIGINEG)*SIGIMEAN > > ie: IMEAN = ( IPLUS*SIGINEG + INEG * SIGIPLUS ) / /(SIGIPLUS+SIGINEG) > > Is that the right thing to do? Not sure! > > Eleanor Dodson > > > > On 11 March 2017 at 15:18, Karthikeyan Subramanian > wrote: > Dear CCP4bb, > > How IMEAN and SIGIMEAN is calculated in scalepack2mtz if the input is with > anomalous intensity (obtained from HKL2000). Any guide/reference is highly > appreciated. > > Thanks in advance, > > With regards > > Karthikeyan S. > > Principal Scientist > > IMTECH, Chandigarh > >
Re: [ccp4bb] How the IMEAN is calculated in scalepack2mtz
Thanks Ian. e On 12 March 2017 at 21:56, Ian Tickle wrote: > > Eleanor, > > Phil is right about the bias of the weighted mean, here's how I do it > using a minimum mean-squared error estimator which seems to give more > accurate results than either the unweighted or the weighted mean: > > http://staraniso.globalphasing.org/Optimal-F-estimator.pdf > > This is actually about Fmean but the same applies to Imean. > > This actually only makes a significant difference to the result if there's > a big difference between sd(I+) and sd(I-), which is obviously not very > common. > > Cheers > > -- Ian > > > > On 12 March 2017 at 17:58, Eleanor Dodson > wrote: > >> You read: >> h k l IPLUS SIGIPLUS INEG SIGINEG >> Then program calculates this: >> >>SIGIMEAN = SIGIPLUS*SIGINEG/(SIGIPLUS+SIGINEG) >> >> IMEAN = (IPLUS/SIGIPLUS + INEG/SIGINEG)*SIGIMEAN >> >> ie: IMEAN = ( IPLUS*SIGINEG + INEG * SIGIPLUS ) / /(SIGIPLUS+SIGINEG) >> >> Is that the right thing to do? Not sure! >> >> Eleanor Dodson >> >> >> >> On 11 March 2017 at 15:18, Karthikeyan Subramanian >> wrote: >> >>> Dear CCP4bb, >>> >>> How IMEAN and SIGIMEAN is calculated in scalepack2mtz if the input is >>> with anomalous intensity (obtained from HKL2000). Any guide/reference is >>> highly appreciated. >>> >>> Thanks in advance, >>> >>> With regards >>> >>> Karthikeyan S. >>> >>> Principal Scientist >>> >>> IMTECH, Chandigarh >>> >> >> >
Re: [ccp4bb] How the IMEAN is calculated in scalepack2mtz
Eleanor, Phil is right about the bias of the weighted mean, here's how I do it using a minimum mean-squared error estimator which seems to give more accurate results than either the unweighted or the weighted mean: http://staraniso.globalphasing.org/Optimal-F-estimator.pdf This is actually about Fmean but the same applies to Imean. This actually only makes a significant difference to the result if there's a big difference between sd(I+) and sd(I-), which is obviously not very common. Cheers -- Ian On 12 March 2017 at 17:58, Eleanor Dodson wrote: > You read: > h k l IPLUS SIGIPLUS INEG SIGINEG > Then program calculates this: > >SIGIMEAN = SIGIPLUS*SIGINEG/(SIGIPLUS+SIGINEG) > > IMEAN = (IPLUS/SIGIPLUS + INEG/SIGINEG)*SIGIMEAN > > ie: IMEAN = ( IPLUS*SIGINEG + INEG * SIGIPLUS ) / /(SIGIPLUS+SIGINEG) > > Is that the right thing to do? Not sure! > > Eleanor Dodson > > > > On 11 March 2017 at 15:18, Karthikeyan Subramanian > wrote: > >> Dear CCP4bb, >> >> How IMEAN and SIGIMEAN is calculated in scalepack2mtz if the input is >> with anomalous intensity (obtained from HKL2000). Any guide/reference is >> highly appreciated. >> >> Thanks in advance, >> >> With regards >> >> Karthikeyan S. >> >> Principal Scientist >> >> IMTECH, Chandigarh >> > >
Re: [ccp4bb] How the IMEAN is calculated in scalepack2mtz
It should be the unweighted mean to avoid bias towards I+ or I- (or Kevin Cowtan had a more complicated way) Phil > On 12 Mar 2017, at 17:58, Eleanor Dodson wrote: > > You read: > h k l IPLUS SIGIPLUS INEG SIGINEG > Then program calculates this: > >SIGIMEAN = SIGIPLUS*SIGINEG/(SIGIPLUS+SIGINEG) > > IMEAN = (IPLUS/SIGIPLUS + INEG/SIGINEG)*SIGIMEAN > > ie: IMEAN = ( IPLUS*SIGINEG + INEG * SIGIPLUS ) / /(SIGIPLUS+SIGINEG) > > Is that the right thing to do? Not sure! > > Eleanor Dodson > > > > On 11 March 2017 at 15:18, Karthikeyan Subramanian > wrote: > Dear CCP4bb, > > How IMEAN and SIGIMEAN is calculated in scalepack2mtz if the input is with > anomalous intensity (obtained from HKL2000). Any guide/reference is highly > appreciated. > > Thanks in advance, > > With regards > > Karthikeyan S. > > Principal Scientist > > IMTECH, Chandigarh >
Re: [ccp4bb] How the IMEAN is calculated in scalepack2mtz
You read: h k l IPLUS SIGIPLUS INEG SIGINEG Then program calculates this: SIGIMEAN = SIGIPLUS*SIGINEG/(SIGIPLUS+SIGINEG) IMEAN = (IPLUS/SIGIPLUS + INEG/SIGINEG)*SIGIMEAN ie: IMEAN = ( IPLUS*SIGINEG + INEG * SIGIPLUS ) / /(SIGIPLUS+SIGINEG) Is that the right thing to do? Not sure! Eleanor Dodson On 11 March 2017 at 15:18, Karthikeyan Subramanian wrote: > Dear CCP4bb, > > How IMEAN and SIGIMEAN is calculated in scalepack2mtz if the input is with > anomalous intensity (obtained from HKL2000). Any guide/reference is highly > appreciated. > > Thanks in advance, > > With regards > > Karthikeyan S. > > Principal Scientist > > IMTECH, Chandigarh >
[ccp4bb] How the IMEAN is calculated in scalepack2mtz
Dear CCP4bb, How IMEAN and SIGIMEAN is calculated in scalepack2mtz if the input is with anomalous intensity (obtained from HKL2000). Any guide/reference is highly appreciated. Thanks in advance, With regards Karthikeyan S. Principal Scientist IMTECH, Chandigarh
