[task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

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Re: [task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

Hi Troels, Looking at page 28, note that they are using the SSE value of sum(Y_data - Y_curve)^2 and not the chi2 value of sum((Y_data - Y_curve)/sigma)^2. This is a major difference! The chi-squared value is the SSE normalised to unit variance. Any statistics or techniques relying on the SSE

Re: [task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

Hi Edward. I have used this regression book. http://www.graphpad.com/faq/file/Prism4RegressionBook.pdf I like the language (fun and humoristic), and goes over a great detail. For example, there is quite a list of weighting methods. I find the comments on page 28 a little disturbing. (See also

Re: [task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

Hi Troels, Do you have a reference for the technique? You mentioned a 'fitting guide' in one of your commit messages, but without a reference to it. I would like to study the technique to understand the implementation. Does it have another name? I would guess so as it breaks the statistical

Re: [task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

Hi Troels, I have used this regression book. http://www.graphpad.com/faq/file/Prism4RegressionBook.pdf I like the language (fun and humoristic), and goes over a great detail. For example, there is quite a list of weighting methods. I find the comments on page 28 a little disturbing. (See

Re: [task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

Hi Troels, You should be very careful with your interpretation here. The curvature of the chi-squared space does not correlate with the parameter errors! Well, it most cases it doesn't. You will see this if you map the space for different Monte Carlo simulations. Some extreme edge cases might

Re: [task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

Hi, Do the R2eff errors look reasonable? Another issue is in clustered analysis, certain parameters can be over-constrained by being shared between multiple data sets. This is the biased introduced by an under-fitted problem. This can artificially decrease the errors. Anyway, you should plot

Re: [task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

Hi Edward. I do not claim that Monte Carlo simulations is not the gold standard. I am merely trying to investigate the method by which one draw the errors. In the current case for dispersion, one trust the R2eff errors to be the distribution. These are individual per spin. Another distribution

Re: [task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

Hi, If you plot the R2eff errors from the Monte Carlo simulations of that model, are they Gaussian? Well, that's assuming you have full dispersion curves. Theoretically from the white noise in the NMR spectrum they should be. Anyway, even if it not claimed that Monte Carlo simulations have

Re: [task #7882] Implement Monte-Carlo simulation, where errors are generated with width of standard deviation or residuals

Hi, Sorry, I meant sum_i(residual_i / error_i)/N 1.0. As for calculating the bias value, it looks like Wikipedia has a reasonable description (https://en.wikipedia.org/wiki/Bias_of_an_estimator). Regards, Edward On 16 January 2015 at 19:07, Edward d'Auvergne edw...@nmr-relax.com wrote: Hi,