Hi, once again, Fine, I'm sure you did. And what is the most plausible, lognormal or gamma? >From the tests specific for least square (pattern fitting) they are equally plausible. And take a combination of the type w*Log+(1-w)*Gam, that will be equally plausible. On the other hand, why should believe that the Baesian deconvolution (or any other sophisticated deconvolution method that can imagine) give the answer much precisely? Both, the least square and deconvolution are ill-posed problems, but the least square is less ill-posed than the deconvolution. At least that say the manuals for statistical mathematics.
Best wishes, Nicolae Popa > Hi, > I pointed out that each model needs to be tested and their plausibility determined. This can be achieved by employing Bayesian analysis, which takes into account the diffraction data and underlying physics. > > I have carried out exactly same analysis for the round robin CeO2 sample for both size distributions using lognormal and gamma distribution functions, and similarly for dislocations: screw, edge and mixed. The plausibility of each model was quantified using Bayesian analysis, where the probability of each model was determined, from which the model with the greatest probability was selected. This approach takes into account the assumptions of each model, parameters, uncertainties, instrumental and noise effects etc. See Sivia (1996)Data Analysis: A Bayesian Tutorial (Oxford Science Publications). > > Best wishes, > Nick > > Dr Nicholas Armstrong > > > > Hi, > > But the diffraction alone cannot determine uniquely the physical > > model. An > > example at hand: the CeO2 pattern from round-robin can be equally well > > described by two different size distributions, lognormal and gamma > > and by > > any linear combinations of these two distributions. Is the situation > > different with the strain profile caused by different types of > > dislocations,possible mixed? > > > > Best wishes, > > Nicolae Popa > > > > > > > > > Best approach is to develop physical models for the line profile > > broadening and test them for their plausibility i.e. model selection. > > > > > > Good luck. > > > > > > Best Regards, Nick > > > > > > > > > Dr Nicholas Armstrong > > > > > > > > > -- > UTS CRICOS Provider Code: 00099F > DISCLAIMER: This email message and any accompanying attachments may contain > confidential information. If you are not the intended recipient, do not > read, use, disseminate, distribute or copy this message or attachments. If > you have received this message in error, please notify the sender immediately > and delete this message. Any views expressed in this message are those of the > individual sender, except where the sender expressly, and with authority, > states them to be the views the University of Technology Sydney. Before > opening any attachments, please check them for viruses and defects. >
