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Questions on the use of Mathematica to construct models for approximating empirical data.

6
votes
Vector-valued variable's input syntax for FindMinimum The Documentation states (emphasis mine): <...> since the value of the function would be meaningless unless x had the correct structure, th …
answered Nov 15 '13 by Alexey Popkov
3
votes
Following Szabolcs advice, it seems that the Documentation page for EvaluationMonitor contains all what you need for Method -> "Newton": data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}, {6, 4}, {7, 5}}; Clea …
answered Aug 22 '15 by Alexey Popkov
6
votes
Anton Antonov has implemented smoothing splines in his Quantile regression with B-splines package (direct link to the M-file). This post (duplicated in this thread) and this WTC2014 talk explain how c …
answered Jun 6 '15 by Alexey Popkov
2
votes
Citing this Demonstration by Darren Glosemeyer (Wolfram Research): Single prediction bands incorporate both the variation in parameter estimates and the overall variation in response values, whi …
answered Aug 9 '14 by Alexey Popkov
1
vote
Yet another approach: img = Import@"https://i.stack.imgur.com/SLkeC.png"; {center, sa, angle} = 1 /. ComponentMeasurements[AlphaChannel@img, {"Centroid", "SemiAxes", "Orientation"}]; Show[Binarize …
answered Jan 17 '18 by Alexey Popkov
25
votes
3answers
There are many questions on this site about wrong exponential fitting in Mathematica but no one considers this well-known problem as a potential bug. Usually people suggest well-known workarounds … FindMinimum related to exponential fitting. Let us take a simple dataset and try to fit it to the exponential model: data = {{0, 20}, {20, 10}, {40, 5}, {60, 2.5}, {80, 1.25}}; fit1 = FindFit[data, a*Exp[b*x …
asked Jan 27 '16 by Alexey Popkov
7
votes
In the comments I supposed that the reason why the algorithm stops is obtaining zero derivative with respect to b at the point {a, b} = {0., 1.} returned as the minimum. Let us check this statement by …
answered Jan 28 '16 by Alexey Popkov
17
votes
A careful method of finding the mountain boundary including what is masked by the snow but not including the clouds: i = Import@"http://i.stack.imgur.com/1Ui83.jpg"; edge = Closing[ DeleteSmallComp …
answered Mar 14 '16 by Alexey Popkov
15
votes
2answers
I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of the model and returns a vector with t …
asked Feb 18 '12 by Alexey Popkov
8
votes
Here is the solution based on Faysal's code: steps=0; FindMinimum[Null, {optimVariables, initialGuess}\[Transpose], Method -> {"LevenbergMarquardt", "Residual" -> Sqrt[2] residualVector[optimV …
answered Dec 20 '12 by Alexey Popkov