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

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Nonlinear least squares on a GPU with Mathematica 9

Update: A Mathematica wrapper for (https://github.com/zitmen/cuLM) should allow for us to directly implement the Levenberg-Marquardt algorithm in CUDA for nonlinear least squares fitting. In a ...
6
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0answers
178 views

Using perpendicular offsets in FindFit

I want to use perpendicular offsets in the built-in FindFit function. Are there any possible ways or do I have to code everything by myself?
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68 views

Third syntax version of LogitModelFit: unexpected result of “BestFit”

The third listed syntax version of LogitModelFit allows one to specify input in a simple way: Only a design matrix (with a row of values of the explanatory input ...
5
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0answers
614 views

Analytical model fitting

I have a special type of model fitting problem that I am trying to solve in Mathematica. Any insight how to attack it using available tools of Mathematica will be great to hear. We have a variable $$ ...
4
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0answers
172 views

Problems extending NelderMeadMinimize into 2D

I've been playing around with Oleksandr's compiled Nelder-Mead Minimization function presented here: Shaving the last 50 ms off NMinimize First, I'll create some sample data. This creates a noisy ...
3
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0answers
121 views

Module in numerical model for NonlinearModelFit is slow and leaks memory

I am trying to make a NonlinearModelFit where the model is the result of a numerical calculation. My code works, but it is very slow and also seems to have a memory ...
3
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0answers
226 views

What exactly is “ParameterErrors” of NonlinearModelFit?

I am trying to get what I call a "$\chi^2$ fit". This means taking a function $f(x,p)$ of the variable $x$ with a parameter $p$ and finding the value of $p$ that minimizes the "distance" from a data ...
3
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0answers
222 views

Is it possible to marginalize one or several parameters obtained from fitting procedure?

Statistical model analysis package has a few fitting functions. Their arguments are data points, fitting model and parameters in the fit. The result is a set of best values for parameters, which ...
3
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0answers
200 views

Mathematica Complains about Non Symmetric Covariance matrix, when it's not the case

I was doing some fitting with Mathematica7 using NonlinearModelFit. It's quite long the program to do the fit and that's why I am not displaying here ... It goes ok, and I can get the fit parameters ...
2
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0answers
88 views

Power::infy: error using FindFit

I have a 2D data to fit (the Airy type pattern from diffraction of Gaussian beam on the circular aperture). Please see the attached picture. I was going to use a function like ...
2
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0answers
41 views

Why do EstimatedDistribution and DistributionFitTest work this way

I am fitting some time-series data to both a stable distribution and a normal distribution in order to assess the goodness of fit of each. Along the way I encountered the following confusing result. ...
2
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0answers
129 views

NonlinearModelFit is not giving the fit with minimum chi^2

First of all, a bit of background, I am using Mathematica to fit angular distributions of gamma rays, so I apologize for some of the serious messiness in the formulas. The data is simple I have three ...
2
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0answers
564 views

Linear regression with x and y errors

I have a question about finding a linear regression weighted with x and y errors. I found the answer provided by 0x4A4D in Estimate error on slope of linear regression given data with associated ...
2
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0answers
200 views

NonLinearModelFit with Two Dimensional List of Weights

I'm currently trying to fit Planck's law (B[λ, T]) to measurements, thereby determining Planck's constant. I have a list of triplets containing wavelength, ...
2
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0answers
546 views

ParametricNDSolveValue or NDSolve + fitting

I have been trying to find the value for the parameter kestim that yields the best fit of a model to some data points. datac has ...
2
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0answers
200 views

How to predict some constant number of values with NeuralNetworks

Example: << NeuralNetworks` data = {Sin[#]} & /@ Range[0, 4 Pi, 0.5]; learn = data[[1 ;; 15]]; Now, lets fit our neural network: ...
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0answers
40 views

Cross-validation of a FittedModel

Although I would know how to perform cross-validation tests after fitting a model using a function like NonLinearModelFit, I wonder if there is a way to do this providing the right parameters to the ...
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0answers
89 views

Developing easy code to apply Delta Method to generate prediction bands for custom distributions

I think that this is an interesting issue for all those who when to not only adjust one prediction function, but also to obtain the prediction bands to asses the graphical or tabular error I'm trying ...
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0answers
35 views

A more efficient way of fitting a non-linear model that returns an entire list?

I have a function that takes two parameters, del and nu, and returns a list npoints long ...
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0answers
114 views

LeastSquares with some parameters missing

I want to do a partial least squares (PLS) regression using LeastSquares on my data. The input parameters are temperature, humidity and pressure for a given date. ...
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0answers
94 views

Can we ask ComponentMeasurements to use NonLinearModelFit to return a covariance matrix for underlying intensity data?

I'd like to be able to calculate a covariance matrix for some data underlying a morphological component. Provided this data, I can write something like: ...
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0answers
560 views

How to Output Chi-Squared Statistics when using NonLinearModelFit

I am using NonLinearModelFit for some curve fitting and I was wondering if NLM is able to output chi-squared/leastsquared statistics from the best-fit parameters and confidence intervals. From my ...
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0answers
191 views

To what extent can NonlinearModelFit be sped up?

Can NonlinearModelFit be parallelized or compiled to allow one to achieve a scalable speedup for a fitting procedure? Attempting to use this function to fit a ...
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0answers
26 views

NonlinearModelFit::nrlnum error using FindFit /NonlinearModelFit

My question is related to my previous post I'm trying to fit experimental data (after suggestion here by David) with Airy type function `data01 = Import["366.0000cm_660.0000nm.png"]; data02 = ...
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74 views

Memory problem in Mathematica 10

I'm having a problem with memory. I'm doing nonliner fits of several data lists to a system of differential equations. When I evaluate the "Do" cycle the memory grows with the iteration step up to my ...
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0answers
53 views

Fit convoluted Gaussian and Lorentzian functions to a peak profile

Thanks in advance for anyone who read this. I have a peak profile data like this: ...
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52 views

No real number fitting double exponential in Mathematica

I am trying to fit a double exponential curve to my data, but I got the error saying there are non real number. Also I tried with starting values for my 4 parameters, but this does not work either. ...
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55 views

Horizontal shift in fitting data by a sinusoidal nonlinear model

I have data that can apparently be fitted by a sinusoidal function in form $D+A\sin(B(x-\frac CB))$. I tried doing the best fit in Mathematica using ...
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0answers
38 views

How do I constrain the result of fitting my non-linear model to be greater then 0

fitresulty21 = NonlinearModelFit[ydata21, {funfit[y, σ, A, B, x1, d, d/2], A > 0}, {{x1, 20}, {σ, 3}, {A, 200}, {B, 2000}, {d, 110}}, y]; ...
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0answers
32 views

Fix Parameters for NonLinearModelFit?

Is it possible to fix the parameters for NonLinearModelFit within the function itself instead of defining the fix parameters at the beginning of the notebook? I am ...
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42 views

How to approximate a computationally expensive 5-dimensional manifold?

I have a 4-parameter family of functions, which I'll refer to as y[a, b, c, d][x]. In this notation, a, b, c, d are the 4 ...
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0answers
43 views

Fitting data involving units

I want to fit some data to a model. However, if the data involves units in the independent variable, fitting seems not to work. As an example, consider the code ...
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0answers
49 views

fitting system of ODEs - “part2 of {} does not exist” errod

I'm trying to fit my data to a system of ODEs: x'[t]==a*x[t]+b*y[t] y'[t]==c*y[t]+d*x[t]+e*z[t] z'[t]==f*z[t]+g*y[t] having t,x[t],y[t],z[t]. I followed the code ...
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0answers
76 views

Speeding up Nonlinearmodelfit by constraining parameters?

I have a complicated parametric PDE that can be fitted to some data with NonlinearModelFit, but takes several hours to estimate the best values of the four free parameters. Currently, the code ...
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0answers
69 views

Simultaneously fitting data sets with many variables as free parameters

I found a partial answer in the documentation centre, but would like to expand on it and know how can I fit multiple sets of data and extract the parameters from them. It is an eigenvalue problem - We ...
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0answers
196 views

histogram fit for probability density

I am trying to fit the (probability density) histogram of some data with the exponential function, but I am having difficulties. My raw data are in file called ...
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0answers
41 views

Supply parameter values in NormFunction of FindFit

As I understand the input to the NormFunction is a list of residuals. Is there a way to get parameter values into the NormFunction as well? I ran into a problem where the norm depends on the values of ...
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0answers
73 views

Find Numerical Derivatives (With Errors) given some data

I have a question. Suposse I have some data with their respective errors: ...
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176 views

Non linear model fit mathematica

I want to fit experimental data (temp,alpha) to the following equation for calculating k and Ea -Log[alpha]^n = function(k,Ea,temp) However i do not know ...
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0answers
131 views

NonlinearModelFit with multiple parameters

I am now trying a slightly more complicated model which actually consists of finding the parameters of 2 particles in an Image (I attached an Plot of an image). Although I put very good initial values ...
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0answers
66 views

Fitting data set with series expansion

I have a function given in a form of a list: ScalarField={{$\epsilon$,$y_1$},..{1,$y_{3000}$}} It is defined in the range $(\epsilon,1)$ (spacing between grid points is homogeneous), where ...
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111 views

Using FindFit for step functions

Having used FindFit like so: ...
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0answers
100 views

Smoothing a function

NDsolve gives me a solution to a certain NL PDE. I want to evaluate the rate of exponential decay of the maxima of the solutions in time. So, I plot ...
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0answers
125 views

How could I code the following nonlinear regression?

I am an extremely limited user of Mathematica. Could someone tell me how to set the following nonlinear regression problem : Y = Sum[a[i] F[i,X] , i = 1,4] ...
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0answers
93 views

Inconsistent results in fits from NArgMin

EDIT: Just realized I had misspelled "inconsistent." I'm using version 7.0. I'm trying to fit a (noisy) data set to a large-order polynomial. (Just for context: there isn't a model for the ...
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0answers
170 views

Interpolating function as a model in Mathematica's procedures for fitting

Is it possible to use interpolating function with parameters as a model for NonLinearModel fit (and other integrated methods for fitting)? Similar question was already posted earlier - How do I find ...
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116 views

FindFit for dimension reduction?

Given an n-dimensional function, can I use FindFit to produce an approximate (n-k)-dimensional function? Here is a simplified illustration of what I am trying to do. I have $$f(x,a,b,\mu,\sigma) = ...
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267 views

Performance in parameter estimation from ParametricNDSolve using varied initial conditions

I have 250 data points from a timecourse exeriment in a list, with columns specifying (1) time, (2-4) initial conditions, (5) absorbance reading. I want to fit 4 parameters (k1, k2, k3, k4) in a DAE ...
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0answers
177 views

Fitting a theoretical density function with log-return sample

I am working on a exercise to fit a theoretical density function,presented below, with log-return series of a stock. $\frac{1}{2}a e^{a(x-\mu)} \quad \text{if x } < \mu $ or $ ...