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

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18
votes
0answers
707 views

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 ...
18
votes
1answer
406 views

Unexpected behavior of confidence bands for data presenting two regions with uneven noise

Let's generate some noisy data with uneven noise. ...
13
votes
3answers
398 views

Disentangling the data

An experiment yields a functional dependence on two variables $F(x,y)$, can be imagined as a 2D map. It is known that the function can be factored as follows $F(x,y)=fx(x) gy(y) +gx(x) fy(y)$. Given ...
9
votes
2answers
2k views

What is the best distribution for my histogram?

I defined a security bound for a random walk (cube with 15 lengh) and i have this code to obtain a sample of the random times at which the random walk crosses the boundary for the first time: ...
7
votes
1answer
151 views

How to derive SinglePredictionBands from a NonlinearModelFit model

I have found NonlinearModelFit to be extremely useful in my work. Here I have fit 4 points to a function and am being asked to explain how the 95% SinglePredictionBands associated with the plot below ...
13
votes
1answer
542 views

Does anyone have experience with performing symbolic regression using Mathematica?

I understand that there is at least one Mathematica package, DataModeler commercially available for symbolic regression. I'm seeking any observations with this or any other similar tool. I'm ...
6
votes
1answer
1k views

How do I find the best parameter to fit my data if the model is a interpolating function?

Hi I have a question regarding to find the best parameters for my model to fit my data. I have 3 ordinary equation, and I now just picked some parameters (...
6
votes
2answers
286 views

2D smoothing spline interpolation

Does Mathematica have 2D smoothing spline interpolation built in? I requires an interpolation method with smooth first derivatives and cubic bivariate splines fulfill this nicely. In python I would ...
4
votes
3answers
197 views

How to fit parameters in a system of coupled differential equations

Problem description: I'm studying a chemical reaction that can be modeled by a system of coupled differential equations, and I want to use measured data to determine the parameters that appear in the ...
0
votes
2answers
173 views

Least Square Fitting

stuck on a mathematica assignment and could really use some help. A) Fit a function with the shape log(Y) = a0 + a1log(U) to the datapoints (log(Ui), log(Yi) with an least square fitting. Show this ...
7
votes
0answers
258 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?
6
votes
1answer
560 views

Having trouble fitting data using NonlinearModelFit

I'm trying to fit data = {{2002, 45000}, {2004, 90000}, {2005, 120000}, {2013, 211000}}; to an exponential function ...
6
votes
2answers
222 views

Implement planar correction for skewed 3D profilometric data

I have some data that represents small-scale surface topography. The data is planar but not flat because it's impractical to level this microscope to a tolerance of microns. It looks like this: I'd ...
5
votes
1answer
135 views

Intersection of a ListPlot3D surface with a plane

I'm trying to use Mathematica to analyze some physics data from an experiment, more precisely, I have to fit a 2D data series with a one dimension function. At the moment I'm able to load and plot ...
5
votes
1answer
216 views

Is there any strategy to have a compiled version of FindFit or NonlinearModelFit?

Disclaimer: This is not a precise question with a definite answer. I know that neither FindFit nor NonlinearModelFit is in the ...
5
votes
3answers
353 views

Determing two Nonlinear model fits with 95% confidence bands from one data set

I have the following data which is postulated to have contributions from two different sources .....as can be seen from the confidence band, many points are out of the band. Question: How can I ...
5
votes
2answers
2k views

In finding a logarithmic fit for some data (of the form a*Log[b*x]), WolframAlpha succeeds where Mathematica 7.0 fails, why?

I would like to fit a function of the form: $a \log(b x)$ to a set of data: ...
4
votes
1answer
198 views

Find a Fourier series from discrete data

I am trying to fit a Fourier cosine series to discrete data. I read through this, but I was not able to understand it. The data should be periodic with a period of $0.2 \text{ m}$, and it is the ...
4
votes
2answers
578 views

Linear regression in a chosen range of points

Hi I'm absolutely newbie in Mathematica and have following problem: My list looks like {{50, 0.75}, {51, 0.76}, ..., and I want to choose a range out of my ...
1
vote
2answers
194 views

Is it possible to monitor the sum of squared errors in a NonlinearModelFit or FindFit procedure during the process?

Since fitting procedures using NonlinearModelFit (or FindFit) sometimes take very long, I would like to monitor the sum of ...
6
votes
3answers
220 views

Looking for ideas for handling a complicated fitting problem

I have the following data: ...
6
votes
2answers
650 views

Find parameters of ODEs to fit solution data

Problem How to find the initial conditions x[0],y[0] and the optimal value of parameters ...
6
votes
1answer
446 views

Mathematica vs Sigmaplot (Non LinearModelFit)

I asked a question in a previous post that was closed because "The title of the question is not correct and the issue here is too trivial to help anyone later". NonLinearModelFit It's possible ...
5
votes
2answers
661 views

Numerical Integration as Model for Nonlinear Fit

I'm trying to do a fit for parameters of a function within an integral but I'm getting errors when I try and run it. Essentially I want the following fit to work out: ...
4
votes
1answer
272 views

FindFit not giving a good fit despite good initial parameters

I'm having a problem with FindFit not giving a good fit to my data, even though the initial parameters I give look really good when plotted. The fitting function is ...
3
votes
1answer
134 views

Troubles with FindFit for ODE

I need to use FindFit for ODE with arbitary number of parameters. This code (from documentation) works: ...
3
votes
3answers
257 views

Plot least squares curve on Linear Log Plot

I have the following Data: ...
3
votes
3answers
338 views
3
votes
2answers
1k views

Line of best fit on LogLog plot

I have a LogLog plot, and i'm unsure about how to fit a line to it. The data represents a calibration curve. ...
3
votes
2answers
335 views

How do I find the best fit?

I am trying to solve following system of three differential equations ...
3
votes
1answer
573 views

How to adjust parameters to experimental data on a NDSolve problem

I have 2 differential equations with 2 variables, x and y,which are a function of t and I have the parameters k1, k2 y k3. ...
3
votes
0answers
384 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 ...
2
votes
1answer
79 views

Fails to apply NonlinearModelFit on a numerically evaluated model defined as a system of ODEs

I call for your help with because I'm getting troubles to fit a model defined through a system of ODEs. The system of ODEs is as follows: ...
2
votes
2answers
118 views

FindFit working with Integrate but not NIntegrate - I am using “?NumericQ”

I'm having some syntax problems with finding a fit to an equation that doesn't have an analytical expression for it's integral. Because I think the problem is one of syntax, I am substituting a ...
2
votes
1answer
2k views

Problem with NonlinearModelFit: “The function value… is not a list of real numbers…”

I'm trying to use NonlinearModelFit to fit the data: ...
2
votes
1answer
149 views

making a function of fit results

I have 13*25 datasets consisting each of around 40 points. They are all linear I can easily fit them using fit function but my problem is when I want to call them I want them to be functions. I want ...
2
votes
0answers
377 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
votes
1answer
666 views

Problem with NIntegrate in NonlinearModelFit

We are receiving many error messages when using NIntegrate with NonlinearModelFit. Here is a much-simplified version of the code. It arrives at the correct answer after several messages saying that it ...
1
vote
1answer
102 views

Interpreting P-Value on ParameterTable

When using LinearModelFit[] we can generate a table of parameter values and statistics for the corresponding model using the property "ParameterTable". Looking in the documentation I can't find an ...
1
vote
0answers
77 views

Simultaneous fitting to multiple data sets with multiple variables and some common parameters [duplicate]

I am trying to fit two data sets to a function model described below which share a few common parameters. Say I have two functions with some common parameter(s) ...
1
vote
1answer
59 views

Why does my Dynamic NonliearModelFit keep running?

I have complex data and which I am fitting to a complex formula. In order to use NonlinearModelFit I split the formula and the data into real and imaginary parts. ...
1
vote
0answers
48 views

How to fit data with numerical solution of system of parametric ODE? [duplicate]

I need to find the parameters (k1,k2,k3,k4,k1r,k2r,k3r,k4r) that fit my data (list of [Intensity, time]) using the function ...
1
vote
2answers
89 views

FindFit is producing a list of imaginary numbers when there is non

I am trying to find the fit of an equation to some data and mathematica thinks there is a list of imaginary values. My data is all real positive number. ...
1
vote
1answer
210 views

NonLinearFit with “complicated” integral model

I have a set of data $y_i (z_i)$ with errors $\Delta y_i$ ...
1
vote
1answer
309 views

FindFit::nrlnum What am I doing wrong?

I have a model called qobs: ...
1
vote
1answer
359 views

Can ParametricNDsolve be used for coupled PDEs with 5 parameters?

I have a system of coupled PDEs with five parameters that I only know ranges for rather than explicit values, and I was wondering if I could define a parametric equation with ParametricNDSolve and ...
1
vote
1answer
450 views

Fitting data using a differential equation

I have data generated from two functions given below. How can I go about finding a fit of the form: y'[x] == -(a + b/(c + d y[x] + e F[x] )) where a,b,c,d,e are ...
1
vote
1answer
204 views

How do I construct a non-linear model from experimental data?

I want to find a function $w=f(x,y,z)$ that fits experimentally determined values of w. For example, assume ...
1
vote
1answer
610 views

Problem using NDSolve

This might be some simple mistake, but I am running out of ideas. I am trying to fit an ODE system to some data. This error keeps appearing NDSolve::nlnum: "The function value {0.299812 - ...
1
vote
1answer
298 views

System Identification with large Input/Output Data

I have some questions about system identification. I made some measurement of current step (input) and voltage response(output) and I want to fine the parameters of my impedance. The sample rate is ...