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

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20
votes
2answers
3k views

How to fit 3 data sets to a model of 4 differential equations?

I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
23
votes
5answers
9k views

Estimate error on slope of linear regression given data with associated uncertainty

Given a set of data, is it possible to create a linear regression which has a slope error that takes into account the uncertainty of the data? This is for a high school class, and so the normal ...
27
votes
5answers
6k views

How to perform a multi-peak fitting?

I am wondering how to implement the multi-peak detecting and fitting in Mathematica. Following is an example of fitting the data using three peaks (such that the data ~ peak1 + peak2 + peak3). The ...
19
votes
5answers
7k views

Problem with NonlinearModelFit

I'm having trouble with a non-linear fit: fit = NonlinearModelFit[data, y0 + A Sin[\[Pi] (x - xc)/w], {y0, xc, A, w}, x] where ...
36
votes
4answers
6k views

Simultaneously fitting multiple datasets

What is the proposed approach if one wants to simultaneously fit multiple functions to multiple datasets with shared parameters? As an example consider the following case: We have to measurements of ...
18
votes
3answers
2k views

Fitting fractional complex data with NonlinearModelfit

I've difficulites with the NonlinearModelFit function. In principle Mathematica should be able to deal with complex data. E.g. if I define the following table ...
15
votes
4answers
6k views

Using FindFit to fit $a\,b^t$: how to avoid introducing complex numbers?

I'd like to find a model $f(t)=a\,b^t$ which matches the following data ...
13
votes
4answers
1k views

Implementation of smoothing splines function

I have some problems in writing a module for spline smoothing. Actually, I have been trying for about two weeks. My listing is here: ...
13
votes
6answers
11k views

How to determine the center and radius of a circle given some points in 3D?

I was wondering if anyone could give me a hand with this problem I have. I have six points on a plane, and I am trying to determine if they form a circle or not. I know that any three points in 2D ...
21
votes
4answers
2k views

Mathematica envelope for the bottom of a plot, a generic function

I have the following set-up: xaxis = Table[x, {x, 0, 10, 0.01}]; yaxis = Table [Sin[x] + Abs[RandomReal[{-1, 1}]], {x, 0, 10, 0.01}]; ListLinePlot[Transpose[{ xaxis, yaxis}]] My ...
12
votes
3answers
3k views

How to use FindFit to fit an implicit function?

Now I am trying to fit some data with a implicit model function. Firstly, I tried a toy example. Toy example with input and output ...
27
votes
5answers
2k views

Fitting points to tilted, off-center ellipse

I have 24 x-y points that are supposed to form an ellipse. ...
8
votes
4answers
7k views

Fitting a two-dimensional Gaussian to a set of 2D pixels

Imagine I have a set of data like the following: ...
11
votes
2answers
3k views

FindFit returns worse result when putting constraints on parameters

I want to fit some data to a model of exponential decay using the FindFit function: ...
9
votes
1answer
733 views

How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
3
votes
1answer
1k views

Combined fitting via NonlinearModelFit

I am trying to fit my data to a combined function model. Say I have two functions with some common parameter(s) f[x_]:= a*x^2 + b*x + c g[x_]:= d*x^2 + e*x + c ...
2
votes
2answers
287 views

Fitting a variable using multiple equations

I would like to find the best fit of two variables for a number of approximate equations, such as: 1x+2y+2=7.04 2x+y+4=7.98 1.5x+1.5y-2=2.53 1.8x+3y-1=6.77 That ...
40
votes
4answers
3k views

How to visualize 3D fit

I have a data set of x,y,z values and I fit a function of x,y to the data. This works, but I can't come up with a nice way to ...
19
votes
1answer
2k views

Finding the area, algebraic curve and jaggedness of an arbitrary shape

I start with a photograph of a shape (physically made by the flow of a liquid into another), of which I can extract the border, manually or using Mathematica's feature detect feature : Using the ...
16
votes
1answer
516 views

Difference between Fitting Algorithms

I am new to Mathematica, and I don´t quite understand, what the difference between the fitting algorithms Fit, FindFit, ...
12
votes
2answers
753 views

Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?

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 ...
5
votes
1answer
2k views

Methods for NonlinearModelFit

I am using NonlinearModelFit for a thesis project. I get quite different results if I change the Method to LevenbergMarquardt or QuasiNewton or ConjugateGradient ...
4
votes
1answer
629 views

Fitting piecewise functions

I have several large data sets which follow the following pattern: A position is measured, a force is applied until a new equilibrium is found. I'd like to find a fit for the position, at least at the ...
4
votes
1answer
1k views

NonlinearModelFit does not find a good fit

I am trying to fit my data to the following function, $$\frac{a b t \left(\log \left(\frac{-a d t+a t-1}{a d t}\right)-2\right)}{4 (a t-1)}-c$$ ...
9
votes
2answers
459 views

Does FindFit support complex numbers or doesn't it?

Inspired by this previous question: Findfit doesn't give the good fit; Changing the starting values will not change the results. Consider the following complex-valued dataset. ...
17
votes
2answers
1k views

FindFit returns Infinity::indet error when data contains {0,0}

Let's consider the following data: data = Table[{q, 2*q^2}, {q, 0, 2}]; and then, do a very simple fitting to this data: ...
4
votes
2answers
190 views

Unable to fit function convolved with NIntegrate with FindFit even with NumericQ

I am attempting to fit to the convolution of a simple function with a Gaussian. (I realize this could be done with Convolve also, but I thought I could make it go faster this way). I am able to ...
4
votes
5answers
2k views

How to plot Fit functions?

If I do something like this f[x_]:=x^2 Plot[f[x],{x,1,10}] Mathematica plots the function $f(x)=x^2$, as expected. However, ...
1
vote
1answer
189 views

how to find curve fitting parameters without an explicit relation between x and y?

Let's say I have some experimental data (x,y) and I want to find some fitting parameters. But in my mathematical model, the fitting parameter are not in a simple equation that relates x and y. For ...
1
vote
2answers
372 views

Can't find a fit for Erf

I have the following numbers ...
2
votes
2answers
365 views
23
votes
5answers
2k views

Mathematica Implementations of the Random Forest algorithm

Is anyone aware of Mathematica use/implementation of Random Forest algorithm?
21
votes
3answers
2k views

Data fitting with Image processing feature detection

I have some 2D data that once plotted looks like the following ...
27
votes
2answers
430 views

What is behind Mathematica's experimental `FindFormula` function?

In version 10.2 there is a new experimental function: FindFormula. I suspect that a genetic programming algorithm (symbolic regression) is behind this new feature ...
14
votes
3answers
1k views

Fitting ellipse to 5 given points on the plane

Five points are required to define a unique ellipse. An ellipse has five degrees of freedom: the $x$ and $y$ coordinates of each focus, and the sum of the distance from each focus to a point on the ...
2
votes
1answer
376 views

Model fitting to noisy data with a custom minimization function

I'm looking into fitting some data with Mathematica. I've got my head around how NonlinearModelFit works (I've been using the Levenberg-Marquardt algorithm for some ...
8
votes
1answer
267 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
8
votes
3answers
1k views

Ηow to create an interpolated CDF from its samples?

I want to use a distribution I have only aggregate statistics on, namely its CDF sampled at certain points. I would like to keep it "nonparametric" (remain noncommittal on the parametric form), but I ...
5
votes
4answers
636 views

Estimating a distribution using binned data

I have data from which information has been irretrievably lost through binning and I am trying to find a plausible distribution from which it derives. There is an academic paper suggesting that the ...
7
votes
1answer
290 views

Computing launch parameters for hitting a point in 3D with projectile under influence of wind

The end goal of this problem is to compute functions which describe the launch parameters which are needed to hit a specified goal in 3D in the presence of wind disturbances. This is as far I have ...
2
votes
0answers
833 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 ...
4
votes
0answers
216 views

Using FindFit to fit nonlinear ODE parameters, subject to a constraint (an inverse problem) [duplicate]

Similar to this post I am finding that constraints tend to make FindFit poor at finding a good fit. However, unlike the previous post, the constraints are required ...
3
votes
1answer
226 views

Test Goodness of fit for FindFit

Is there any way to get an estimate of the goodness of fit from FindFit, for instance getting the final error? The documentation doesn't provide any hints, and a quick Google search didn't return any ...
4
votes
2answers
664 views

What can I do to eliminate the error FindFit::nrjnum:?

I am testing the "Power Law with finite-time singularity" hypothesis for world population growth for a project. The data I'm using (same behaviour should also be exhibited by the stock market, thats ...
3
votes
2answers
795 views

How can I consistently get a good logistic regression fit?

I'm executing the command NonlinearModelFit[data, c/(1 + a Exp[-b x]), {a, b, c}, x] with the data being ...
2
votes
1answer
108 views

FindDistributionParameters and Hypothesis Testing

Please excuse me if I am making any logical error in posting this question since I am not a math major. However, let me post my question. I am trying to fit multivariate parametric distribution to ...
1
vote
0answers
220 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 ...
1
vote
1answer
1k views

Keeping Nonlinear Model Fit Real

So I am using the NonlinearModelFit (NLM) command with a fairly simple function. There are 4 unknowns and the (x, y) points that ...
0
votes
1answer
122 views

Non linear model fit

I need to fit this, but for some reason I cannot... data = {{0.617,0.8}, {0.605,0.6}, {0.5997,0.4}, {0.5972,0.2}, {0.5985,0.1}}; soln = NonlinearModelFit[data, {y - 2478.82*wlog[kc + 1]}, {y,w,k}, ...
27
votes
4answers
749 views

What is the natural way of using Dataset to get a FittedModel?

The new Dataset in Mathematica 10 is a great addition to the language, potentially reducing the convenience gap with R. Given this, I would like to understand what the equivalent simple or natural ...