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

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6
votes
2answers
860 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
0answers
290 views

Problems extending NelderMeadMinimize into 2D

Update The eventual route I followed was to adapt a version of the NM-simplex written in C and link to it with MathLink. Once I've tested this out fully I'll post it here. I've been playing around ...
5
votes
3answers
934 views

Finding exponential model from data [duplicate]

I'm trying to find an exponential model from data for a homework problem. There is an accompanying video explaining how to do the bigger problem but it omits any instructions on the step where the ...
5
votes
3answers
239 views

Removing background from peak function

Let's say I have a a very large list of data in the format {{n,f[n]}} so something like {{1,600},{2,700},{3,1100}...} and if this data is plotted, then it will look like a sum of Gaussian functions+a ...
5
votes
1answer
288 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
4answers
938 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 ...
5
votes
1answer
262 views

FindFit returns “tensors have incompatible shapes”

I'm trying to fit experimental data with FindFit and implicitly calculated function. It seems, that function works fine and satisfactorily approximates data when parameters are fed manually. However ...
5
votes
1answer
259 views

Forcing NonLinearModelFit through a point

Like the title says, is there a way to make an NLM fit pass through a specific point.
5
votes
3answers
407 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
1answer
320 views

LinearModelFit with millions of rows

I'd like to do a simple regression with millions of rows of (x,y) data. It seems to be too long for Mathematica. Is there a way to speed it up? It shouldn't be that hard to do, I am not sure what ...
5
votes
2answers
646 views

How to fit one distribution to another?

I have a custom distribution created to model some experimental observations. While too complicated to include in this question, I can provide an example and some illustrations to convey a sense of ...
5
votes
1answer
238 views

How are p-values in fittings estimated?

I am trying to understand how p-values retrieved in a ParameterTable estimated but I couldn't find any specific information in the documentation about this. For instance, considering ...
5
votes
2answers
468 views

How to find Matano plane

I have discrete collection of data points (10 to 10^4). I want to describe them by a continuous function and find a x value z, ...
5
votes
1answer
105 views

Why is NonlinearModelFit not working?

I have a set of x,y-values ...
5
votes
1answer
498 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 ...
5
votes
3answers
175 views

Better output for NonlinearModelFit “ParameterTable”

The Standard table fo parameters of NonlinearModelFit is obtained from NonlinearModelFit[{{0, 1}, {1, 2}, {3, 3}}, a + b*x, {a, b}, x] %["ParameterTable"]] I ...
5
votes
2answers
186 views
5
votes
1answer
968 views

Does LinearModelFit perform an ordinary linear regression (least squares)?

Does LinearModelFit give an ordinary linear regression? I see lots of options, but nothing like "least squares" or OLR.
5
votes
1answer
186 views

How to fit data to a convolution equation

How to fit data to a convolution equation: ...
5
votes
2answers
3k 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: ...
5
votes
1answer
135 views

What does LinearModelFit depend on except for its arguments?

I thought this would be always true, but most likely it returns false. ...
5
votes
1answer
683 views

Fit data with linear combinations of Cos and Sin

Recall that if $f$ is a piecewise continuous function on the interval $[-\pi, \pi]$, then the Fourier series of $f$ is $$f(x) = \sum_{n=0}^{\infty} (a_n \cos(nx) + b_n \sin(nx)).$$ See for example, ...
5
votes
1answer
259 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
389 views

Specify a constraint on an interval under FindMinimum

I have an interpolated function that looks like this: $\hskip1.2in$ and, based on extreme and critical points, I want to use a polynomial to approximate the function. The points in question are: ...
5
votes
1answer
325 views

ODE fitting to dataset

So, I have a ODE system, it is a complex biochemical kinetic mechanism with six species changing over time. ...
5
votes
2answers
849 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: ...
5
votes
1answer
516 views

Time approximation of decrypting RSA algorithm

I've written a function that encrypts a text using the RSA algorithm. It then decrypts it using prime factorization, and takes the time it took to decrypt it and puts it in a vector together with the ...
5
votes
1answer
1k 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 ...
5
votes
1answer
211 views

Modeling of soccer results using GeneralizedLinearModelFit

I am trying to recreate the regression in "Analysis of sports data by using bivariate Poisson models," which can be found here, ...
5
votes
0answers
93 views

Ridge and lasso regression missing? [closed]

There is no implemented command to perform ridge or lasso regression? I couldn't find it in the documentation. Might be there are add-on packages I am not aware of.
5
votes
0answers
110 views

Multivariate Adaptive Regression Splines (MARS) - Mathematica implementation?

Does anybody have or know of a Mathematica implementation of the Multivariate Adaptive Regression Splines (MARS) algorithm?
5
votes
0answers
160 views

Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code ...
5
votes
0answers
94 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
votes
0answers
749 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
votes
3answers
784 views

Output of NonlinearModelFit differs from the correct result

I'm having a bad time dealing with the NonlinearModelFit in Mathematica 8, since the result given is a bit imprecise. An example is given on potential regression, ...
4
votes
1answer
2k views

NonlinearModelFit does not find a good fit

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

Problem with fit on a numerical function

My question is related to a previous one: Problem with simple fit, where I had a problem to fit a simple analytic function $\dfrac{a}{\sqrt{b^2-x^2}}$. The solution proposed in Problem with simple ...
4
votes
4answers
782 views

Remove linear trend from data

I have a large data set with 150k lines and two data columns. I noticed that there is a linear trend, which I want to remove. So, I do the following: first fit with a linear model ...
4
votes
1answer
2k views

How to make a multi-peak histogram fitting

I got a multipeak histogram from my data and want to fit it using a Gaussian Distribution function. ...
4
votes
4answers
187 views

Fitting Coxian distribution to some data

I'm trying to fit a transformed (actually shifted to the right) Coxian distribution to some data ( if needed an example set is here Sim data ). I've tried a number of ways for this: ...
4
votes
5answers
3k 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, ...
4
votes
2answers
590 views

Best fit equation from a scanned image

I am trying to extract a curve from a scanned graph and find a best fit equation. For example, starting from: How could one find an equation starting from the image file ?
4
votes
3answers
333 views

Plot least squares curve on Linear Log Plot

I have the following Data: ...
4
votes
2answers
795 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 ...
4
votes
1answer
2k 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 ...
4
votes
2answers
165 views

How to find analytical expresion for data from image

I need to find an analytical expression for the data collected from an image. I found a relevant topic on how to extract the data in here. But there are some differences in my question. I have this ...
4
votes
2answers
96 views

Problem with a simple Fit

I have defined two functions to fit $\dfrac{a}{\sqrt{x^2-b^2}}$ and $\dfrac{a}{\sqrt{b^2-x^2}}$. ...
4
votes
1answer
1k 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
744 views

How do I draw a credible velocity vs. time graph using Locators?

This is partly a math question, partly a Mathematica question. For educational purposes, I'm making a simple demonstration to create a velocity over time graph from six locators. On the basis of ...
4
votes
2answers
224 views

Fit model with two dependent variables

Say I have an experiment that produces two values, for a given input. For example you get a complex response value. Now I have a model that - of course - also produces two dependent values for one ...