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

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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 ...
0
votes
0answers
46 views

Incorporating sophisticated constraints on the approximating function into NMinimize

Following the approach as given in the answer of Belisarius here I just wonder how one could incorporate some more sophisticated requirements on the approximating function. Suppose the approximating ...
3
votes
1answer
134 views

Estimated Variance in LinearModelFit

Suppose that lmModel is a linear model which is fit using LinearModelFit. How come ...
4
votes
2answers
169 views

FindFit and NMinimize to fit a parametric model (minimize the distance of two curves)

I am trying to find a fit to the cumulative distribution of a set of points using FindFit or NMinimize. In particular, I would like to find the parameters of the cdf of the Beta Distribution that ...
7
votes
2answers
394 views

Maxwell fit in 2 dimensions

The histogram below shows the 2D-velocities v of a micrometer sized particle in a plasma measured from image to image (60 Hz) over 33,33 sec. I would like to fit ...
1
vote
0answers
57 views

FindFit with a sophisticated function (2), with corrected question and code

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simplier functions. In particular, I observe T(x) (this ...
0
votes
0answers
30 views

EstimatedBackground function on Mathematica 9

Is there a way to replicate the EstimatedBackground function on Mathematica 9?
1
vote
1answer
105 views

FindFit algorithm?

Does anyone know how to program a mathematica algorithm that does the same thing that FindFit does? Is there documentation of it somewhere? I assume it is a least ...
2
votes
3answers
153 views

Use NMinimize instead of FindFit for constrained search (of coefficients)

(My problem is more complex, but let us formulate it through this example) I am trying to find the best polynomial approximation to the following function ...
0
votes
0answers
61 views

Using the results of FindPeak in FindFit

Using FindPeak on some datapoints, I have found the positions and values of likely Gaussian peaks which form the data. The format is ...
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 ...
3
votes
3answers
183 views

FindFit with a sophisticated function (integral)

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simpler functions (two polynomials), that is the model. ...
4
votes
1answer
76 views

Proper command to fit a distribution with data incomplete in a known way

Here is my scenario: got some data that I have to fit to a specific parametric family of probability distributions (cannot be changed). Data consist of several bunches of integers between, say, 0 and ...
3
votes
0answers
57 views

LinearModelFit gives bad fit for simple data set [closed]

I want to fit the rather simple data set: ...
0
votes
1answer
87 views

Meaning of << >> in Mathematica [duplicate]

I used NonlinearModelFit to fit some data and although Mathematica thinks it has got the result, the answer is enclosed in these double angular brackets. What does it mean? More importantly, I cannot ...
2
votes
2answers
282 views

Help with NonLinearModelFit

I have a question about fitting data with a model. I have a quite complicated model, based on Arctans, modified Bessel functions, etc, that I want to fit to my data, a table of couples (minimal ...
-2
votes
1answer
107 views

A piecewise function with way too many pieces

I'm currently calculating a periodic square wave current function to feed into a particle accelerator. It's a square wave that ramps up to a certain frequency and then drops back to the base frequency ...
0
votes
0answers
60 views

FindFit giving many errors when given model produced by ParametricNDSolveValue

I am trying to use FindFit to determine 7 parameters using 7 differential equations based on data imported from Excel. A sample of the data is: ...
8
votes
2answers
121 views

Behaviour of RegionDistance with Ellipse?

The data is: data = {{13, 60}, {36, 35}, {70, 29}, {106, 41}, {118, 72}, {94, 94}, {49, 99}, {24, 85}}; When I try to find a fit circle,So my method is work ...
0
votes
2answers
75 views

Fit a polynomial/curve to an NIntegrate result

I want to NIntegrate a function which also contains some parameter. In the end, I would like to plot the result as a function of one of these parameters. The thing ...
1
vote
0answers
159 views

NonLinearFit running too slowly when the model contains an integral [closed]

I am new to Mathematica and am learning to use it. I have come up with the following situation where I have to fit the data. ...
1
vote
1answer
98 views

Problem with NIntegrate and FindFit [closed]

I fit the experimental curve with the model using the following equation, ...
1
vote
0answers
48 views

Problem with curve fit using integral [closed]

I need fitting a Langevin function on a experimental data, but one parameter must be firstly optimized by using a Lognormal distribution. The complete expression could be written as: The integrate ...
1
vote
2answers
132 views

stop rule for Nonlinearfit and best fit

I want to understand the rule under which the function Nonlinearfit stops to give the final result. I know that if the number of iterations exceeds ...
2
votes
1answer
65 views

Negative adjusted coefficients of determination - why?

I am trying to fit a polynomial function to some multi-dimensional data. However, I am getting a negative $R_{adj}^2$ as you can see: ...
1
vote
2answers
55 views

Find function to relate two lists of values

I know Mathematica has the FindFit function to determine the parameters of a known function that fits a sequence of points, but what if you do not know the relationship (linear, log, quadratic, etc)? ...
2
votes
2answers
112 views

Solving coupled ODEs with NDSolve to fit experimental data

I need to fit a multi-exponential data (Intensity x Time) using a model consisting of three differential equations. I want to find the parameters that gives the best fit to the experimental data. ...
2
votes
1answer
224 views

Non-linear curve fit problem

I am having a problem with making a fit to data in Mathematica, which may involve my understanding of the methods available. I am trying to fit the derivative of a Frota function (which is a Single ...
1
vote
3answers
194 views

Fit dataset with customized discontinuous distribution

I have the following parametric CDF: F[x_, λ_, β_, γ_] = Piecewise[{ {0, x < 0}, {1 - (1 - β) E^(-x λ), 0 <= x < γ }, {1, x >= γ} }]; ...
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
2answers
96 views

Problem with a simple Fit

I have defined two functions to fit $\dfrac{a}{\sqrt{x^2-b^2}}$ and $\dfrac{a}{\sqrt{b^2-x^2}}$. ...
0
votes
0answers
29 views

Save lists to re-open with Mathematica [duplicate]

I want to save a result of a computation in a file to re-open then in Mathematica in a new session. What is the most efficient and simple way to do this? To be specific, I am using ...
1
vote
0answers
47 views

Evaluation of likelihood very slow

I am trying to implement a simple statistical model for the first time in Mathematica. My model is made my one random variable which is the sum of background and signal. Background is an exponential ...
7
votes
0answers
128 views

FindFormula Control [closed]

FindFormula is great start on the path to full symbolic regression and I realize it's level of development is only experimental at this stage. But if I happen to ...
10
votes
1answer
316 views

Fittting data with combination of an unknown number of Gaussians

I have data that I want to fit with a constant plus a combination of Gaussians, with their actual number being one parameter of the fit (besides the average and the variance of every one of them). ...
0
votes
1answer
55 views

Extract coefficient from LinearModelFit [closed]

I want to know how to extract the coefficients from the result of LinearModelFit. The functions used to fit are complicated and being in different forms. For ...
6
votes
1answer
94 views

Extracting fit weights directly from a FittedModel object

Suppose I have the following data: ...
7
votes
3answers
199 views

Fitting data with interdependence

I have an issue, of which I'm not sure it can be solved, with or without Mathematica. I feel as if it should be possible, but I'm quite clueless as to how. Some introduction is required. I'm working ...
3
votes
2answers
184 views

Automatically detect higher slope in numerical data (within a certain range)

Suppose the dataset data is part of some simulations whose results should follow a certain model. Here is data and its ...
1
vote
1answer
157 views

Linear Fit of multidimensional data

I am trying to find linear decomposition of vector B (of arbitrary dimension $n$) in the form : $B = \alpha_{1} C_{1} + \alpha_{2} C_{2} + ...$ where $C_{i}$ are known vectors (of dimension $n$) ...
3
votes
2answers
248 views

Finding the FWHM of a NonlinearModelFit gaussian [duplicate]

I have a NonlinearModelFit in a very large program, f1 = NonlinearModelFit[d1, a Exp[-(b (x - c1))^2] + yoff, {a, b}, x] Which is used in my program to produce ...
19
votes
2answers
401 views

Sensitivity of NonlinearModelFit to model

I have come across a circumstance where NonlinearModelFit is very sensitive to the model used. I am aware that NonlinearModelFit ...
7
votes
3answers
172 views

Make NonlinearModelFit return continuous function

Suppose I want to fit the dataset ...
4
votes
0answers
171 views

Goodness of Fit of Copula Distribution

I am trying to find out goodness of fit of copula distribution, but Mathematica 10 gives me the same answer for each copula type. e.g ...
3
votes
2answers
148 views

Estimate parameters of AR1 process

I am trying to estimate the parameters of a series $Z_t=W_t^\beta$, where W_t follows an AR1 process with mean 2, $\rho=0.9$ and $\sigma=0.1$: $W_t = \rho W_{t-1} + (1-\rho) \bar{W} + \epsilon_t$ ...
2
votes
1answer
164 views

Why does FindFit work and NonlinearModelFit does not?

I have a somewhat complicated function that I have defined. ...
4
votes
2answers
100 views

How to use Evaluation Monitor in conjunction with NonlineaModelFit?

I am trying to find out how many function, gradient and hessian evaluations are made when i run NonlinearModelFit for example in this case ...
0
votes
1answer
146 views

How to speed up NonlinearModelFit applied on a NDSolve solution?

I'm trying to perform fittings of a model defined through a system of ODEs to data consisting of time courses of a measured quantity. As described in a previous question, the system of ODEs is as ...
2
votes
1answer
202 views

Fitting one set of data with two function

I have a set of data (42 points): ...
2
votes
1answer
106 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: ...