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

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4
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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
167 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
99 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
755 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
248 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 ...
4
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1answer
124 views

Mystifying failure of NonlinearModelFit

Fitting the following two time-series (two repeats of the same exponential growth process) ...
4
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1answer
304 views

Removing Linear drift from an oscillating data

I have an array of 800,000 data measured at 1.1s time gap. It is oscillating data but has clear linear drift. I want to remove this linear drift. But the estimates by ...
4
votes
1answer
690 views

How to get confidence bands of parameters from a fitting procedure?

I have done fitting of data points with a given model that has two parameters (A and B), using NonlinearModelFit. The result of the fit is the maximum of the ...
4
votes
2answers
187 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 ...
4
votes
2answers
297 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
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1answer
3k views

NonlinearModelFit::cvmit: Failed to converge to the requested accuracy or precision within 100 iterations

I have got a problem in my program with NonlinearModelFit: ...
4
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2answers
106 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 ...
4
votes
3answers
314 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 ...
4
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1answer
426 views

Fitting numerical model to experimental data

I have diffusion equation with the initial/boundary conditions: ...
4
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1answer
414 views

Using a user defined NormFunction in FindFit or NDSolve

I would like to use a different norm instead of the 2-norm in FindFit (Mathematica 9). For example, instead of using $$\sqrt{\sum (x_{\mathrm{model}} - x_{\mathrm{...
4
votes
1answer
659 views

Why FindFit could not exactly fulfill condition?

I tried to fit some data with boundary conditions, but FindFit just could not work. Does anyone know the reason? Details: The function to be fitted is ...
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 ...
4
votes
1answer
348 views

TimeSeriesModelFit incorrect?

I am trying to determine the optimal model for time series data (1592 observations). When I run TimeSeriesModelFit, Mathematica selects $AR(1)$ model, the estimated ...
4
votes
2answers
371 views

NonlinearModelFit: fit a vector-valued function to a data vector

I have a vector of data points: data = 10 Sin[#/10] + RandomVariate@NormalDistribution[] & /@ Range[200]; And I have model that provides the complete ...
4
votes
1answer
116 views

FindFit runs extremely slow for my Function,how do I optimize this?

My function is the first order Bessel Function, and I am basically just trying to get this to fit in a way that does not take forever. I define the function as follows, (it seems to work faster if I ...
4
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2answers
2k 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. ...
4
votes
1answer
317 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 ...
4
votes
2answers
808 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 ...
4
votes
1answer
92 views

Fitting real and imaginary parts of a function

I have an analytic form of a function G[w_] = -I*z0*w/(1 + I*z0*w*a) I know this function can be obtained (up to some overall normalization) from solving a ...
4
votes
1answer
124 views

Substituting ParametricNDSolve for NDSolve

This is my first post so let me know if I need to format things differently. I have been using NDSolve for most problems which optimize parameters for ODEs. I believe that ParametricNDSolve would be ...
4
votes
1answer
348 views

Fitting triangular function with HeavisideTheta

I have a problem fitting a triangular function (like potential vs. time in cyclic voltammetry) with a HeavisideTheta function. I just want to get used to ...
4
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2answers
170 views

Remove redundant parameters from equation

I have random expressions like (b1 x + b2 x)/(b3 + b4/b5 x) + Sin[b6 x] where $x$ is a variable and {b1, ..., b6} are parameters to be fitted. This expression is ...
4
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1answer
2k views

How does Mathematica estimate error on fit parameters?

When performing a fit using NonlinearModelFit (or any of Mathematica fitting functions, but I am particularly interested in nonlinear models), Mathematica makes a ...
4
votes
2answers
793 views

FindFit for a differential equation model with multiple variables?

I'm trying to figure out how to use FindFit with a multivariable differential equation model and data. I've successfully made it work for the one-variable version ...
4
votes
1answer
241 views

How to Use ProbabilityScalePlot with Censored Data?

I am trying to reproduce a ProbabilityScalePlot of censored data shown here (see Sample Analysis Plot). Here is my Mathematica code. First I deal with the uncensored case. ...
4
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0answers
98 views

Fitting data with unique variable per measurement

Imagine we are in the following situation, we have a nonlinear system of functions $f$ with coördinates $x_i$, and unknown parameters $\delta_i$'s and $t$. Let this system be defined as, \begin{...
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0answers
173 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 ...
4
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0answers
317 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 ...
4
votes
0answers
219 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 ...
4
votes
0answers
410 views

To what extent can NonlinearModelFit be sped up? [on hold]

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 ...
3
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3answers
438 views
3
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3answers
991 views

Fitting - Exponential

I'm trying to fit the following data using Mathematica, but unfortunately im not getting any decent results. ...
3
votes
2answers
221 views

Is there is a decreasing function that fits my data?

Cross-posted in http://tieba.baidu.com/p/4440556337 http://tieba.baidu.com/p/4440547130 I was wondering if there is a function that fits the following data perfectly or properly. There is a ...
3
votes
2answers
178 views

Low quality of estimated parameters with NonlinearModelFit

I'm trying to fit formula: ...
3
votes
2answers
226 views

Multiple regression curve fitting

I've got some data with 2 independent variables and 1 dependent variable I'm trying to fit a curve to. I'm really kind of a dummy with Mathematica except for the most basic things, so I looked ...
3
votes
2answers
255 views

Why can't FindFit get the proper result in this problem?

Cross-posted in http://tieba.baidu.com/p/4425634583 The mathematica helps me solve one differential equation in numerial method and got the data of the answer,but the taylor series fit is not good in ...
3
votes
2answers
696 views

Gauss Fit to List of 2D Points

I've been trying to find a solution to what I think is a common problem. I have a list of Data like ...
3
votes
3answers
234 views

Zero-order interpolation not going fully around

Connected to this question, I want to do a zero-order interpolation of a bunch of datapoints which is periodic. The code I use is as follows: ...
3
votes
1answer
297 views

Getting slightly different results in fitting a logit model in R and Mathematica

I'm fitting some data to a Logit model in both Mathematica and R and I'm getting slightly different results. R code: ...
3
votes
2answers
67 views

Problem with FindFit: Low quality of estimated parameters

I'm trying to fit a Cole-Davidson formula: ...
3
votes
2answers
258 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 ...
3
votes
1answer
607 views

Fitting data to a circle with FindFit

I'm currently trying to use the Mathematica's FindFit command to fit a curve of some data to the bottom half of a circle. The data is of the form ...
3
votes
2answers
537 views

fit a curve in a three dimensional space

I have a list of points of a curve in a three dimensional space, like ...
3
votes
2answers
255 views

Mathematica Interpolation or approximation

I have lists of points X and Y. {1212,1216,1217,1219...}, {1,2,3,4,5,6...} I combine ...