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

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0
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0answers
95 views

Smoothing a function

NDsolve gives me a solution to a certain NL PDE. I want to evaluate the rate of exponential decay of the maxima of the solutions in time. So, I plot ...
0
votes
1answer
118 views

Fitting a function

I defined and evaluated a function Max2[t_?NumericQ] := Log[Abs[-1 + First[Maximize[sol1[[2]][x, t], 0 <= x <= L, x]]]]; Now, I expect this to be close to ...
0
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3answers
180 views

Getting an equation of particular curve

How can I get an equation of the similar shaped curve? I've tried to get it like y = a + c x^2 + d x^3: ...
2
votes
1answer
166 views

FindMaximum of loglikelihood in Gaussian Process

I am trying to implement a Gaussian Process and have problems to maximize the loglikelihood because the function consists of a determinant of a matrix that is dependent of 2 variables and the product ...
7
votes
1answer
318 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: ...
6
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2answers
163 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 ...
4
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0answers
183 views

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

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 ...
5
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2answers
350 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 ...
0
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0answers
120 views

How could I code the following nonlinear regression?

I am an extremely limited user of Mathematica. Could someone tell me how to set the following nonlinear regression problem : Y = Sum[a[i] F[i,X] , i = 1,4] ...
3
votes
2answers
230 views

fit a curve in a three dimensional space

I have a list of points of a curve in a three dimensional space, like ...
0
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0answers
41 views

How to fit ODE's coefficient, just like using NMinimize [duplicate]

I want to fit ODE's coefficients to a model. I tried using NMinimize, but it seems it does symbolic instead of numerical calculations. ...
1
vote
0answers
121 views

NonlinearModelFit is not giving the fit with minimum chi^2

First of all, a bit of background, I am using Mathematica to fit angular distributions of gamma rays, so I apologize for some of the serious messiness in the formulas. The data is simple I have three ...
2
votes
1answer
158 views

Judging the quality of fitting an EventData object to a distribution using LogRankTest

I have $389$ data points defined in an EventData object and want to judge the quality of fit of this data to a fitted $3$-parameter Weibull distribution. This ...
1
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0answers
104 views

LeastSquares with some parameters missing

I want to do a partial least squares (PLS) regression using LeastSquares on my data. The input parameters are temperature, humidity and pressure for a given date. ...
4
votes
1answer
385 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 ...
12
votes
1answer
348 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 ...
0
votes
1answer
126 views

Curve Fitting Errors

I am trying to fit a part of a dataset to the function $$ae^{-b\sqrt{x-c}}$$. My friend was using GNUPlot to this and got reasonably good results. However when I try to this with Mathematica : ...
3
votes
1answer
119 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. ...
0
votes
1answer
66 views

LMS distance from a point to an InterpolatingFunction

I have a short script to NDSolve a second-order nonlinear BVP, which as its output produces an InterpolatingFunction object. I ...
2
votes
1answer
435 views

Nonlinear least squares

I have a typical nonlinear least square problem and it seems very similar to the example provided in the section on parameter fitting at the Wolfram website. Unfortunately I always get some error ...
3
votes
2answers
426 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 ...
2
votes
2answers
661 views

How to enter an equation into FindFit?

I have the equation ...
6
votes
1answer
112 views

Why LinearModelFit is slower than NonlinearModelFit?

Why LinearModelFit is slower than NonlinearModelFit? ...
0
votes
1answer
123 views

fit recursive function to data

I have a function $g(x, n)$, which is a recursive expression: $x$ is a variable and $n$ the number of iterations. In my case $n=3$ for all $x$. An example is the following: ...
1
vote
1answer
194 views

SinglePredictionBands versus MeanPredictionBands from NonlinearModelFit

From my Statistics lectures I know the term confidence and prediction interval, whereas the confidence interval is smaller than the prediction interval. If I plot the mean and single prediction bands ...
2
votes
1answer
940 views

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

I'm trying to use NonlinearModelFit to fit the data: ...
9
votes
1answer
724 views

Measure length and diameter of objects in an image

I am new to Mathematica, and I am trying measure length and diameter of rectangular objects in an image. I wanted to fit rectangles in the objects, and then get the values. Can I do that with ...
0
votes
1answer
206 views

FindFit: why do I get negative value as result?

I am trying fo fit a model to data using FindFit. ...
0
votes
1answer
159 views

Nonlinear model fit: not getting correct numerical values from model [closed]

I tried to nonlinear fit a set of data as described below. However, it appears to yield a fit solution that in appearance looks good with the plotted data set, 'dat1', however, actual fit solution ...
5
votes
2answers
176 views

Transforming noisy multivariate data

I’ve been racking my brain all afternoon on trying to solve this… I have a set of noisy co-ordinate data data = {{x1,y1,z1}…..{xn,yn,zn}} that forms an ...
2
votes
2answers
677 views

Find a best fitting curve for some data with no regular pattern

Suppose some data with no regular pattern is given, so common patterns of functions all fail to fit it. Then how can one find the best fitting curve? I believe there will be some data for which we can ...
2
votes
1answer
269 views

RSquared Mathematica Excel incoherence

I've done a NonLinearRegression with this data ...
0
votes
0answers
40 views

NonLinearModelFit not generating a model without the use of “BestFit”, not sure why [duplicate]

This is my first time using NonLinearModelFit and I have run into an issue that I can't find an explanation for. The fitted model contains a ...
0
votes
1answer
258 views

Nonlinear model fit and Log Log plot [closed]

I am trying to fit the log of a set of five data points (NOTE: the second coordinate(y coordinate) in each data point is already a log quantity): ...
1
vote
0answers
93 views

Can we ask ComponentMeasurements to use NonLinearModelFit to return a covariance matrix for underlying intensity data?

I'd like to be able to calculate a covariance matrix for some data underlying a morphological component. Provided this data, I can write something like: ...
4
votes
2answers
147 views
2
votes
2answers
274 views

How do I find the best fit?

I am trying to solve following system of three differential equations ...
1
vote
2answers
204 views

Plotting a dynamical NonlinearModelFit Function

Currently I'm playing around with dynamics and the NonlinearModelFit function. To be precise, I want to fit a function the data, which range I want to specify ...
3
votes
1answer
347 views

Generating a “best fit” curve to a set of noisy data corresponding to a moving object

Please note that this is an extension of a previous question: Interpolating a sparse list of two-dimensional coordinates We have an ordered array of coordinates corresponding to the position of an ...
0
votes
0answers
518 views

How to Output Chi-Squared Statistics when using NonLinearModelFit

I am using NonLinearModelFit for some curve fitting and I was wondering if NLM is able to output chi-squared/leastsquared statistics from the best-fit parameters and confidence intervals. From my ...
1
vote
1answer
107 views

How to find best MLE using `FindDistributionParameters`

This question is an extension of this question, if we change the initial values ...
0
votes
2answers
184 views
2
votes
1answer
228 views

Problem with Covariance Matrix Output in NonlinearModelFit

I am running NonlinearModelFit based off of some simulated data and trying to fit to a function with more than one parameter. Eventually, I would like to fit to 5 ...
14
votes
2answers
1k 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 ...
3
votes
1answer
553 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
2answers
389 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: ...
2
votes
3answers
158 views

Removing of artificial sampling step effects

Look at this plot, it represents an underground interface between two formations, this interface should dip very gently left-downward, all the steps are artificial effects due to sampling. The natural ...
1
vote
1answer
533 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 ...
3
votes
1answer
94 views

How do I test for the occurrence of an error message and act on it?

I want to see how well some curves fit a data set. If a curve doesn't fit after 100 iterations, I get the error cvmit. How do I test for and handle this error ...
12
votes
0answers
469 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 ...