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

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1answer
864 views

Fit implicit function

Can anyone help me with fitting an implicit function to data? The function is given by: a*x^2 + 2*b*x*y + c*y^2 = e under the condition ...
0
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1answer
121 views

Solving one equation, then inputting the values into another for NonlinearModelFit

Considering the equation a*x^3 + a*x^2 + x + b == 0 I'm looking to find the best value for a and ...
0
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1answer
257 views

Fitting a theoretical density function with log-return sample

I am working on a exercise to fit a theoretical density function,presented below, with log-return series of a stock. $\frac{1}{2}a e^{a(x-\mu)} \quad \text{if x } < \mu $ or $ \frac{1}{...
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1answer
660 views

Multivariate Function Approximation With a Large Dataset

I have a nice amount of data from a trading strategy I am working on, where I have two different liquidity parameters as x, y variables. Before entering a trade I am taking the moving average of <...
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2 views

Maximum Likelihood Approach for parameter estimation of multi response data, could you provide a tutorial? [migrated]

I was trying to fit the parameters a time dependent system coupled of ODES relate to a kinetic experiment with multi response data. example: A->B+H A+H->C+H A->D dcA(t)/dt=-k1Ca(t)-k2Ca(t)*Ch(t)-k3*Ca(...
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0answers
68 views

Chi-squared test for a fitted function [closed]

I have some experimental data, and I have used Mathematica to fit a function. Now I would like test the goodness of my fit. Something analogous to R^2 in linear regression but which applies to a ...
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0answers
38 views

Constrain a series of parameters while using FindMinimum

I'm working on fitting some experimental data using a model function that consists of sum of Lorentzians with width parameters A[1], ...
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0answers
30 views

Priority on Fitparameters

I try to fit a function using the FindFit expression. My problem is that ZL has to be ...
0
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1answer
67 views

Plotting a dataset and its fit dynamically

I have the dataset ...
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0answers
61 views

Solve equations involving summation expressions in Mathematica

I am trying to solve the simple linear regression equation analytically in Mathematica (not using builtin functions). I managed to calculate the gradient as follows f is loss function using RSS and ...
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0answers
29 views

data fit using second order PDE

I'm trying to find the parameter for second order PDE using data. i don't know what is the error of that, ...
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0answers
58 views

Numerical fitting trajectory to model that has NDSolve

I have a model which describes the motion of an object on a plane. ...
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0answers
31 views

Use “FindFit” for Multi-variable Polynomial Fit

I'm interested in defining three input vectors: $L=\{L_{1}, \ldots, L_{N} \}$ $W=\{W_{1}, \ldots, W_{N} \}$ $Q=\{Q_{1}, \ldots, Q_{N} \}$ and I'm hoping to be able to input a number for each of ...
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0answers
37 views

Is it possible to get the error estimates of predicted values computed by FindMinimum using the Levenberg Marquardt method?

I use the LevenbergMarquardt method of the FindMinimum function to minimize a residual function (mathematical-optimization). This residual function is computed from experimental data and the solution ...
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0answers
51 views

How to fit a plot with error bar as weight?

I try to fit a line which can fit through the points considering the error weight of each coordinate. Is it possible to do in Mathematica? I can only find Fit function which did not do what I really ...
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0answers
48 views

Fitting 6 differential equations to 6 sets of data

I am using the newest Mathematica and I am trying to fit a set of 6 linear differential equations to a set of experimental data for each of the six variables. I am a baby beginner at this and could ...
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0answers
69 views

Exact meaning of `VarianceEstimatorFunction`

After reading the documentation, it's still unclear for me what VarianceEstimatorFunction does when fed with two arguments: ...
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0answers
46 views

fit multiple dataset with a single ODE to extract parameters

I found my problem very similar to the one discussed in here. But I'm having difficulties to fit multiple dataset (with varied temperatures) to a single ODE. The hurdle for me now is since the rate ...
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0answers
83 views

Maximum Likelihood Estimation of Gamma-distribution Scale parameter

I have the following tasks: Generate random sample with given parameters shape = 2, scale = 0.001 and shape = 2, scale = 1/1200 for the right censored sample; Using Maximum Likelihood Method ...
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0answers
44 views

Plotting error bars in both dimensions for straight line model [duplicate]

I want to fit a straight line model of the form $y_i = a+ b\ x_i$ to the list of $(x, y)$ pairs given below. How can I plot the data with error bars in both coordinates? ...
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0answers
35 views

How to calculate a required definition only once for each iteration of NonlinearModelFit [on hold]

This is my first post here. I've been using Mathematica for about 4 years now to analyze data, but am still very new and have no background in formal programming. This is the first question I couldn't ...
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0answers
48 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 ...
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0answers
33 views

EstimatedBackground function on Mathematica 9

Is there a way to replicate the EstimatedBackground function on Mathematica 9?
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0answers
62 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 ...
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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 ...
0
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1answer
161 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 ...
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0answers
74 views

Modify measured values to improve NonlinearModelFit results

Problem: Measured data points have a random distribution of DC offsets (either +/- 0.65 mV), that came from an incorrect setting on the 24-bit ADC we were using. Essentially for each measured voltage ...
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0answers
95 views

How to make a twice-differentiable function that approximates some data?

I have some time series data that I would like to approximate with a twice-differentiable function. Each time series has ~10,000 datapoints, so I definitely do not want a function that passes through ...
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0answers
40 views

How to use FindFit to find the parameter in Laplace space(numerically inverting Laplace transforms)

I am trying to find the parameter in Laplace space, and a very simple example is shown below: I have known the solution $y_{laplace}$ in the laplace space is $a/s^2$, and I also have some discrete ...
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2answers
544 views

Log Linear Fitting of a data: e.g. {xi,Log [yi]} and plotting the fit

I have a Log-Linear plot, and i'm unsure about how to fit a line to it. The data represents a I (current) vs V (voltage) curve. The exponential portion of this curve (linear in a Log-Linear plot) is: ...
0
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1answer
195 views

Simultaneously fitting two data sets to two functions is too slow [closed]

I have to fit two data sets to two functions(eps1,eps2) with same parameters (w0,f,g) Initially, I know only one function ...
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0answers
224 views

Decompose Point-Spread Function into Seidel Aberration/Zernike Polynomials

I have measured the point spread function (PSF of a microscope) and I want to quantify it. For that purpose I want to fit my PSF data to the primary Seidel optical aberrations (or Zernike Polynomials, ...
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0answers
113 views

Fit a complicated function to a constant with NonlinearModelFit

I wish to fit a complicated parametric function (logder, with lambda parameters) to a constant (L) in order to minimize its dependence with the variable k in a given interval. To do that, I use a ...
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0answers
57 views

NonlinearModelFit not hunting for good values

I have the following data which come from complex values but I have turned them into a 3D list ...
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0answers
532 views

Extracting parameters from a fitted function

Let's say I have written a function which performs convolution and returns value calculated for the time, t. ...
0
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1answer
333 views

NonlinearModelFit - “Encountered a gradient that is effectively zero”, all variables are 1, 1, 1 [duplicate]

I have data of the form {149.45, 0.371093}, {149.362, 0.375976}, {149.277, 0.380858}, ... }, where each element of the list is {x, y}. The plot of this, using ListPlot, gives an approximate Gaussian. ...
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0answers
352 views

Multi-peak fitting [duplicate]

Suppose we have a data set that looks like this: I have to fit this data to 9 peaks knowing μ and σ beforehand & have to ...
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0answers
143 views

How to perform a distribution fit test to censored data

With following code I will get an error: ...
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0answers
96 views

Horizontal shift in fitting data by a sinusoidal nonlinear model [duplicate]

I have data that can apparently be fitted by a sinusoidal function in form $D+A\sin(B(x-\frac CB))$. I tried doing the best fit in Mathematica using ...
0
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1answer
614 views

How do I fit NDSolve result to experimental data? [duplicate]

I have two coupled ordinary differential equations which I solve numerically in Mathematica, but now I want to fit the solution with experimental data. I do following, (the experimental data ...
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0answers
36 views

Data Fitting with xerrors and yerrors using findfit [duplicate]

I'm trying to fit data with xerror and yerror using "Findfit", so i'm trying the same form than in tuto : http://reference.wolfram.com/applications/eda/FittingDataToLinearModelsByLeast-...
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0answers
60 views

Fitting for multiple data in Mathematica [duplicate]

I've just started to use Mathematica for programming and I was wondering how I could do Fitting for several data sets. For example, I have one curve. For this curve I need to plot a fit curve, if my ...
0
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1answer
92 views

Trouble fitting an explicitly complex model with the TransformedFit package

This is follow up from a previous question in which @Oleksandr R. suggested the use of a package he developed for splitting a model and data into real and imaginary parts to avoid a problem with ...
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0answers
102 views

Fitting data set with series expansion

I have a function given in a form of a list: ScalarField={{$\epsilon$,$y_1$},..{1,$y_{3000}$}} It is defined in the range $(\epsilon,1)$ (spacing between grid points is homogeneous), where $\...
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0answers
228 views

Using FindFit for step functions

Having used FindFit like so: ...
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0answers
129 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 ...
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0answers
45 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. ...
0
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0answers
43 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
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0answers
381 views

Performance in parameter estimation from ParametricNDSolve using varied initial conditions [duplicate]

I have 250 data points from a timecourse exeriment in a list, with columns specifying (1) time, (2-4) initial conditions, (5) absorbance reading. I want to fit 4 parameters (k1, k2, k3, k4) in a DAE ...
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1answer
242 views

Formatting and inserting a parameter table into a plot

I'm fitting data, and I want to put the parameter table generated by NoninearModelFit into the plot. How can I do that in a reasonable way? I want to format the ...