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

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212 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. ...
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105 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: ...
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1k 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 ...
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433 views

Interpolating function as a model in Mathematica's procedures for fitting

Is it possible to use interpolating function with parameters as a model for NonLinearModelFit (and other integrated methods for fitting)? Similar question was ...
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184 views

FindFit for dimension reduction?

Given an n-dimensional function, can I use FindFit to produce an approximate (n-k)-dimensional function? Here is a simplified illustration of what I am trying to ...
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31 views

How to calculate a required definition only once for each iteration of NonlinearModelFit

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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87 views

Find the (gaussian) function to fit a series of points?

I have a series of measurements for concentration of pollutant on a river C(x,t) where x is the location on the river and t is the timestamp. When plotted these data suggests a bell curve like Gauss ...
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46 views

Iterative process of least squares solution

I'm doing an inversion of gravity data in which the least squares solution is: V^(k+1) = V^(k) + Inverse[W].(Transpose[A.(Inverse[W])]).α; where ...
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44 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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28 views

EstimatedBackground function on Mathematica 9

Is there a way to replicate the EstimatedBackground function on Mathematica 9?
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58 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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51 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: ...
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68 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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39 views

Fitting problem: InterpolatingFunction can not be localised

I got simple data looking as follows {{541.447, 311752.}, {540.359, 311723.},.. I tried to fit it in mathematica for the first time with a function that usually ...
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78 views

Finding values of a variable fitting a function and minimizing a list of expressions

I am trying to implement bootstrapping (https://en.wikipedia.org/wiki/Bootstrapping_(finance)) of CDS curve. To implement it I am trying to minimize a series of expressions so that each expression is ...
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88 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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39 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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54 views

Why does ParallelMap throw errors where Map does not?

I am encountering a problem with ParallelMap. I have a call in a large code base, part of which attempts to fit data in parallel using ...
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183 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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92 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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54 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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287 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. ...
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283 views

Multi-peak fitting

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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115 views

How to perform a distribution fit test to censored data

With following code I will get an error: ...
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75 views

No real number fitting double exponential in Mathematica

I am trying to fit a double exponential curve to my data, but I got the error saying there are non real number. Also I tried with starting values for my 4 parameters, but this does not work either. ...
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315 views

Non linear model fit mathematica

I want to fit experimental data (temp,alpha) to the following equation for calculating k and Ea -Log[alpha]^n = function(k,Ea,temp) However i do not know ...
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186 views

NonlinearModelFit with multiple parameters

I am now trying a slightly more complicated model which actually consists of finding the parameters of 2 particles in an Image (I attached an Plot of an image). Although I put very good initial values ...
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90 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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210 views

Using FindFit for step functions

Having used FindFit like so: ...
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122 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 ...