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

learn more… | top users | synonyms (1)

15
votes
0answers
606 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 ...
8
votes
0answers
115 views

How can the Theil-Sen estimator be made to work on larger datasets?

The Theil-Sen estimator finds the slope and intercept of a line passing through a set of points by calculating the median slope and median intercept of the set of lines passing through all possible ...
6
votes
0answers
142 views

Implementation of Partial Least Squares (PLS)?

I'm looking for a PLS implementation for Wolfram Mathematica. I just cant seem to find any implementation for it - do you know one? In general, I'm a bit confused that there exist only so few ...
6
votes
0answers
219 views

Using perpendicular offsets in FindFit

I want to use perpendicular offsets in the built-in FindFit function. Are there any possible ways or do I have to code everything by myself?
5
votes
0answers
128 views

PenaltyFunction Option in NMinimize

I am curious if anybody has some experience in using the built-in Option "PenaltyFunction" in any of the numerical optimization functions like NMinimize. According to the documentation the user ...
5
votes
0answers
221 views

Problems extending NelderMeadMinimize into 2D

Update The eventual route I followed was to adapt a version of the NM-simplex written in C and link to it with MathLink. Once I've tested this out fully I'll post it here. I've been playing around ...
5
votes
0answers
79 views

Third syntax version of LogitModelFit: unexpected result of “BestFit”

The third listed syntax version of LogitModelFit allows one to specify input in a simple way: Only a design matrix (with a row of values of the explanatory input ...
5
votes
0answers
467 views

What exactly is “ParameterErrors” of NonlinearModelFit?

I am trying to get what I call a "$\chi^2$ fit". This means taking a function $f(x,p)$ of the variable $x$ with a parameter $p$ and finding the value of $p$ that minimizes the "distance" from a data ...
5
votes
0answers
664 views

Analytical model fitting

I have a special type of model fitting problem that I am trying to solve in Mathematica. Any insight how to attack it using available tools of Mathematica will be great to hear. We have a variable $$ ...
4
votes
0answers
88 views

Plots to check all assumptions of linear regression

I'm running a linear regression with LinearModelFit and would like to plot graphs to check the assumptions of linear regression: linearity, independence of the ...
3
votes
0answers
151 views

Memory problem in Mathematica 10

I'm having a problem with memory. I'm doing nonliner fits of several data lists to a system of differential equations. When I evaluate the "Do" cycle the memory grows with the iteration step up to my ...
3
votes
0answers
183 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 ...
3
votes
0answers
258 views

To what extent can NonlinearModelFit be sped up?

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
votes
0answers
299 views

Is it possible to marginalize one or several parameters obtained from fitting procedure?

Statistical model analysis package has a few fitting functions. Their arguments are data points, fitting model and parameters in the fit. The result is a set of best values for parameters, which ...
3
votes
0answers
214 views

Mathematica Complains about Non Symmetric Covariance matrix, when it's not the case

I was doing some fitting with Mathematica7 using NonlinearModelFit. It's quite long the program to do the fit and that's why I am not displaying here ... It goes ok, and I can get the fit parameters ...
2
votes
0answers
44 views

ANCOVA (ANalysis of COVAriance)

I have two time series of the form {time, value} I have linear fits of each set individually, and I am interested in the statistical differences between the ...
2
votes
0answers
49 views

Kalman filter estimation

Does anyone have any examples of the estimation of Kalman filters in Mathematica? I am new to these filters and struggling to compose the likelihood function. Some examples would be really helpful. ...
2
votes
0answers
43 views

Is there a way to produce a FittedModel object as the solution to a regularized regression?

I can get the Ridge or Tikhonov regression solution to Y = \[Beta].X easily enough as ...
2
votes
0answers
55 views

Why do EstimatedDistribution and DistributionFitTest work this way

I am fitting some time-series data to both a stable distribution and a normal distribution in order to assess the goodness of fit of each. Along the way I encountered the following confusing result. ...
2
votes
0answers
314 views

Speeding up Nonlinearmodelfit by constraining parameters?

I have a complicated parametric PDE that can be fitted to some data with NonlinearModelFit, but takes several hours to estimate the best values of the four free parameters. Currently, the code ...
2
votes
0answers
158 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
0answers
700 views

Linear regression with x and y errors

I have a question about finding a linear regression weighted with x and y errors. I found the answer provided by 0x4A4D in Estimate error on slope of linear regression given data with associated ...
2
votes
0answers
317 views

NonLinearModelFit with Two Dimensional List of Weights

I'm currently trying to fit Planck's law (B[λ, T]) to measurements, thereby determining Planck's constant. I have a list of triplets containing wavelength, ...
2
votes
0answers
719 views

ParametricNDSolveValue or NDSolve + fitting

I have been trying to find the value for the parameter kestim that yields the best fit of a model to some data points. datac has ...
2
votes
0answers
218 views

How to predict some constant number of values with NeuralNetworks

Example: << NeuralNetworks` data = {Sin[#]} & /@ Range[0, 4 Pi, 0.5]; learn = data[[1 ;; 15]]; Now, lets fit our neural network: ...
1
vote
0answers
53 views

Fitting data to a derivative model

I just started using Mathematica. I would like to use Mathematica to do non-linear regression. My model equation is : ...
1
vote
0answers
19 views

Fit a custom process to a data: inhomogeneous 2-state Markov chain

I would like to fit a custom process - a time inhomogeneous 2-state Markov chain, to data. The time inhomogeneity is a result of the transition probabilities varying sinusoidally through time with a ...
1
vote
0answers
77 views

Fitting curves with NonLinearModelFit not working with charge and discharge like data

I'm trying to get a reasonable fit out of mathematica, but i'm not very practical with it. I'm not that good with mathematica at all actually(like cleaniness of the code...). btw, here's my problem: ...
1
vote
0answers
57 views

Error associated with parameters in Minimize (or NMinimize) in discrete fitting

my problem goes as follows: I need to a discrete fit of a discrete function. Say I have the following made up data points, which are generated by the parabola ...
1
vote
0answers
69 views

Updating procedural fitting algorithm to more efficient style?

For some time now, I have used this procedural programming approach to fit data in my research that is too cumbersome for the built in Mathematica functions. (Although this simple example works fine ...
1
vote
0answers
92 views

Comparing two ways of fitting systems of ODEs to data

I'd like to ask you if you see any difference between the two following ways of estimating parameters. Given my system of ordinary differential equations that I want to use to find the values of all ...
1
vote
0answers
95 views

Cross-validation of a FittedModel

Although I would know how to perform cross-validation tests after fitting a model using a function like NonLinearModelFit, I wonder if there is a way to do this providing the right parameters to the ...
1
vote
0answers
176 views

Developing easy code to apply Delta Method to generate prediction bands for custom distributions

I think that this is an interesting issue for all those who when to not only adjust one prediction function, but also to obtain the prediction bands to asses the graphical or tabular error I'm trying ...
1
vote
0answers
46 views

A more efficient way of fitting a non-linear model that returns an entire list?

I have a function that takes two parameters, del and nu, and returns a list npoints long ...
1
vote
0answers
163 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. ...
1
vote
0answers
99 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: ...
1
vote
0answers
874 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 ...
0
votes
0answers
42 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, ...
0
votes
0answers
39 views

combining separate data into pairs after reading from excel so I can run regression

I have the following code that reads data from an excel spreadsheet: ...
0
votes
0answers
26 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 ...
0
votes
0answers
40 views

How to control precision of parameters in NonlinearModelFit?

I am using NonlinearModelFit for fitting a dataset to some complex numerical model function that depends on a few parameters. The final required precision of these parameters is very low, like 3 ...
0
votes
0answers
40 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 ...
0
votes
0answers
35 views

How do I add custom deviation when using LinearModelFit?

I have a set of data in the form a list S1={{x,y},{x,y}} etc. I also have a function that calculates a corrected standard deviation in the y direction for ...
0
votes
0answers
76 views

Expand a fitting using FindFit[]

I need to implement multidimensional optimization using FindFit[]. But it's essential to exclude some parameters from the main procedure of optimization and to move on from direct optimization in ...
0
votes
0answers
76 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 чtч. ...
0
votes
0answers
18 views

Binomial Regression where n > 1

I am not well versed in Generalized Linear Models, but am trying to use this approach to model some discrete data. I have binomial data where the sample size for each observation is the same size, ...
0
votes
0answers
39 views

Troubles with FindFit for ODE (elaboration)

I have asked a question Troubles with FindFit for ODE and get a good-working answer from @belisarius. Nevertheless I need to clarify is it possible to define the same model with ...
0
votes
0answers
95 views

NonlinearModelFit indeterminate or not a list of real numbers

I'm trying to fit my data using NonlinearModelFit but keep getting errors that I don't quite understand how to correct ...
0
votes
0answers
42 views

Using List/Histogram Data As A Weighted Function?

I have a list of data points that I would like to use as a weighted fucntion. The data represents the number of particles within a bin of a particle distribution. Ultimately I would like to multiply ...
0
votes
0answers
99 views

Non linear curve fit

I am trying to fit a non linear curve to my data which looks like following The code I am using is following. You can see I have six unknown variables ...