Questions tagged [curve-fitting]
Methods used to fit curves (as in linear or non-linear regression) to data.
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Power-law fitting with x-y relationship [closed]
I would like to fit a power-law distribution to data taking into account the x-y-relationship. I tried plfit & powerlaw package for python. But the problem with them is that if I shuffle the y-...
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Time Series Prediction for Variable-Length Input with Fixed Sampling Period
I'm working on a time series prediction task where I need to predict the parameters (amp, phase, freq, offset) that best fit a variable-length input series. The samples are always at the same period.
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How to visualize trends
I am working on a paper where we plotted BMI trends as a function of age in the population. We plotted trends for six databases, then we plotted for each sex, then for race, in three categories. I ...
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How can I fit my experimental curve using this equation using python? [closed]
The equation is
$ Y = \left(a*\arctan\left(\frac{x \pm b}{b} * c\right)\right) + d x $
I tried fitting using scipy.optimize but could not include $\pm$
Here $ a , b,...
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Knots selection testing for Natural Cubic Splines model in R
I have a dataset of Japan's Mortality rate and want to fit a natural cubic spline to this mortality data. The choice of knots are subjectively chosen at 10, 20, 30,...,90.
I want to know whether or ...
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Need guidance to fit logistic distributions to compare performances in multiple events
Ok, here's the thing. I'm trying to compare performances in different running events (i.e. all registered performances in each event from 1990 to 2023), to estimate equivalent performances. After ...
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How to know errorbars on accuracy to nonlinear fit: $A(1-\cos(x+\phi))$ with poisson noise?
I am trying to write some code that accurately estimates the parameters for the following function:
$$ Y = A(1-V \cos(X+\phi)) $$,
where this output data is poisson distributed.
To do this, I first ...
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Is it possible to have an Indicator-spesific Trait factor model within a multiple indicator second order growth model?
I am running a multiple-indicator growth curve model over 7 time points.
One of my items has a large residual variance and seems to covary very well among themselves.
Thus, I assumed that it has a ...
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Cubic spline with circular predictor [duplicate]
I have a set of observations $y_i$ for a set of values of the independent variable $x_i$. $x_i$ takes values of angles, so it is a circular variable. Is there some method to perform cubic splines or ...
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Invariance coding for running a latent growth model running under partial (scalar or metric) invariance
I am running a second-order latent growth curve with 7 time points.
The model has a four indicator latent variables at the measurement level so I ran a longitudinal invariance test.
The model holds ...
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Curve fitting: Scaling the sigmas so that the reduced chi-squared statistic = 1. Is this a good heuristic?
In the official documentation for the python function scipy.optimize.curve_fit, the following description is given for a boolean-typed parameter absolute_sigma.
If False (default), only the relative ...
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Double exponential decay with values going below the start point of the fitted curve
I have a small dataset with 5 points where x values are log(time) and y = obs. It is known that the behavior is an exponential increase for the first and second (x,y) values and then decreases ...
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Uncertainty of the area of a Gaussian curve atop a linear background
I have some data from a counting-based spectroscopy experiment. Each data point is an (Energy, Rate) pair. One such data set looks like this:
I choose to fit this data to a Gaussian curve plus a ...
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Non-Linear data fitting for kinetic data
I am trying to fit a two_site model which I derived, (basically, rate as a function of pressures of reactants and products) to my experimental data. Just want to check if the logic below is fine, ...
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Help with (what should be?) a simple exponential curve [closed]
I'm admittedly not a math expert. I'm in the process of reverse engineering a piece of software and am stuck on finding a curve. The curve is used to convert a value (0-1) into a real world value. The ...
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How to find the curvature of a noisy function with few evaluations?
I'm working on a project in computational solid state physics where I have to find the curvature of a smooth function $f \ : [0,\infty] \rightarrow \mathbb{R}$ around the minimum point $x_0 = 0$.
The ...
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Learning Curve on two classifiers
I am using a logistic regression classifier and Gridsearch to optimize negative log loss.
After generating its learning curve to test for overfitting/underfitting, my model seems to return this ...
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Optimizing Constants in a Function with a Square Root Term
I am working on a curve fitting problem where I have a series of real data points, and I want to fit a curve to this data. The derivative of the function I am trying to fit has the form:
f'(x) = -sqrt(...
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Regression with random vs uniform distribution of a covariate
Suppose we have some population of individuals, each having X and Y variable. I know that in the population, most individuals have low values of X, but I want to find regression formula for low as ...
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Best interpolation technique for ODE-data
Let's assume we have an ODE $\dot{x}=F(x)$ where $F: \mathbb{R}^n \rightarrow \mathbb{R}^n$ is a vector field. And we observe a trajectory $\gamma: [t_0,t_1] \rightarrow \mathbb{R}^n$ from this ODE ...
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Consequences for not estimating autocorrelated residuals in a growth curve model
I am fitting a second order growth model with 7 time points on Mplus.
When I estimate the model with autocorrelated residuals in it
the model will not run because of identification issues.
(when I ...
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Logistic regression assessing the fit of variables
In a logistic regression with multiple independent variables what are some approaches to assess how well the model fits against the continuous variables in the model?
I have a model with multiple ...
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How to model breakage events for electronic devices using a Weibull distribution?
I got age data (in years) of gas heatings from a random sample of about N=700 participants.
So participants were asked how old their gas heating is in years.
Now I like to model that age distribution (...
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Test of good fitting on a sigmoid [closed]
as you can see on the figure i linked i am currently fitting my data (which looks like a sigmoid) using a function i defined with 5 parameters.
...
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Conditional Expectation of Multivariate Normal
I'm trying to calculate a good mean shrinkage parameter for a custom quadratic discriminant analysis (QDA), and I ran into a math problem. Suppose $X=(X_1, X_2, \ldots, X_k)^T\sim{\mathcal{N}(\textbf{...
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Estimating a censored distribution curve
I have a sample of only 142 numbers from a distribution of 3852 numbers ranging from 0 to 53, but it is censored below 35 (The values exist, but I don't have access.), so I have only the values in ...
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How to fit data with asymmetric error bars?
General question: How do I fit a model to data when the data points have asymmetric error bars? What is the cost function I use to calculate residuals, and from that, how do I calculate confidence ...
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How to calculate heteroskedastic standard errors
I'm doing curve fitting, but my error is non-stationary. The variance decreases:
I'm looking for a signal in the noise (In this case at x=90, y=50).
I'd like to calculate the "standard error&...
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Testing the goodness of fit of a Zipf distribution [duplicate]
I have several ranking distributions and would, for each one, like to fit a [Zipf distribution][1], and estimate the goodness of fit relative to some standard benchmark.
With the Matlab code below, I ...
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Testing goodness of fit for a Zipf distribution (in Matlab)
I have several ranking distributions and would, for each one, like to fit a [Zipf distribution][1], and estimate the goodness of fit relative to some standard benchmark.
With the Matlab code below, I ...
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Fitting data taking into account for the spread in data, which are zero for some data points
I'm trying to use scipy to fit a $\tanh$ function to some data. The data is of the form $(x_i, y_i)$ for $i=1,\cdots,N$, where $0\leq y_i \leq 1$. I choose $x_i$ to be linearly spaced, such that $x_0=...
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Fitting a power law model with an additional linear term
A model of the form $y=a\cdot x^b$ can be linearly fitted by taking logs on both sides - giving $\ln(y)=\ln(a)+b\cdot\ln(x)$, where $\ln(y)$ is regressed against $\ln(x)$. This is a standard textbook ...
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Statistcially assessing how similar curves are?
I have intensity curves (~9 reps) of bacterial fluorescence over 2.2 cm from 4 groups (A, B, C and D unknown) and three treatments (10 mM, 1 mM and 0 mM). My current code is below. I wish to show how ...
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Is it possible to use some form of curve identifcation algorithm or model in R to identify a curve based on data from three different treatments?
I was wondering if it is possible to train a model or algorithmn to identify a curve shape based on experimental data.
Say we have 3 treatments 0 mM sugar, 1 mM sugar and 10 mM sugar and three ...
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How to plot a learning curve for 10-fold cross validation?
I am working on a dataset. I built several models using 10-fold cross validation (not a train-test split).
Now, I want to plot a learning curve for each model to show if it is overfitting, ...
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Latent growth curve models (SEM): determining the shape of curve with unconditional time-varying covariates
I have a question about determining the shape of a curve (linear vs. quadratic) in latent growth curve models within a structural equation model framework.
If you are including time-varying covariates ...
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How to find the linearity of 5 points
I am currently developing a software in C. I have an array (matrix) that contains some coordinate points like this (125 points for now):
\begin{bmatrix}x1&x2&x3&x4&x5&...&x125\\...
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How to evaluate whether peaks extracted from time-series are approximately Gaussian shaped?
I am analysing environmental time-series of the pollutant concentration that is measured every 3 seconds. From these time-series I'm extracting peaks (i.e. the signal of the pollutant concentration ...
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Measure of goodness of polynomial fit at specific points or weighted analysis?
I have some astrophysics data of "particle density vs orbital position" of a moon that emits a lot of particles. My research deals with the intensity of the scattered light which is ...
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Parameter transformation after fitting transformed data
this might be a basic question but I've had some doubts analyzing my data after fitting some parameters.
For some background I'm using a non-linear LS method to fit data to the following function:
$$
...
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In machine learning, why do we say "curve fitting" when really fit the hypersurface?
Curve and surface are distinct concepts yet they seem to be used interchangeably in the context of model fitting.
For a single argument function f(x) the concept of curve fitting is clear. The ...
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How do I perform a regression when I know there is a multiplicative relationship between the regression coefficients?
Suppose I'm attempting to use linear regression but instead of
$$y_i = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + \beta_4 x_4 + \varepsilon_i,$$
for scientific reasons, I know that $β_2=\...
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Good fitting but high variances ($SEIR $ type model)
I am working on a susceptible ($S = S_1$ or $S=S_2$), exposed ($E$), infected ($I$), hospitalised ($H$), deceased ($D$) and recovered ($R$) model. Below is my model,
\begin{equation}
\begin{split}
\...
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Computing the error in best fit parameters using chi-square grid
Suppose I have a scatter plot and I have fitted it with a curve that has two parameters 'a' and 'b'. I try various values of 'a' and 'b' between a certain range and plot a grid of chi-square values ...
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Calculating a percentile for a slice in a curve fit
Currently I have a of around 20000 datapoints, with the independent variable being time and the dependent variable being an arbitrary skill measure [Image 1]. I have fit a curve to the data using ...
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Getting point estimation and confidence interval for gaussian fit
I have a task where I should fit the data sample with curve_fit and get the peak's position and amplitude. I fitted data and got these values and their standard errors. I also need to find point ...
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Fit inverse polynomial function $1/x^n$
I am trying to fit the function $A/x³$ to some data points (X,Y). I tried using least squares to fit the function $A x^3$ to the data points (1/X,Y) using least squares. However I do not obtain a good ...
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Perfect Prediction: Why Would We Ever Use a Statistical Model?
Dear statistics experts
I need your help with something that has bothered me for a while now. My problem revolves around perfect prediction and essentially boils down to:
Why would we ever set up and ...
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Fit Gompertz curve to growth data with decline phase
I measured the change in three traits (y1, y2, y3) over time (x). The three traits each reached a maximum at different times and then declined. I am interested in the phase until the max and would ...
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Loss is growing between epochs in simple model [duplicate]
I am new to ML and trying to write a very simple model that can predict the future of a function given the past. That is to say, I define a simple cubic function (y = x^3 + x^2 + x) and apply it to a ...
