Finding a,b,c for Gaussian Model: A Puzzling Task

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SUMMARY

The discussion focuses on determining the parameters a, b, and c for a Gaussian model represented by the equation y = a exp (-(x-c) / b)². The user seeks clarification on how to find these parameters when the data set does not include the point (0, a), which is typically the maximum height of the curve. It is established that a controls the height of the Gaussian curve, while b influences its spread. The proposed method for finding these parameters involves evaluating the Gaussian function at the data points and minimizing the sum of squared differences between the observed and predicted values.

PREREQUISITES
  • Understanding of Gaussian functions and their properties
  • Familiarity with optimization techniques, specifically least squares
  • Knowledge of data fitting methods
  • Basic proficiency in mathematical notation and functions
NEXT STEPS
  • Learn about least squares optimization techniques for parameter estimation
  • Explore the use of Python libraries such as SciPy for curve fitting
  • Study the properties of Gaussian distributions in statistics
  • Investigate alternative methods for fitting curves to data, such as polynomial regression
USEFUL FOR

Data scientists, statisticians, and researchers involved in modeling data with Gaussian distributions will benefit from this discussion, particularly those interested in parameter estimation and curve fitting techniques.

h00zah
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If given a set of data points, how do I find a,b,c to input into a gaussian model?

y = a exp (-(x-c) / b)2

I know it's centered at x=c
Intersects at (0,a), but if the data doesn't have a "0", how do you find it?
Also, a controls the height, but in what way? and b controls the spread, but in what way?

Or do I have this completely wrong?

I figured at (0,a) it would be the max height because a controls height, but that means a=c because c=center where y is at its maximum height, so that doesn't make sense.
 
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This could be an idea: given your gaussian y(x) which depends on the three (for the moment arbitrary) constants a, b and c, evaluate it at the x's of your data. Then calculate

f(a, b, c) = (y1 - y(x1))^2 + (y2 - y(x2))^2 + ...

where (x1, y1), (x2, y2), ... are you data points.
Finally, choose a, b and c in such a way to minimize f.
 

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