PYTHON For Physicist, Engineer & Mathematician | Multi-Peak Gaussian Fitting With Scipy | DESI ASTRO

A Gaussian, a normal distribution or bell curve, is a mathematical function that describes a symmetric, bell-shaped probability distribution. It is named after the mathematician Carl Friedrich Gauss. The Gaussian function is widely used in various fields, including statistics, physics, signal processing, and data analysis.

Chapter Timestamps:
00:00:00 Introduction
00:01:25 Import library and Creating Gaussian Plots
00:06:36 Define Multi-Gaussian Function
00:09:15 Fitting With Scipy
00:12:17 Customize Gaussian Plot

Key characteristics of the Gaussian distribution include symmetry around the mean, with the majority of the data concentrated near the mean and tailing off as values move away from the mean. The standard deviation parameter influences the width of the distribution: a larger standard deviation results in a wider and flatter curve.

The Gaussian distribution is fundamental in statistical modeling due to the Central Limit Theorem, which states that the sum (or average) of a large number of independent, identically distributed random variables tends to follow a Gaussian distribution, regardless of the original distribution of the variables. This makes the Gaussian distribution a common choice for modeling and analyzing various natural phenomena and experimental data.

Objective Function:

You start by defining a function that represents the model you want to fit to your data. This function should take the independent variable as its first argument and the parameters to be optimized as subsequent arguments.
Experimental Data:

Prepare your experimental data in arrays: one for the independent variable (e.g., x-values) and another for the dependent variable (e.g., y-values).
Curve Fitting:

Call the curve_fit function, passing your objective function, the independent variable data, and the dependent variable data as arguments. The function returns a tuple containing the optimized parameters and the covariance of the parameters.
Optimized Parameters:

Extract the optimized parameters from the result of the curve_fit function. These parameters represent the values that best fit the model to your experimental data.
Model Evaluation:

Use the optimized parameters to evaluate your model function and generate the fitted curve. This allows you to visually compare the fitted curve with your experimental data.

PYTHON MULTIPLE LINEAR REGRESSION|SCIPY| MATPLOTLIB| FIT LINE ON SCATTER PLOT| CURVE FIT USING SCIPY

Gaussian fitting
Scatter plot
Data analysis
Curve fitting
Scipy
Python programming
Data science
Signal processing
Peak identification
Data visualization

Welcome to our Data Science Tutorial! In this video, we'll explore the powerful world of curve fitting using Scipy, a popular scientific computing library in Python. Specifically, we'll dive into the process of fitting Gaussian curves to your data, a fundamental skill in data analysis and signal processing.

🔍 Understanding how to fit a Gaussian curve to your data is crucial for various applications, such as peak identification, signal analysis, and noise filtering. With Scipy's curve_fit function, we can efficiently optimize the parameters of a Gaussian function to best match our data.

🚀 Topics covered in this tutorial:

Introduction to Gaussian curves and their significance in data analysis.
Overview of the Scipy library and its curve fitting capabilities.
Explanation of the curve_fit function and its usage.
Understanding the parameters of a Gaussian function and how they influence the curve.
Practical tips and insights on fine-tuning the curve fitting process for accurate results.
Whether you're a beginner in data science or an experienced practitioner looking to enhance your skills, this tutorial is designed to provide valuable insights into the world of curve fitting. Make sure to subscribe for more data science tutorials, and don't forget to hit the like button if you find this video helpful!
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