Sampling from a multivariate Gaussian distribution

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SUMMARY

The discussion centers on the concept of sampling from a multivariate Gaussian distribution, specifically addressing the confusion between univariate and multivariate distributions. The participant highlights that multiplying by sigma does not shift the distribution but rather affects its shape. The example provided fails to illustrate a true multivariate distribution, instead depicting two separate univariate distributions, which do not accurately represent the characteristics of a multivariate Gaussian distribution.

PREREQUISITES
  • Understanding of Gaussian distributions, including univariate and multivariate forms.
  • Familiarity with statistical concepts such as mean (μ) and variance (σ²).
  • Knowledge of probability density functions and their graphical representations.
  • Basic skills in linear regression analysis and its applications.
NEXT STEPS
  • Research the properties and applications of multivariate Gaussian distributions.
  • Learn about the mathematical formulation of multivariate normal distributions.
  • Explore sampling techniques from multivariate distributions using tools like NumPy or SciPy.
  • Study the differences between univariate and multivariate statistical analyses in depth.
USEFUL FOR

Statisticians, data scientists, and machine learning practitioners who are working with multivariate data and require a clear understanding of Gaussian distributions for modeling and analysis.

asilvester635
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I was watching a lecture on youtube about linear regression and there's a section where it had the statement below (written in purple). Does multiplying by sigma rotate the distribution to make it look like x - N(mew, sigma^2)? Mew in this case is 0 so it doesn't shift the distribution.

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To me ##x## and ##y## are just dummy variables, and both are on the x-axis, or should be, because the y-axis represents the distribution of the probability density, which in this case is a normal distribution. ##y## has its peak at zero on the x-axis, and ##x## has its peak at ##\mu## on the x-axis.
 
asilvester635 said:
Sampling from a multivariate Gaussian distribution

The example you gave doesn't illustrate a "multivariate" distribution. It illustrates two univariate distributions.
 

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