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under the Gaussian assumption vs under the Gaussian assumptions

Both phrases are correct, but they are used in different contexts. 'Under the Gaussian assumption' is used when referring to a single assumption, while 'under the Gaussian assumptions' is used when referring to multiple assumptions. Choosing between plural and singular is dependent upon how many assumptions there are.
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Explained by Gregg
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Last updated: June 15, 2024 • 743 views

under the Gaussian assumption

This phrase is correct and commonly used when referring to a single assumption.

This phrase is used when discussing a single assumption that is based on the Gaussian distribution. It is important to use the singular form 'assumption' when referring to a single concept.

Examples:

  • Under the Gaussian assumption, the data is normally distributed.
  • Parameter estimation point of viewv. Preliminary definitions and notations. Estimation under the Gaussian assumption. Estimation under the linearity assumption ...
  • Nov 21, 2012 ... Therefore, any optimization based on the CRLB under the Gaussian assumption can be considered to be min-max optimal in the sense of ...
  • volume that contains a given probability mass under the Gaussian assumption. When in (4.2) rather than having an inequality there is an equality, (4.2), i.e.,.
  • Apr 21, 2011 ... Consequently, the Gaussian CRB (i.e., the CRB that holds under the Gaussian assumption) is the worst-case one (over the distribution class), ...

Alternatives:

  • Under the assumption that the data follows a Gaussian distribution

under the Gaussian assumptions

This phrase is correct and commonly used when referring to multiple assumptions.

This phrase is used when discussing multiple assumptions that are based on the Gaussian distribution. It is important to use the plural form 'assumptions' when referring to multiple concepts.

Examples:

  • Under the Gaussian assumptions, the model considers various aspects of the data distribution.
  • efficient and conditionally valid only under the Gaussian assumptions. 2. Bayesian ridge regression. Much of the notation introduced in this section will be used ...
  • The asymptotic distribution—under the Gaussian assumptions just described—of the maxi- mum likelihood estimates (the solutions ˆβ and ˆΛ1,...,ˆΛk of (2.1)) ...
  • As a consequence of the results derived so far, under the Gaussian assumptions, the following properties hold. 1) With Gaussian assumption on messages from ...
  • Under the Gaussian assumptions, the density (5.17) turns out to be Gaussian, and hence uniquely characterized by its mean and covariance matrix. The condi-.

Alternatives:

  • Under the assumptions that the data follows a Gaussian distribution

Related Comparisons

under dark vs under the dark under the recommendation vs out of recommendation under the recommendation vs by recommendation based on the Gaussian assumption of data vs based on the Gaussian assumption under the pretension vs under the guise of

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