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This is one of my first questions so sorry in advance for any rules that I break.

Is there any mainstream convention for the symbol of the precision and precision matrix?

I have seen the following ones:

  • In Information theory, inference and learning algorithms by MacKay:

$$ \text{Precision: }\tau = 1 / \sigma^2$$ $$ \text{Precision matrix: }\mathbf{A} = \boldsymbol{\Sigma}^{-1} $$

  • In Pattern recognition and machine learning by Bishop:

$$ \text{Precision: }\beta = 1 / \sigma^2$$ $$ \text{Precision matrix: }\boldsymbol{\Lambda} = \boldsymbol{\Sigma}^{-1} $$

Is any of them preferred over the others?

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I change a lot but in the Gaussian Process literature, it's usually $K$ (for kernel matrix) or $\Sigma$. Precision matrices also change a lot but as you say $A$ and $\Lambda$ are pretty common. As long as you clearly introduce the term though you can use whichever convention you want.

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