# Bayesian Graphical Models Notes

Stochastic systems are described using multivariate distributions.

### Example:

- Random variables are capital leters e.g. $X, Y$
- Deterministic variables are small letters e.g. $x, y$
- Parameters are lowercase greek letters e.g. $\theta$
- Vectorized variables are lowercase **bold** letters e.g. $\mathbb{x}$
- Matrices are uppercase **bold** letters e.g. $\mathbb{X}$
- Parameter vectors are capital greek letters e.g. $\Theta$

Say we have $Y_i = \beta_0 + \beta_1x + \epsilon_i$ (Simple linear regression)

We could write: $\beta = \begin{pmatrix}\beta_0\\\beta_1\end{pmatrix}$

Noise is distributed as: $\epsilon_i \sim N(0, \sigma^2)$

- Circle is used to represent stochastic variables
- Square is used to represent deterministic variables