Learning objectives
What you will be able to explain
- Distribution supports
- Distribution roles
- Multivariate Gaussian density structure
- Dirichlet and multinomial
- Heavy-tail limiting behavior
- Wishart versus inverse Wishart
Section 01
Distribution supports to Multivariate Gaussian density structure
01
Distribution supports
Support is the first guard against applying a density to an invalid object.
Guided checkpoint
Match each distribution to its natural support or object.
Source: Secs. 7.1-7.9, pp. 37-39
02
Distribution roles
The chapter collects density forms and normalization constants for these distinct domains.
Guided checkpoint
Match the family to its defining role.
Source: Secs. 7.1-7.8, pp. 37-38
03
Multivariate Gaussian density structure
The determinant controls volume and the precision controls Mahalanobis geometry.
Guided checkpoint
For and positive-definite .
Source: Secs. 7.3 and 7.5, p. 37
Section 02
Dirichlet and multinomial to Wishart versus inverse Wishart
01
Dirichlet and multinomial
The simplex constraint and count constraint are complementary.
Guided checkpoint
Judge the conjugate pair.
Source: Secs. 7.2 and 7.6, p. 37
02
Heavy-tail limiting behavior
The t family approaches Gaussian behavior as degrees of freedom increase.
Guided checkpoint
What happens to multivariate Student's t as degrees of freedom grow?
Source: Sec. 7.7, p. 37
03
Wishart versus inverse Wishart
Inversion changes determinants, trace terms, and normalization through the transformation Jacobian.
Guided checkpoint
Check each distinction.
Source: Secs. 7.8-7.9, pp. 38-39
Knowledge check
Turn understanding into recall.
The quiz now follows the same concepts in scored form. You can return to this lesson from the quiz whenever a gap appears.