Announcement

• HW5 (last hw) posted. Due 6/16.

• Extra office hour. Today, Thu @ 2p-3p.

Qs on HW4

• Overflow. Avoid using factorial, use lfact, lgamma, digamma, trigamma, …

• Expected information matrix. Look at alternative expression for log-likelihood, score, Hessian.

• Concavity or nonconcavity of log-likelihood. For non-concavity, one counter example, e.g., from your Newton’s safeguard, suffices.

• Method of moment estimator. Easier to work with moments of Dirichlet distribution. If $P=(P_1, \ldots, P_d)$ is distribubted as Dirichlet with parameter $\alpha = (\alpha_1, \ldots, \alpha_d)$, then \(E P_j = \frac{\alpha_j}{|\alpha|}, \quad E P_j^2 = \frac{\alpha_j(\alpha_j + 1)}{|\alpha|(|\alpha| + 1)}.\)

Last time

• MM algorithm.

Today

• MM algorithm (cont’d).

• Quasi-Newton.