Parameter Estimation in Probability Models Quiz

Is the maximum likelihood estimation (MLE) used to find the values of $\mu$ and $\sigma$ that maximize the likelihood?

Is the log function monotonically increasing?

Is the derivative of the log likelihood function with respect to $\mu$ equal to 0 at its maximum?

Is the derivative of the log likelihood function with respect to $\sigma$ equal to 0 at its maximum?

Is the derivative of the log likelihood function with respect to $\mu$ equal to $\sum_{i=1}^{n} (x_i - \mu)$?

What is the derivative of the log likelihood function with respect to $\ ext{𝜇}$?

What does the log function's monotonicity mean in the context of the likelihood function?

What is the derivative of the log likelihood function with respect to $\ ext{𝜎}$ when finding the MLE?

What does it mean when the derivative of the log likelihood function with respect to $\ ext{𝜇}$ is equal to 0?

What is the purpose of maximum likelihood estimation (MLE) in this context?

What is the purpose of Probabilistic Graphical Models (PGMs)?

In the context of PGMs, what does the decomposition of a joint probability allow us to do?

What does the expression $P(A, B, C, D) = P(A)P(D)P(B|A)P(C|B, A)$ represent in the context of a Directed Acyclic Graph (DAG)?

What is the significance of the nodes being white and gray in the Naïve Bayes example?

What does the expression $P(y, x_{1:D}) = P(y)$ represent in the context of PGMs?