Chapter 6 Maximum Likelihood Estimation

In general, when we observe independent and identically distibuted data $y_1,\dots,y_n\sim p(y;\theta)$, the maximum likelihood estimate of the parameter vector $\theta$ is the value that maximizes the log-likelihood of $\theta$, which can be written as $\sum_{i=1}^n \log p(y_i; \theta)$. However, what if the data are not independent? How can we write down and maximize the log-likelihood?