In every field of study, decision-making is fundamental, whether it's determining optimal questions in a medical questionnaire or guiding a Mars rover to select the best location for soil sampling. Moreover, after making decisions and receiving feedback, how do we leverage this knowledge to make better choices in the future? This presentation introduces the fundamentals of information theory, particularly Mutual Information, as a framework for formalizing decision-making processes. We will explore the computational challenges associated with Mutual Information and how variational methods aim at approximating it. Specifically, we will examine optimal solutions of traditional variational distributions and extend the methodology to incorporate more expressive distributions based on normalizing flows. We will demonstrate these methodologies applied to epidemiology by showing how we can gather information during an epidemic, integrate previous observations to guide future decisions, and ultimately attempt to predict infection and recovery rates of an unknown disease.