What term describes probabilities before any sample information is gathered?

The term that describes probabilities before any sample information is gathered is "prior probabilities." This concept is foundational in probability theory and Bayesian statistics. Prior probabilities represent the beliefs or knowledge about the likelihood of various outcomes or events based solely on existing information before any new data is collected.

For instance, if you are considering the probability of a specific event occurring based on historical data or general assumptions, you would use prior probabilities. These probabilities set a baseline that can be updated with new data, leading to what are known as posterior probabilities. This process of updating beliefs helps in making informed decisions as new evidence emerges.

In contrast, other terms like independent probabilities refer to events whose occurrence does not influence each other, joint probabilities involve the probability of two events happening simultaneously, and posterior probabilities relate to the updated probabilities after new information has been obtained. Each of these concepts operates within different frameworks and contexts but does not pertain to the state of knowledge before data collection, which is why prior probabilities is the accurate answer.