Suppose we have a set of events $\Omega$, containing events $A$ and $B$. My econometrics professor tried to distinguish the following three terms today.
- Causation --- $A$ causes $B$ if the occurrence of $A$ always leads to another specific outcome $B$. For example, clapping my hands causes a sound to be emitted.
- Prediction --- $A$ predicts $B$ if on average, $B$ is the expected outcome from $A$ occurring. In other words, whereas causality is deterministic, prediction is probabilistic. For example, studying for a test would predict doing well on the exam. But there's no guarantee.
- Correlation --- $A$ and $B$ are correlated if when one occurs the other does too. But there may be some hidden variable causing both.
Are these distinctions meaningful? Or did he make these terms up?
- What is the difference between causation and correlation?
- Are "causes" always deterministic?