I think you’re basically right: Correlation is just one way of measuring dependence between variables. Being correlated is a sufficient but not necessary condition for dependence. We talk about correlation so much because:
We don’t have a particularly convenient general scalar measure of how related two variables are. You might think about using something like mutual information, but for that you need the densities not datasets.
We’re still living in the shadows of the times when computers weren’t so big. We got used to doing all sorts of stuff based on linearity decades ago because we didn’t have any other options, and they became “conventional” even when we might have better options now.
Suppose we don’t have any prior information about the dataset, only our observations. Is any metric more accurate than assuming our dataset is the exact distribution and calculating mutual information? Kind of like bootstrapping.
I think you’re basically right: Correlation is just one way of measuring dependence between variables. Being correlated is a sufficient but not necessary condition for dependence. We talk about correlation so much because:
We don’t have a particularly convenient general scalar measure of how related two variables are. You might think about using something like mutual information, but for that you need the densities not datasets.
We’re still living in the shadows of the times when computers weren’t so big. We got used to doing all sorts of stuff based on linearity decades ago because we didn’t have any other options, and they became “conventional” even when we might have better options now.
Suppose we don’t have any prior information about the dataset, only our observations. Is any metric more accurate than assuming our dataset is the exact distribution and calculating mutual information? Kind of like bootstrapping.