Errors in a more general sense
For a two-type classification problem: There are two different types of errors: $\varepsilon_1$ and $\varepsilon_2$. You can calculate them like so:
- Type I Error: $\int_{\Omega_2} p(x|\omega_1)dx$
- Type II Error: $\int_{\Omega_1} p(x|\omega_2)dx$
If you call $\omega_2$ the positive group and $\omega_1$ the negative group. Type I becomes false negative and Type II becomes false positive.