Make silent option to be really silent

[avehtari]

brm says

  silent: Logical; If TRUE (the default), most of the informational
          messages of compiler and sampler are suppressed. The actual
          sampling progress is still printed. Set ‘refresh = 0’ to turn
          this off as well. If using ‘backend = "rstan"’ you can also
          set ‘open_progress = FALSE’ to prevent opening additional
          progress bars.

I wish silent option could be used to suppress all possible messages, especially the ones generated by brms package itself or the ones that can be easily suppressed when calling other packages. Specifically, I was surprised that silent=TRUE still prints Start sampling and I would prefer that it would already be suppressed with silent=TRUE. For suppressing messages from other packages I'm open for silent to have additional possible values.

[hsbadr]

I vote for verbosity level (e.g., 0-2) where 0 suppresses everything [NONE], 1 keeps main/important info messages [INFO], and 2 verbose all messages for debugging [DEBUG]. The number of levels can change depending on what you want to show, but if it ends up with 2 levels, then silent logical is obviously enough.

[paul-buerkner]

I agree using verbosity levels (3 or even 4 levels) is a good idea!

[paul-buerkner]

I just implemented silent = 2 for more silence.