On: Logs, Tails, Long Tails (2013)

[tmalsburg2]

It's possible that I misunderstood the text but what's the alternative interpretation of "The log function asymptotes at 0"? Also note that the text says log probabilities when it actually refers to log densities.

[moultano → tmalsburg2]

The log function has a vertical asymptote as x approaches 0.

[tmalsburg2 → moultano]

Ah, that's likely the interpretation that the author had in mind. But it didn't help that he wrote log probability when he actually talked about log probability density.

[kgwgk → tmalsburg2]

If the author himself tells you so, it’s more than likely. :-)

[kgwgk → tmalsburg2]

When x goes to minus infinity log(x) approaches zero.

[tmalsburg2 → kgwgk]

No, the logarithm is only defined for positive values. Plus probability densities are strictly non-negative. https://en.m.wikipedia.org/wiki/Logarithm

[kgwgk → tmalsburg2]

You're absolutely right! I meant it the other way around:

As x approaches 0, log(x) goes to minus infinity.

I think that's what he means (the next sentence about "visualiz[ing] very small values of a function by expanding their range" makes sense in that context), but I agree it is not very clear.