To find the value of \( b \) in the equation \( y = \log_b x \) given that it passes through the point \( (16, -1) \), we will substitute \( x = 16 \) and \( y = -1 \) into the equation.
Starting with the equation:
\[ -1 = \log_b 16 \]
This can be rewritten in its exponential form:
\[ b^{-1} = 16 \]
Which can be rearranged to:
\[ \frac{1}{b} = 16 \]
Now, we can solve for \( b \) by taking the reciprocal of both sides:
\[ b = \frac{1}{16} \]
Thus, the value of \( b \) is:
\[ \boxed{\frac{1}{16}} \]