Given a finite set of non-negative numbers $S={s_1,…,s_n}$, we can divide them by a normalization constant $Z$ (i.e. their sum) to get a probability distribution.
Then we typically say (and write) something like: the probability of event $x_i$ is $p(x_i)=\frac{s_i}{Z}$.
In this context, is there any standard name and notation conventions for the "unnormalized probability" $s_i$?
I usually just call these unnormalized probabilities and use some arbitrary notation (e.g. $\tilde{p}(x_i)$), but I am not very fond of this name.
Best Answer
Probability is a measure that assigns the value 1 to the entire space. Without that, you just have a non-negative measure (i.e., its just measure theory w/o any probabilistic interpretation)