# Name and notation convention for “unnormalized probability”

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.

## 1 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)

• Thanks. I know these are just non-negative numbers, but when used in in this probabilistic context they have an additional "meaning" and it is sometimes useful to talk about the quantities before and after the normalization. I am just wondering if there is some standard name/notation for this. – Bitwise Jan 24 '14 at 1:09
• @Bitwise the best term I can think of is likelihood as it is a measure of relative support as opposed to absolute support – user76844 Jan 24 '14 at 16:22
• I see how this would work in a Bayesian context, however in my case I actually use likelihood later for a different term so it is not suitable. I will wait to see if I get other answers before proceeding. – Bitwise Jan 24 '14 at 16:29
• @Bitwise based on your description in the post, you are dividng a number by its sum to get a probability. In that case, mustn't your $s_i$'s be raw counts of some sort? Why wouldn't you just call them counts? – user76844 Jan 24 '14 at 17:21
• Actually, these are not the counts. It is more of a parametrized probability distribution, e.g. $p(x_i)=\frac{e^{i}}{Z}$. – Bitwise Jan 24 '14 at 19:10