reading from the first example of https://onlinecourses.science.psu.edu/stat414/node/283/ (
)
where the likelihood of poisson can be factored into two components Phi(T(x),theta) and h(x1...xn) then T(x) is said to be sufficient.
However I don't understand that to compute the actual likely hood won't be have to compute h(x1...xn) also which does require knowledge of the individual values. So how have we reduced the problem? I understand the case where summation of xi is sufficient for multiple Bernoulli as h(x1...xn)=1 so indeed no knowledge of the individual values is required but can't get this one.
The point is that the factor $h(x_1,\ldots,x_n)$ doesn't depend on the parameter(s) and is thus irrelevant for your knowledge about them. For instance, if you add two Poisson variables with the same rate parameter $\lambda$, you're twice as likely to get $1$ and $1$ than to get $2$ and $0$; but this factor $2$ is the same for any $\lambda$, so remembering whether you got $1$ and $1$ or $2$ and $0$ doesn't help you in estimating $\lambda$. For instance, if you have a prior $p(\lambda)$ and obtain data $x_1,\ldots,x_n$, the posterior distribution is
$$ p(\lambda\mid x_1,\ldots,x_n)=\frac{p(x_1,\ldots,x_n\mid\lambda)p(\lambda)}{\int\mathrm d\lambda p(x_1,\ldots,x_n\mid\lambda)p(\lambda)}\;, $$
and the factor $h(x_1,\ldots,x_n)$ cancels.