statistics

The essence of statistical inference:
We want to find the probability of the parameters $\theta$ of a probability distribution, given data $X$: $P(\theta \mid X)$ (likelihood).
This is the inverse of the usual probability distribution, where we have the probability of the data given the parameters: $P(X\mid \theta )$

Statistics is all about building models and testing them, what part of the data is explained by noise and what part is explained by the model.

References

mathematics