statistics

The essence of statistical inference:
Given observed data $X$, we want to learn about the unknown parameters $\theta$ that generated it.

Two fundamental quantities:

• Likelihood $P(X\mid \theta )$ - probability of observing data given parameters
• Posterior $P(\theta \mid X)$ - probability of parameters given observed data

The posterior is what we’re after - it tells us what parameter values are plausible given our observations. We compute it using Bayes Theorem: posterior $\propto$ likelihood $\times$ prior.

Statistics is all about building models and testing them, separating signal from noise.

References

mathematics