Probability Is a Belief with a Number

Probability has a long-running identity crisis, and ML picks a side:

• Frequentist: probability is long-run frequency. '0.7' means 'repeat this forever and it happens 70% of the time'
• Bayesian: probability is degree of belief. '0.7' means 'given everything I know, I'm 70% confident'

A model saying 'this tumor is malignant with probability 0.7' is pure Bayesian: not '70% of this tumor is malignant' — a statement about how strongly the evidence supports malignant, with the leftover uncertainty kept honestly in view.

A good model's numbers should mean something: among all its 0.7 predictions, about 70% should come true. That property is called calibration.