Section 4 Foundations of inference

4.1 Philosophy of statistics

In general it is a good habit to (re-)examine one’s beliefs, but there are also good reasons to study philosophy specific to statistics and data science.

What is the meaning of probability? Kolmogorov’s axioms describe a kind of mathematical model, but what relation do such models have to the real world, if any? The same set of axioms can be used (and fruitfully!) to describe:

  • Hypothetical properties of the physical world, as in most interpretations of quantum physics, or the “propensity” of a dice to land on a particular side
  • Degrees of subjective belief, or confidence, that a given individual has about states of the world
  • Logical rules governing quantitative relationships between hypotheses and evidence

4.2 Hypothesis testing background

4.2.1 Hypothesis formulation: a neglected topic in data science education?

4.3 Causality