11 Statistical thinking and inference
We approach statistical inference from a Bayesian perspective, treating probability as a measure of uncertainty about the world rather than merely the limiting frequency of repeatable events. This framing places uncertainty quantification at the center of statistical practice—we are not just seeking point estimates but rather probability distributions that represent our knowledge (and ignorance) about quantities of interest.
This is not to suggest that frequentist methods have no value; rather, we build from Bayesian foundations because they provide a coherent framework for learning from data and updating beliefs. When we observe data, we update our prior understanding to obtain a posterior distribution. This process mirrors the scientific cycle: form hypotheses, collect evidence, revise understanding.
[Content to be developed following Bayesian-first approach]