The Golem of Prague

McElreath, R. Statistical Rethinking: A Bayesian Course with Examples in R and Stan. (CRC Press/Taylor & Francis Group, 2016).

A golem (goh-lem) is a clay robot known in Jewish folklore, constructed from dust and fire and water. It is brought to life by inscribing emet, Hebrew for “truth,” on its brow.

Scientists also make golems. Our golems rarely have physical form, but they too are often made of clay, living in silicon as computer code.

For some, the toolbox of pre-manufactured golems is all they will ever need.

The classical procedures of introductory statistics tend to be inflexible and fragile.

Instead, what researchers need is some unified theory of golem engineering, a set of principles for designing, building, and refining special-purpose statistical procedures.

Instead, we need some statistical epistemology, an appreciation of how statistical models relate to hypotheses and the natural mechanisms of interest.

All models are wrong; some models are useful. - George Box

If it turns out that all of the process models of interest make very similar predictions, then you know to search for a different description of the evidence, a description under which the processes look different.

First, observations are prone to error, especially at the boundaries of scientific knowledge. Second, most hypotheses are quantitative, concerning degrees of existence, rather than discrete, concerning total presence or absence.

• Continuous hypotheses also exists
• Falsification is consensual

1. Bayesian data analysis
2. Multilevel models
3. Model comparison using information criteria

Bayes Theorem is a formula for calculating a new probability of a hypothesis being true, after new evidence is considered. It is based on the idea that if a new piece of evidence is more likely if a hypothesis is true than if it is false, then it raises the probability that the hypothesis is true.

An Essay towards solving a Problem in the Doctrine of Chances

• Extensive information in the text
• Multilevel models
  • To adjust estimates for repeat sampling
  • To adjust estimates for imbalance in sampling
  • To study variation
  • To avoid averaging
• Information criteria
  • Evaluate model accuracy based on information theory