Figure of Hypotheses vs. Process Models vs. Statistical Models

- Process models indicate causality through their structure
- Statistical models do not indicate causality
- Statistical models can correspond to more than one process model and more than one hypothesis
- Hypotheses can also correspond to more than one process model 

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- Scientific models are designed for making calculations, but they cannot determine causality on their own. 
- To determine the most appropriate statistical model to use, researchers ask questions about the type of data they have and what they wish to measure. 
- Frequentist approach is based on re-sampling methods, and it is a special case of Bayesian analysis
- We have models that are defined to do certain tests, but as researchers, you need to get behind the methods and determine if results are practically significant 

Statistical Golems 

McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd ed.). Chapman and Hall/CRC.

Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd edition)

Figure of Statistical Procedures

1. Frequentist consider a single estimator $\theta$ to make all predictions. Bayesian statisticians use all possible values of $\theta$ to make predictions.
2. Frequentist view $\theta$ as fixed and dataset as variable. Bayesian view dataset as fixed and $\theta$ as variable.

Difference between Frequentist and Bayesian statistics

- Bayesian data analysis
- Model comparison and prediction
- Multilevel models
- Graphical causal models

Tools for Golem Engineering


Hypotheses are not models

- Need to account for overfitting 
- Falsification is consensual - it’s not about how logical your arguments are, but how well you are able to prove that to the scientific community in a way that is understandable

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